diff --git a/.editorconfig b/.editorconfig index 0f178672..d84c6741 100644 --- a/.editorconfig +++ b/.editorconfig @@ -7,3 +7,6 @@ indent_size = 2 indent_style = space insert_final_newline = true trim_trailing_whitespace = true + +[*.py] +indent_size = 4 \ No newline at end of file diff --git a/.github/workflows/build-and-test.yml b/.github/workflows/build.yml similarity index 59% rename from .github/workflows/build-and-test.yml rename to .github/workflows/build.yml index 30ee9811..9f001b35 100644 --- a/.github/workflows/build-and-test.yml +++ b/.github/workflows/build.yml @@ -1,8 +1,9 @@ -name: Build and Test +name: Build on: pull_request: paths-ignore: + - CODEOWNERS - LICENSE - README.md push: @@ -27,19 +28,31 @@ jobs: ref: ${{ github.head_ref }} token: ${{ steps.generate-token.outputs.token }} - - name: Setup NodeJS - uses: actions/setup-node@v3 + - name: Setup Python + uses: actions/setup-python@v5 with: - node-version: 20 + python-version: '3.13' + + - name: Install poetry + run: python -m pip install poetry==2.1.1 + + - name: Configure poetry + run: poetry config virtualenvs.in-project true + + - name: Cache the virtualenv + uses: actions/cache@v4 + with: + path: ./.venv + key: ${{ runner.os }}-venv-${{ hashFiles('**/poetry.lock') }} - name: Install dependencies - run: npm ci + run: poetry install - - name: Fix - run: npm run fix + - name: Run format + run: poetry run format - - name: Build - run: npm run build + - name: Run lint + run: poetry run lint - name: Commit if: ${{ github.ref != 'refs/heads/main' }} @@ -49,7 +62,3 @@ jobs: author_name: github-actions[bot] author_email: github-actions[bot]@github.com message: Automatic commit via GitHub Actions - - - name: Test - if: ${{ steps.commit.outputs.committed == 'false' }} - run: npm run test diff --git a/.gitignore b/.gitignore index a73f32ec..8171ea59 100644 --- a/.gitignore +++ b/.gitignore @@ -1,7 +1,9 @@ -build/ -coverage/ -dist/ -node_modules/ +__pycache__/ +.env/ +.mypy_cache/ +.venv/ +.vscode/ -*.tgz -.env +*.egg-info/ +*.pyc +*.pyo \ No newline at end of file diff --git a/.prettierignore b/.prettierignore deleted file mode 100644 index 480be400..00000000 --- a/.prettierignore +++ /dev/null @@ -1,18 +0,0 @@ -build/ -coverage/ -dist/ -node_modules/ - -# Ignore all the dotfiles in the repository root. -*.* - -# Ignore specific file patterns in the repository. -*.snap -LICENSE - -# Unless they are a certain file type or explicitly included. -package.json -tsconfig.json -!*.js -!*.mjs -!*.ts diff --git a/Makefile b/Makefile index ba988109..cd10acd3 100644 --- a/Makefile +++ b/Makefile @@ -1,4 +1,4 @@ .PHONY: % %: - npm run test -- -t="problem $@" + poetry run pytest project_euler/$@.py diff --git a/README.md b/README.md index 078123f7..0b0d0f0a 100644 --- a/README.md +++ b/README.md @@ -4,12 +4,8 @@ These are solutions to [Project Euler](https://projecteuler.net/) problems. It's easy to find solutions on the net, so if you don't want to spoil the fun, don't look at these. -## Usage +## Development -1. Run `npm install`. -1. Run `npm run all` to build the entire project. -1. Run `make ` to run a specific solution. - -Some solution explanations on the [GitHub Pages](http://retiman.github.io/project-euler/) for this repository (published from the `docs` directory). - -Some solutions are written in Racket. \ No newline at end of file +1. Install poetry: `curl -sSL https://install.python-poetry.org | python` +1. Install dependencies: `poetry install` +1. Run tests: `poetry run test` diff --git a/eslint.config.mjs b/eslint.config.mjs deleted file mode 100644 index af6470de..00000000 --- a/eslint.config.mjs +++ /dev/null @@ -1,150 +0,0 @@ -import eslint from '@eslint/js'; -import tselint from 'typescript-eslint'; -import uimports from 'eslint-plugin-unused-imports'; - -export default tselint.config({ - extends: [eslint.configs.recommended, tselint.configs.recommended], - files: ['**/*.ts'], - languageOptions: { - parserOptions: { - project: './tsconfig.json', - tsconfigRootDir: import.meta.dirname, - ecmaVersion: 2020, - sourceType: 'module' - } - }, - plugins: { - 'unused-imports': uimports - }, - rules: { - '@typescript-eslint/explicit-function-return-type': 'off', - '@typescript-eslint/explicit-module-boundary-types': 'off', - // Permits the violation of naming conventions for unused variables with a leading underscore. - // - // See https://typescript-eslint.io/rules/naming-convention/ - '@typescript-eslint/naming-convention': [ - 'error', - { - selector: 'variable', - format: ['camelCase', 'PascalCase', 'snake_case'], - leadingUnderscore: 'allow', - modifiers: ['unused'] - }, - { - selector: 'parameter', - format: ['camelCase', 'PascalCase', 'snake_case'], - leadingUnderscore: 'allow' - } - ], - // Enabled because one should not assign the result of a void function. - // - // See https://typescript-eslint.io/rules/no-confusing-void-expression/ - '@typescript-eslint/no-confusing-void-expression': 'error', - '@typescript-eslint/no-meaningless-void-operator': 'error', - '@typescript-eslint/no-unused-expressions': 'error', - '@typescript-eslint/no-unused-vars': 'off', - '@typescript-eslint/no-useless-constructor': 'error', - '@typescript-eslint/no-use-before-define': 'off', - '@typescript-eslint/no-var-requires': 'off', - // Disabled because there's no reason to enable this except to be pedantic. Code organization desires may dictate - // that methods not using this should still be methods. For example, there are situations where it's desirable to - // define only instance methods for ease of use, or you would prefer that the caller not have to know or care that - // a method actually uses instance variables or not. - // - // In other situations, nothing is stopping you from declaring a function outside of a class, which is functionally - // the same as a static method. - // - // See https://eslint.org/docs/latest/rules/class-methods-use-this - 'class-methods-use-this': 'off', - // Disabled because this rule cannot detect if a dependency is only for development. For example, if you have a - // postbuild.js and you include it in tsconfig.json, then this plugin will incorrectly assume that any packages - // required there should be in dependencies. - // - // In that situation, postbuild.js is included in tsconfig.json so that JavaScript files (even ones not included - // in the final build) should be linted according to @typescript-eslint. - // - // See https://stackoverflow.com/questions/61956555/why-is-typescript-eslint-parser-including-files-outside-of-those-configured-in - // See https://www.typescriptlang.org/tsconfig#include - 'import/no-extraneous-dependencies': 'off', - // Disabled because named exports are more explicit. - // - // See https://github.com/airbnb/javascript/issues/1365 - // See https://blog.neufund.org/why-we-have-banned-default-exports-and-you-should-do-the-same-d51fdc2cf2ad - 'import/prefer-default-export': 'off', - 'jest/no-disabled-tests': 'off', - 'max-classes-per-file': 'off', - // Disabled because continue ESLint specifically is concerned about continue being used with labels. Using this - // with labels is akin to a goto statement, which makes code hard to reason about. Proper use of the continue - // statement makes code easier to read. - // - // The ESLint recommendations around avoiding continue involve using if statements, which do actively degrade code - // readability. ESLint, for whatever reason, recommends this even when labels are not required. Good readability, - // in contrast, would call for using continue statements with guard clauses. - // - // See https://eslint.org/docs/latest/rules/no-continue - // See https://refactoring.com/catalog/replaceNestedConditionalWithGuardClauses.html - 'no-continue': 'off', - // Disabled because prettier can fix this. - 'no-irregular-whitespace': 'off', - // Disabled because it is handled by @typescript-eslint rules. - 'no-shadow': 'off', - // Disabled for convenience. Enable again if this ends up hurting the project. - // - // See https://eslint.org/docs/latest/rules/no-plusplus - 'no-plusplus': 'off', - 'no-restricted-syntax': [ - 'error', - { - selector: 'ForInStatement', - message: 'for..in loops iterate over the prototype chain, which is virtually never what you want' - }, - { - selector: 'LabeledStatement', - message: 'labels are a form of goto; using them makes code confusing and hard to maintain' - }, - { - selector: 'WithStatement', - message: 'with is disallowed in strict mode because it makes code impossible to predict and optimize' - } - ], - // Disabled because we do want to have underscore prefixed identifiers to indicate a variable is ignored. - // - // See https://eslint.org/docs/latest/rules/no-underscore-dangle - 'no-underscore-dangle': 'off', - 'no-unused-expressions': 'off', - 'no-unused-vars': 'off', - 'no-use-before-define': 'off', - 'no-useless-constructor': 'off', - // Disabled because `let [a] = arr;` or `[a] = arr` is just silly sometimes. - // - // See https://eslint.org/docs/latest/rules/prefer-destructuring - 'prefer-destructuring': [ - 'error', - { - object: false, - array: false - } - ], - 'unused-imports/no-unused-imports': 'error', - 'unused-imports/no-unused-vars': [ - 'warn', - { - args: 'all', - argsIgnorePattern: '^_', - caughtErrorsIgnorePattern: '^_', - vars: 'all', - varsIgnorePattern: '^_' - } - ], - // Enabled because it is useful for some problems. ESLint disables this by default because it assumes that a single - // & or | is a mistyped && or ||. - // - // See https://eslint.org/docs/latest/rules/no-bitwise - 'no-bitwise': 'off', - // Disabled because some solutions can be implemented more naturally with a while (true) loop. - 'no-constant-condition': 'off', - // Disabled because some solutions run more optimally if you do mutate the inputs. This will trigger even if you - // reassign a field in an object, which makes it more convenient if turned off. - 'no-param-reassign': 'off' - } -}); diff --git a/package-lock.json b/package-lock.json deleted file mode 100644 index 0ec8e57a..00000000 --- a/package-lock.json +++ /dev/null @@ -1,5589 +0,0 @@ -{ - "name": "@retiman/project-euler", - "version": "2.0.0", - "lockfileVersion": 3, - "requires": true, - "packages": { - "": { - "name": "@retiman/project-euler", - "version": "2.0.0", - "license": "CC0-1.0", - "dependencies": { - "@datastructures-js/priority-queue": "6.3.1", - "lodash": "^4.17.21" - }, - "devDependencies": { - "@eslint/js": "^9.17.0", - "@tsconfig/recommended": "^1.0.8", - "@types/jest": "^29.5.14", - "@types/lodash": "^4.17.13", - "@types/node": "^22.10.2", - "editorconfig": "^2.0.0", - "eslint": "^9.17.0", - "eslint-plugin-unused-imports": "^4.1.4", - "fs-extra": "^11.2.0", - "jest": "^29.7.0", - "prettier": "^3.4.2", - "ts-jest": "^29.2.5", - "ts-node": "^10.9.2", - 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'avoid', - bracketSameLine: true, - bracketSpacing: true, - endOfLine: 'lf', - printWidth: 120, - proseWrap: 'never', - quoteProps: 'as-needed', - semi: true, - singleQuote: true, - tabWidth: 2, - // Prettier and ESLint will fight over trailing commas. The latter has more options for configuring trailing commas, - // so disable here and let ESLint do all the work. - trailingComma: 'none', - useTabs: false -}; diff --git a/project_euler/1.py b/project_euler/1.py new file mode 100644 index 00000000..2cd9a485 --- /dev/null +++ b/project_euler/1.py @@ -0,0 +1,11 @@ +# Problem 1: Multiple of 3 and 5 +# +# Find the sum of all the multiples of 3 or 5 below 1000. +# +# See https://projecteuler.net/problem=1 +def run(limit=1_000) -> int: + return sum([n for n in range(limit) if n % 3 == 0 or n % 5 == 0]) + + +def test_run(): + assert run() == 233168 diff --git a/project_euler/10.py b/project_euler/10.py new file mode 100644 index 00000000..edeba2ec --- /dev/null +++ b/project_euler/10.py @@ -0,0 +1,23 @@ +# Problem 10: Summation of Primes +# +# Find the sum of all the primes below two million. +# +# See https://projecteuler.net/problem=10 +from typing import cast +from sympy import primerange +from toolz import pipe +from toolz.curried import filter, map, reduce + + +def run(limit=2_000_000) -> int: + result = pipe( + primerange(2, limit), + map(lambda p: cast(int, p)), + filter(lambda p: p < limit), + reduce(lambda a, b: a + b), + ) + return cast(int, result) + + +def test_run(): + assert run() == 142913828922 diff --git a/project_euler/107.py b/project_euler/107.py new file mode 100644 index 00000000..b68ee8cf --- /dev/null +++ b/project_euler/107.py @@ -0,0 +1,96 @@ +# Problem 107: Minimal Network +# +# Find the maximum saving which can be achieved by removing redundant edges whilst ensuring that the network remains +# connected. +# +# See https://projecteuler.net/problem=107 +from heapq import heappop, heappush +import math +from pathlib import Path + + +Graph = list[list[float]] +Edge = tuple[int, int] + + +def create_graph() -> Graph: + file = Path(__file__).parent / "data" / "107.txt" + data = file.read_text().strip().splitlines() + graph: Graph = [] + + for line in data: + # fmt: off + row = [ + math.inf + if x == "-" else int(x) + for x in line.strip().split(",") + ] + # fmt: on + graph.append(row) + + return graph + + +def weight_of_network(graph: Graph) -> float: + total = 0 + + for i, row in enumerate(graph): + for j, x in enumerate(row): + if x != math.inf: + total += x + + # Divide by 2 to avoid double counting in undirected graph. + return total / 2 + + +def weight_of_mst(graph: Graph, edges: list[Edge]) -> float: + return sum(graph[u][v] for u, v in edges) + + +def neighbors(graph: Graph, u: int) -> list[tuple[int, float]]: + # fmt: off + return [ + (v, graph[u][v]) + for v in range(len(graph)) + if graph[u][v] != math.inf + ] + # fmt: on + + +def mst(graph: Graph) -> list[Edge]: + n = len(graph) + visited: set[int] = set() + edges: list[Edge] = [] + min_heap: list[tuple[float, int, int]] = [] + + visited.add(0) + + for v, weight in neighbors(graph, 0): + heappush(min_heap, (weight, 0, v)) + + while len(visited) < n and min_heap: + _, u, v = heappop(min_heap) + if v in visited: + continue + + visited.add(v) + edges.append((u, v)) + for w, weight in neighbors(graph, v): + if w not in visited: + heappush(min_heap, (weight, v, w)) + + return edges + + +def run() -> int: + graph = create_graph() + edges = mst(graph) + + network_weight = weight_of_network(graph) + mst_weight = weight_of_mst(graph, edges) + + return int(network_weight - mst_weight) + + +def test_run(): + assert run() == 259679 diff --git a/project_euler/11.py b/project_euler/11.py new file mode 100644 index 00000000..a3c9cd04 --- /dev/null +++ b/project_euler/11.py @@ -0,0 +1,72 @@ +# Problem 11: Largest Product in a Grid +# +# What is the greatest product of four adjacent numbers in the same direction (up, down, left, right, or diagonally) in +# the 20x20 grid? +# +# See https://projecteuler.net/problem=11 +from pathlib import Path +from typing import cast +from toolz import pipe +from toolz.curried import map + + +DIRECTIONS = { + "U": [-1, 0], + "R": [0, 1], + "UR": [-1, 1], + "DR": [1, 1], +} + + +def create_row(line: str) -> list[int]: + row = pipe( + line.split(" "), + map(str.strip), + map(int), + list, + ) + return cast(list[int], row) + + +def create_grid() -> list[list[int]]: + file = Path(__file__).parent / "data" / "11.txt" + lines = file.read_text().strip().splitlines() + return [create_row(line) for line in lines] + + +def product(m: list[list[int]], i: int, j: int, direction: str) -> int: + (di, dj) = DIRECTIONS[direction] + p = 1 + + # Safely compute the product of the four elements in the matrix starting at position (i, j) and moving in the + # direction indicated by (di, dj). + for k in range(4): + try: + p *= m[i + k * di][j + k * dj] + except: + return 0 + + return p + + +def run(): + m = create_grid() + rows = len(m) + cols = len(m[0]) + result = 0 + + for i in range(rows): + for j in range(cols): + result = max( + result, + product(m, i, j, "U"), + product(m, i, j, "R"), + product(m, i, j, "UR"), + product(m, i, j, "DR"), + ) + + return result + + +def test_run(): + assert run() == 70600674 diff --git a/project_euler/12.py b/project_euler/12.py new file mode 100644 index 00000000..1b382d66 --- /dev/null +++ b/project_euler/12.py @@ -0,0 +1,21 @@ +# Problem 12: Highly Divisible Triangular Number +# +# What is the value of the first triangle number to have over five hundred divisors? +# +# See https://projecteuler.net/problem=12 +from project_euler.common.divisors import tau + + +def run(limit=500) -> int: + n = 0 + i = 1 + + while tau(n) <= limit: + n += i + i += 1 + + return n + + +def test_run(): + assert run() == 76576500 diff --git a/project_euler/120.py b/project_euler/120.py new file mode 100644 index 00000000..f8135587 --- /dev/null +++ b/project_euler/120.py @@ -0,0 +1,13 @@ +# Problem 120: Square Remainders +# +# See https://projecteuler.net/problem=120 +def r_max(a: int) -> int: + return 2 * a * ((a - 1) // 2) + + +def run(limit=1_000) -> int: + return sum(r_max(a) for a in range(3, limit + 1)) + + +def test_run(): + assert run() == 333082500 diff --git a/project_euler/123.py b/project_euler/123.py new file mode 100644 index 00000000..2bf7b80e --- /dev/null +++ b/project_euler/123.py @@ -0,0 +1,31 @@ +# Problem 123: Prime Square Remainders +# +# Find the least value of n for which the remainder first exceeds 10^10. +# +# See https://projecteuler.net/problem=123 +from typing import cast +from sympy import primerange + + +def r(p: int, n: int) -> int: + if n % 2 == 0: + return 2 + + return 2 * p * n + + +def run(limit=10**10) -> int: + n = 1 + + for x in primerange(2, limit): + p = cast(int, x) + if r(p, n) >= limit: + return n + + n += 1 + + raise ValueError("no solution") + + +def test_run(): + assert run() == 21035 diff --git a/project_euler/13.py b/project_euler/13.py new file mode 100644 index 00000000..e1fd4526 --- /dev/null +++ b/project_euler/13.py @@ -0,0 +1,17 @@ +# Problem 13: Large Sum +# +# Work out the first ten digits of the sum of the one-hundred 50 digit numbers. +# +# See https://projecteuler.net/problem=13 +from pathlib import Path + + +def run(): + file = Path(__file__).parent / "data" / "13.txt" + xs = [int(x) for x in file.read_text().splitlines()] + value = str(sum(xs)) + return int(value[:10]) + + +def test_run(): + assert run() == 5537376230 diff --git a/project_euler/14.py b/project_euler/14.py new file mode 100644 index 00000000..fba4b904 --- /dev/null +++ b/project_euler/14.py @@ -0,0 +1,33 @@ +# Problem 14: Longest Collatz Sequence +# +# Which starting number, under one million, produces the longest Collatz sequence? +# +# See https://projecteuler.net/problem=14 +from functools import cache + + +@cache +def collatz_len(n: int) -> int: + if n == 1: + return 0 + + next = n // 2 if n % 2 == 0 else 3 * n + 1 + return 1 + collatz_len(next) + + +def run(limit=1_000_000) -> int: + max_len = 0 + current_len = 0 + result = 1 + + for i in range(1, limit): + current_len = collatz_len(i) + if current_len > max_len: + max_len = current_len + result = i + + return result + + +def test_run(): + assert run() == 837799 diff --git a/project_euler/15.py b/project_euler/15.py new file mode 100644 index 00000000..3a0cbeea --- /dev/null +++ b/project_euler/15.py @@ -0,0 +1,21 @@ +# Problem 15: Lattice Paths +# +# How many paths are there through a 20x20 grid? +# +# See https://projecteuler.net/problem=15 +import math + + +def run(): + # It's not necessary to actually generate the routes; we can count them directly. Starting at the upper left, one + # must move down exactly 20 times, and right exactly 20 times in order to reach the bottom right. Represent the + # downward movement as a 'D' and the rightward movement as an 'R', then the number of routes to the bottom right is + # equal to the number of permutations of a 'word' with 20 D's and 20 R's. + # + # This can be viewed as a multiset permutation whose cardinality is the multinomial coefficient: (20 + 20)! / 20!20! + # You can compute this as math.comb(20 + 20, 20). + return math.comb(20 + 20, 20) + + +def test_run(): + assert run() == 137846528820 diff --git a/project_euler/16.py b/project_euler/16.py new file mode 100644 index 00000000..65f3b2e1 --- /dev/null +++ b/project_euler/16.py @@ -0,0 +1,12 @@ +# Problem 16: Power Digit Sum +# +# What is the sum of the digits of the number 2^1000? +# +# See https://projecteuler.net/problem=16 +def run(): + s = str(2**1000) + return sum(int(c) for c in s) + + +def test_run(): + assert run() == 1366 diff --git a/project_euler/17.py b/project_euler/17.py new file mode 100644 index 00000000..aac9017f --- /dev/null +++ b/project_euler/17.py @@ -0,0 +1,61 @@ +# Problem 17: Number Letter Counts +# +# If all the numbers from 1 to 1000 inclusive were written out in words, how many letters would be used? +# +# See https://projecteuler.net/problem=17 +MAPPING = { + 1: "one", + 2: "two", + 3: "three", + 4: "four", + 5: "five", + 6: "six", + 7: "seven", + 8: "eight", + 9: "nine", + 10: "ten", + 11: "eleven", + 12: "twelve", + 13: "thirteen", + 14: "fourteen", + 15: "fifteen", + 16: "sixteen", + 17: "seventeen", + 18: "eighteen", + 19: "nineteen", + 20: "twenty", + 30: "thirty", + 40: "forty", + 50: "fifty", + 60: "sixty", + 70: "seventy", + 80: "eighty", + 90: "ninety", +} + + +def say(n: int) -> str: + if n == 1000: + return "one thousand" + elif n >= 100 and n % 100 != 0: + key = n // 100 + return f"{MAPPING[key]} hundred and {say(n % 100)}" + elif n >= 100: + key = n // 100 + return f"{MAPPING[key]} hundred" + elif n >= 20 and n % 10 != 0: + key = n - (n % 10) + return f"{MAPPING[key]} {say(n % 10)}" + else: + return MAPPING[n] + + +def run(): + result = 0 + for i in range(1, 1001): + result += len(say(i).replace(" ", "")) + return result + + +def test_run(): + assert run() == 21124 diff --git a/project_euler/18.py b/project_euler/18.py new file mode 100644 index 00000000..5540539c --- /dev/null +++ b/project_euler/18.py @@ -0,0 +1,59 @@ +# Problem 18: Maximum Path Sum I +# +# Find the maximum total from top to bottom of the triangle. +# +# See https://projecteuler.net/problem=18 +def create_row(line: str) -> list[int]: + return [int(s.strip()) for s in line.strip().split(" ")] + + +def create_triangle(): + input = """ + 75 + 95 64 + 17 47 82 + 18 35 87 10 + 20 04 82 47 65 + 19 01 23 75 03 34 + 88 02 77 73 07 63 67 + 99 65 04 28 06 16 70 92 + 41 41 26 56 83 40 80 70 33 + 41 48 72 33 47 32 37 16 94 29 + 53 71 44 65 25 43 91 52 97 51 14 + 70 11 33 28 77 73 17 78 39 68 17 57 + 91 71 52 38 17 14 91 43 58 50 27 29 48 + 63 66 04 68 89 53 67 30 73 16 69 87 40 31 + 04 62 98 27 23 09 70 98 73 93 38 53 60 04 23 + """ + lines = input.strip().splitlines() + return [create_row(line) for line in lines] + + +def run(): + triangle = create_triangle() + + # Rather than calculating the path sums going down, look at the bottom row and the row above it. + # + # For example, assume that the tree has height 4 and that these are the last 2 rows: + # + # 17 47 82 + # 18 35 87 10 + # + # At 17, you will never take the left path containing 18, because 35 + 17 is greater. At 47, you will never take the + # left path for 35, because 47 + 87 is greater, and so on. + # + # Therefore, these last 2 rows can be reduced to a single row once the optimal path is taken: + # + # 52 134 169 + # + # Once this reduction is done, compare this newly constructed row to the one above it and perform the same reduction + # until only one row remains with one value. + for i in range(len(triangle) - 2, -1, -1): + for j in range(len(triangle[i])): + triangle[i][j] += max(triangle[i + 1][j], triangle[i + 1][j + 1]) + + return triangle[0][0] + + +def test_run(): + assert run() == 1074 diff --git a/project_euler/188.py b/project_euler/188.py new file mode 100644 index 00000000..f7a6e4b3 --- /dev/null +++ b/project_euler/188.py @@ -0,0 +1,14 @@ +# Problem 188: Hyperexponentiation +# +# Find the last 8 digits of 1777^^1855. +# +# See https://projecteuler.net/problem=188 +from project_euler.common.modular_tetration import hpow + + +def run(): + return hpow(1777, 1855, 10**8) + + +def test_run(): + assert run() == 95962097 diff --git a/project_euler/19.py b/project_euler/19.py new file mode 100644 index 00000000..ead7f5bf --- /dev/null +++ b/project_euler/19.py @@ -0,0 +1,19 @@ +# Problem 19: Counting Sundays +# +# How many Sundays fell on the first of the month during the twentieth century (1 Jan 1901 to 31 Dec 2000)? +# +# See https://projecteuler.net/problem=19 +from datetime import date + + +def run() -> int: + count = 0 + for year in range(1901, 2001): + for month in range(1, 13): + if date(year, month, 1).weekday() == 6: + count += 1 + return count + + +def test_run(): + assert run() == 171 diff --git a/project_euler/2.py b/project_euler/2.py new file mode 100644 index 00000000..612a0ffd --- /dev/null +++ b/project_euler/2.py @@ -0,0 +1,23 @@ +# Problem 2: Even Fibonacci Numbers +# +# Find the sum of all the even Fibonacci numbers below 4_000_000. +# +# See https://projecteuler.net/problem=2. +from itertools import takewhile +from typing import cast +from toolz import curried, pipe +from project_euler.common.fibonacci_numbers import fibs + + +def run(limit=4_000_000) -> int: + result = pipe( + fibs(), + lambda xs: takewhile(lambda x: x < limit, xs), + curried.filter(lambda x: x % 2 == 0), + curried.reduce(lambda a, b: a + b), + ) + return cast(int, result) + + +def test_run(): + assert run() == 4613732 diff --git a/project_euler/20.py b/project_euler/20.py new file mode 100644 index 00000000..0ebdde35 --- /dev/null +++ b/project_euler/20.py @@ -0,0 +1,14 @@ +# Problem 20: Factorial Digit Sum +# +# Find the sum of the digits in the number 100! +# +# See https://projecteuler.net/problem=20 +import math + + +def run(n=100) -> int: + return sum(int(c) for c in str(math.factorial(n))) + + +def test_run(): + assert run() == 648 diff --git a/project_euler/21.py b/project_euler/21.py new file mode 100644 index 00000000..533d2720 --- /dev/null +++ b/project_euler/21.py @@ -0,0 +1,21 @@ +# Problem 21: Amicable Numbers +# +# Evaluate the sum of all the amicable numbers under 10_000. +# +# See https://projecteuler.net/problem=21 +from project_euler.common.divisors import sigma + + +def run(n=10_000) -> int: + result = 0 + + for a in range(2, n + 1): + b = sigma(a) - a + if a > b and sigma(b) - b == a: + result += a + b + + return result + + +def test_run(): + assert run() == 31626 diff --git a/project_euler/22.py b/project_euler/22.py new file mode 100644 index 00000000..22826e11 --- /dev/null +++ b/project_euler/22.py @@ -0,0 +1,34 @@ +# Problem 22: Names Scores +# +# What is the total of all the name scores in the file? +# +# See https://projecteuler.net/problem=22 +from pathlib import Path + + +def read_names(): + file = Path(__file__).parent / "data" / "22.txt" + names = file.read_text().split(",") + return [name[1:-1] for name in names] + + +def create_score_map(): + codes = [chr(c) for c in range(ord("A"), ord("Z") + 1)] + values = range(1, len(codes) + 1) + return dict(zip(codes, values)) + + +def run(): + mapping = create_score_map() + names = sorted(read_names()) + result = 0 + + for i, name in enumerate(names): + score = sum([mapping[c] for c in name]) + result += score * (i + 1) + + return result + + +def test_run(): + assert run() == 871198282 diff --git a/project_euler/23.py b/project_euler/23.py new file mode 100644 index 00000000..e671c2c1 --- /dev/null +++ b/project_euler/23.py @@ -0,0 +1,25 @@ +# Problem 23: Non-Abundant Sums +# +# Find the sum of all the positive integers which cannot be written as the sum of two abundant numbers. +# +# See https://projecteuler.net/problem=23 +from project_euler.common.divisors import sigma + + +def run(limit=28123) -> int: + abundants = list(filter(lambda n: sigma(n) - n > n, range(1, limit + 1))) + numbers = list(range(0, limit + 1)) + + for i in range(len(abundants)): + for j in range(i, len(abundants)): + k = abundants[i] + abundants[j] + if k <= limit: + numbers[k] = 0 + else: + break + + return sum(numbers) + + +def test_run(): + assert run() == 4179871 diff --git a/project_euler/24.py b/project_euler/24.py new file mode 100644 index 00000000..09c80fc5 --- /dev/null +++ b/project_euler/24.py @@ -0,0 +1,24 @@ +# Problem 24: Lexicographic Permutations +# +# What is the millionth lexicographic permutation of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9? +# +# See https://projecteuler.net/problem=24 +from itertools import permutations +from typing import cast +from toolz import curried, pipe + + +def run() -> int: + result = pipe( + range(10), + permutations, + curried.map(lambda xs: int("".join(map(str, xs)))), + sorted, + lambda xs: xs[999_999], + ) + + return cast(int, result) + + +def test_run(): + assert run() == 2783915460 diff --git a/project_euler/25.py b/project_euler/25.py new file mode 100644 index 00000000..5851016c --- /dev/null +++ b/project_euler/25.py @@ -0,0 +1,17 @@ +# Problem 25: 1000-digit Fibonacci Number +# +# What is the index of the first term in the Fibonacci sequence to contain 1000 digits? +# +# See https://projecteuler.net/problem=25 +from project_euler.common.fibonacci_numbers import fibs + + +def run() -> int | None: + for i, n in enumerate(fibs()): + count = len(str(n)) + if count >= 1000: + return i + + +def test_run(): + assert run() == 4782 diff --git a/project_euler/26.py b/project_euler/26.py new file mode 100644 index 00000000..15294a7d --- /dev/null +++ b/project_euler/26.py @@ -0,0 +1,33 @@ +# Problem 26: Reciprocal Cycles +# +# Find the value of d < 1000 for which 1/d contains the longest recurring cycle in its decimal fraction part. +# +# See https://projecteuler.net/problem=26 +from math import gcd +from project_euler.common.order import ord + + +def run(limit=1_000) -> int: + best_n = 0 + best_t = 0 + + for n in range(limit - 1, 1, -1): + if n % 2 == 0 or n % 5 == 0: + continue + + if gcd(10, n) != 1: + continue + + t = ord(10, n) + if t == n - 1: + return n + + if t > best_t: + best_t = t + best_n = n + + return best_n + + +def test_run(): + assert run() == 983 diff --git a/project_euler/27.py b/project_euler/27.py new file mode 100644 index 00000000..dbb4182f --- /dev/null +++ b/project_euler/27.py @@ -0,0 +1,42 @@ +# Problem 27: Quadratic Primes +# +# Find the product of the coefficients, a and b, for the quadratic expression that produces the maximum number of primes +# for consecutive values of n, starting with n = 0. +# +# Only consider |a| < 1000 and |b| < 1000. +# +# See https://projecteuler.net/problem=27 +from typing import cast +from sympy import primerange + + +def f(n: int, a: int, b: int) -> int: + return n**2 + a * n + b + + +def count_primes(a: int, b: int, ps: set[int]) -> int: + n = 0 + while True: + y = f(n, a, b) + if y < 2 or y not in ps: + return n + n += 1 + + +def run(limit=1_000): + candidates: dict[int, tuple[int, int]] = {} + ps = set([cast(int, p) for p in primerange(2, limit)]) + bs = ps.union([-p for p in ps]) + + for b in bs: + for a in range(-limit, limit + 1): + c = count_primes(a, b, ps) + candidates[c] = (a, b) + + best = max(candidates.keys()) + (a, b) = candidates[best] + return a * b + + +def test_run(): + assert run() == -59231 diff --git a/project_euler/28.py b/project_euler/28.py new file mode 100644 index 00000000..3164e2a6 --- /dev/null +++ b/project_euler/28.py @@ -0,0 +1,52 @@ +# Problem 28: Number Spiral Diagonals +# +# What is the sum of the numbers on the diagonals in a 1001x1001 spiral formed in the same way? +# +# See https://projecteuler.net/problem=28 +import numpy as np + + +def turn(direction: str) -> str: + return {"R": "D", "D": "L", "L": "U", "U": "R"}[direction] + + +def next(position: tuple[int, int], direction: str) -> tuple[int, int]: + i, j = position + + return {"R": (i + 1, j), "D": (i, j - 1), "L": (i - 1, j), "U": (i, j + 1)}[direction] + + +def create_spiral(n: int) -> np.ndarray: + spiral = np.zeros((n, n), dtype=int) + + mid = n // 2 + heading = "U" + (i, j) = (mid, mid) + + for x in range(1, n * n + 1): + # NumPy is row-major order; that is spiral[i][j] == spiral[j, i]. + spiral[j, i] = x + next_heading = turn(heading) + (ni, nj) = next((i, j), next_heading) + + if 0 <= ni < n and 0 <= nj < n and spiral[nj, ni] == 0: + heading = next_heading + (i, j) = (ni, nj) + else: + (i, j) = next((i, j), heading) + + return spiral + + +def run(limit=1_001) -> int: + spiral = create_spiral(limit) + # Compute sum from top left to bottom right. + main_diag = np.trace(spiral) + # Compute sum from bop right to bottom left but horizontally flipping the spiral. + anti_diag = np.trace(np.fliplr(spiral)) + # Center is double counted, so subtract 1. + return int(main_diag + anti_diag - 1) + + +def test_run(): + assert run(1001) == 669171001 diff --git a/project_euler/29.py b/project_euler/29.py new file mode 100644 index 00000000..103420bd --- /dev/null +++ b/project_euler/29.py @@ -0,0 +1,16 @@ +# Problem 29: Distinct Powers +# +# How many distinct terms are in the sequence generated by a^b for 2 ≤ a ≤ 100 and 2 ≤ b ≤ 100? +# +# See https://projecteuler.net/problem=29 +def run() -> int: + terms: set[int] = set() + for a in range(2, 101): + for b in range(2, 101): + terms.add(a**b) + + return len(terms) + + +def test_run(): + assert run() == 9183 diff --git a/project_euler/3.py b/project_euler/3.py new file mode 100644 index 00000000..2c1da5c9 --- /dev/null +++ b/project_euler/3.py @@ -0,0 +1,14 @@ +# Problem 3: Large Prime Factor +# +# Find the largest prime factor of a 600851475143. +# +# See https://projecteuler.net/problem=3 +from project_euler.common.prime_factors import prime_factors + + +def run(limit=600851475143) -> int: + return max(prime_factors(limit)) + + +def test_run(): + assert run() == 6857 diff --git a/project_euler/30.py b/project_euler/30.py new file mode 100644 index 00000000..a2cfcc8e --- /dev/null +++ b/project_euler/30.py @@ -0,0 +1,23 @@ +# Problem 30: Digit Fifth Powers +# +# Find the sum of all the numbers that can be written as the sum of fifth powers of their digits. +# +# See https://projecteuler.net/problem=30 +def digital_sum(n: int) -> int: + return sum(int(d) ** 5 for d in str(n)) + + +def run() -> int: + x = 9**5 + + digits = 1 + while 10 ** (digits - 1) <= digits * x: + digits += 1 + + limit = digits * x + result = sum(i for i in range(10, limit) if i == digital_sum(i)) + return result + + +def test_run(): + assert run() == 443839 diff --git a/project_euler/31.py b/project_euler/31.py new file mode 100644 index 00000000..d0072a4a --- /dev/null +++ b/project_euler/31.py @@ -0,0 +1,56 @@ +# Problem 31: Coin Sums +# +# How many different ways can £2 be made using any number of coins? +# +# See https://projecteuler.net/problem=31 +from functools import cache +from typing import Callable + + +def run() -> int: + P: dict[int, Callable[[int], int]] = {} + + # Number of ways to make change for n using coins of value 1p. + P[1] = lambda n: 1 if n >= 0 else 0 + + # Generate P[x] for x = 2, 5, 10, 20, 50, 100. Each function P[xk] can be created based previous values of xk. + def define_px(x, y): + # Number of ways to make change for n using coins of value x or less. + @cache + def px(n): + # Get the function that computes ways to make change for n using y or less. + py = P[y] + + # Number of ways to make change for n using a higher denomination of coin (x). + cx = px(n - x) if n >= x else 0 + + # Number of ways to make change for n using a lower denomination of coin (y). + cy = py(n) + + return cx + cy + + # Now that px(n) has been defined, store it in the dictionary. + P[x] = px + + # Define function that computes ways to make change for n using 2p and 1p. + define_px(2, 1) + # Define function that computes ways to make change for n using 5p, 2p, and 1p. + define_px(5, 2) + # Define function that computes ways to make change for n using 10p, 5p, 2p, and 1p. + define_px(10, 5) + # Define function that computes ways to make change for n using 20p, 10p, 5p, 2p, and 1p. + define_px(20, 10) + # Define function that computes ways to make change for n using 50p, 20p, 10p, 5p, 2p, and 1p. + define_px(50, 20) + # Define function that computes ways to make change for n using £1, 50p, 20p, 10p, 5p, 2p, and 1p. + define_px(100, 50) + # Define function that computes ways to make change for n using £2, £1, 50p, 20p, 10p, 5p, 2p, and 1p. + define_px(200, 100) + + # Get the function that computes ways to make change for £2. + p200 = P[200] + return p200(200) + + +def test_run(): + assert run() == 73682 diff --git a/project_euler/32.py b/project_euler/32.py new file mode 100644 index 00000000..f5b99bf0 --- /dev/null +++ b/project_euler/32.py @@ -0,0 +1,42 @@ +# Problem 32: Pandigital Products +# +# Find the sum of all products whose multiplicand/multiplier/product identity can be written as a 1 through 9 +# pandigital. +# +# See https://projecteuler.net/problem=32 +from itertools import permutations + + +def tuple2int(cs: tuple[str, ...]) -> int: + return int("".join(cs)) + + +def pandigital_product_values(p: tuple[str, ...], i: int, j: int) -> tuple[int, int, int]: + a = tuple2int(p[:i]) + b = tuple2int(p[i : i + j]) + c = tuple2int(p[i + j :]) + return (a, b, c) + + +def run(): + seen: set[int] = set() + products: set[int] = set() + + for p in permutations("123456789"): + # Check form: a * bcde = fghi (1 digit × 4 digits = 4 digits) + (a, b, c) = pandigital_product_values(p, 1, 4) + if c not in seen and c == a * b: + products.add(c) + seen.add(c) + + # Check form: ab * cde = fghi (2 digits × 3 digits = 4 digits) + (a, b, c) = pandigital_product_values(p, 2, 3) + if c not in seen and c == a * b: + products.add(c) + seen.add(c) + + return sum(products) + + +def test_run(): + assert run() == 45228 diff --git a/project_euler/33.py b/project_euler/33.py new file mode 100644 index 00000000..a80d83e2 --- /dev/null +++ b/project_euler/33.py @@ -0,0 +1,68 @@ +# Problem 33: Digit Cancelling Fractions +# +# Find four non-trivial examples of digit cancelling fractions, less than one in value, express them in lowest common +# terms, multiply them, and return the denominator of the product. +# +# See https://projecteuler.net/problem=33 +from functools import reduce +from math import gcd + + +def int2list(n: int) -> list[int]: + return [int(d) for d in str(n)] + + +def list2int(ds: list[int]) -> int: + return int("".join(map(str, ds))) + + +def denominators(n: int) -> list[int]: + a, b = int2list(n) + xs: set[int] = set() + + for i in range(a, 10): + xs.add(list2int([i, b])) + xs.add(list2int([b, i])) + + for i in range(a, 10): + xs.add(list2int([i, a])) + xs.add(list2int([a, i])) + + return sorted(x for x in xs if x > n) + + +def cancellable(m: int, n: int) -> bool: + m_digits = int2list(m) + n_digits = int2list(n) + + if 0 in m_digits or 0 in n_digits: + return False + + v = m / n + a, b = m_digits + c, d = n_digits + + return ( + (a == c and d != 0 and v == b / d) + or (a == d and c != 0 and v == b / c) + or (b == c and d != 0 and v == a / d) + or (b == d and c != 0 and v == a / c) + ) + + +def run(): + fracs = [] + for n in range(11, 100): + for d in denominators(n): + if cancellable(n, d): + fracs.append((n, d)) + + ns = reduce(lambda a, b: a * b, (n for n, _ in fracs)) + ds = reduce(lambda a, b: a * b, (d for _, d in fracs)) + x = gcd(ns, ds) + + return ds // x + + +def test_run(): + assert run() == 100 diff --git a/project_euler/34.py b/project_euler/34.py new file mode 100644 index 00000000..cb2cad91 --- /dev/null +++ b/project_euler/34.py @@ -0,0 +1,33 @@ +# Problem 34: Digit Factorials +# +# Find the sum of all numbers which are equal to the sum of the factorial of their digits. +# +# See https://projecteuler.net/problem=34 +from math import factorial, log10 + + +def digit_factorial(n: int) -> int: + return sum(factorial(int(d)) for d in str(n)) + + +def is_factorion(n: int) -> bool: + return n == digit_factorial(n) + + +def max_digits(limit: float) -> int: + d = 1 + while (d - 1 - log10(d)) < limit: + d += 1 + return d - 1 + + +def run() -> int: + limit = sum(log10(i) for i in range(1, 10)) + digits = max_digits(limit) + max_factorion = factorial(9) * digits + + return sum(n for n in range(3, max_factorion + 1) if is_factorion(n)) + + +def test_run(): + assert run() == 40730 diff --git a/project_euler/35.py b/project_euler/35.py new file mode 100644 index 00000000..59bd33a2 --- /dev/null +++ b/project_euler/35.py @@ -0,0 +1,43 @@ +# Problem 35: Circular Primes +# +# A circular prime is a number for which all rotations of its digits are also prime. For example: 197 → 971 → 719. +# +# How many circular primes are there below one million? +# +# See https://projecteuler.net/problem=35 +from typing import cast +from sympy import isprime, primerange +from toolz import pipe +from toolz.curried import filter, map, reduce + + +def rotate(xs: list[str]) -> list[str]: + return xs[1:] + [xs[0]] + + +def rotations(n: int) -> list[int]: + digits = list(str(n)) + xs: list[int] = [] + for _ in range(len(digits)): + digits = rotate(digits) + xs.append(int("".join(digits))) + return xs + + +def is_circular_prime(n: int) -> bool: + return all(isprime(p) for p in rotations(n)) + + +def run(limit=1_000_000) -> int: + result = pipe( + primerange(2, limit), + map(lambda p: cast(int, p)), + filter(lambda p: is_circular_prime(p)), + map(lambda p: 1), + reduce(lambda a, b: a + b), + ) + return cast(int, result) + + +def test_run(): + assert run() == 55 diff --git a/project_euler/36.py b/project_euler/36.py new file mode 100644 index 00000000..33d0f318 --- /dev/null +++ b/project_euler/36.py @@ -0,0 +1,21 @@ +# Problem 36: Double-base Palindromes +# +# Find the sum of all numbers, less than one million, which are palindromic in base 10 and base 2. +# +# See https://projecteuler.net/problem=36 +def is_palindrome(s: str) -> bool: + return s == s[::-1] + + +def is_double_base_palindrome(n: int) -> bool: + base_10 = str(n) + base_2 = bin(n)[2:] + return is_palindrome(base_10) and is_palindrome(base_2) + + +def run(limit=1_000_000) -> int: + return sum(n for n in range(limit + 1) if is_double_base_palindrome(n)) + + +def test_run(): + assert run() == 872187 diff --git a/project_euler/37.py b/project_euler/37.py new file mode 100644 index 00000000..33526ea0 --- /dev/null +++ b/project_euler/37.py @@ -0,0 +1,50 @@ +# Problem 37: Truncatable Primes +# +# Find the sum of the only eleven primes that are both truncatable from left to right and right to left. +# +# See https://projecteuler.net/problem=37 +from sympy import isprime + + +def truncate(n: int, direction: str) -> int: + s = str(n) + + if direction == "L": + return int(s[1:]) + elif direction == "R": + return int(s[:-1]) + + raise ValueError("invalid direction") + + +def is_truncatable(n: int, direction: str) -> bool: + if not isprime(n): + return False + + if n < 10: + return True + + return is_truncatable(truncate(n, direction), direction) + + +def is_fully_truncatable(n: int) -> bool: + return is_truncatable(n, "L") and is_truncatable(n, "R") + + +def run(limit=11) -> int: + result: list[int] = [] + + # Exclude 2, 3, 5, and 7; they are not truncatable. + p = 11 + while len(result) < limit: + if is_fully_truncatable(p): + result.append(p) + + # Exclude even numbers; they cannot be prime. + p += 2 + + return sum(result) + + +def test_run(): + assert run() == 748317 diff --git a/project_euler/38.py b/project_euler/38.py new file mode 100644 index 00000000..6602a391 --- /dev/null +++ b/project_euler/38.py @@ -0,0 +1,32 @@ +# Problem 38: Pandigital Multiples +# +# What is the largest 1 to 9 pandigital 9 digit number that can be formed as the concatenated product of an integer with +# (1,2, ... , n) where n > 1? +# +# See https://projecteuler.net/problem=38 +from itertools import permutations + + +def create_pandigitals() -> set[int]: + return set(int("".join(p)) for p in permutations("123456789")) + + +def pandigital_product(pandigitals: set[int], n: int) -> int: + s = "" + i = 1 + + while len(s) < 9: + s += str(n * i) + i += 1 + + return int(s) if len(s) == 9 and (int(s) in pandigitals) and i > 2 else 0 + + +def run() -> int: + pandigitals = create_pandigitals() + products = [pandigital_product(pandigitals, n) for n in range(1, 9999)] + return max(products) + + +def test_run(): + assert run() == 932718654 diff --git a/project_euler/4.py b/project_euler/4.py new file mode 100644 index 00000000..cec0e4ad --- /dev/null +++ b/project_euler/4.py @@ -0,0 +1,25 @@ +# Problem 4: Largest Palindrome Product +# +# Find the largest palindrome made from the product of two 3-digit numbers. +# +# See https://projecteuler.net/problem=4 +def is_palindrome(n): + return str(n) == str(n)[::-1] + + +def run(): + max_product = 0 + + # To speed up the search, we can limit the search space and search backwards. We want to find the largest + # palindrome, so we start with the largest numbers first. + for i in range(999, 99, -1): + for j in range(999, 99, -1): + n = i * j + if is_palindrome(n) and n > max_product: + max_product = n + + return max_product + + +def test_run(): + assert run() == 906609 diff --git a/project_euler/40.py b/project_euler/40.py new file mode 100644 index 00000000..5b2701bd --- /dev/null +++ b/project_euler/40.py @@ -0,0 +1,31 @@ +# Problem 40: Champernowne's Constant +# +# Find the product of the digits at the following positions in Champernowne's constant: +# +# 1, 10, 100, 1000, 10000, 100000, 1000000. +# +# See https://projecteuler.net/problem=40 +def generate_champernownes_constant(limit: int) -> str: + s = "" + n = 1 + + while len(s) < limit: + s += str(n) + n += 1 + + return s + + +def run(limit=1_000_000) -> int: + s = generate_champernownes_constant(limit) + + result = 1 + for i in [10**k for k in range(7)]: + digit = int(s[i - 1]) + result *= digit + + return result + + +def test_run(): + assert run() == 210 diff --git a/project_euler/41.py b/project_euler/41.py new file mode 100644 index 00000000..2b88b94f --- /dev/null +++ b/project_euler/41.py @@ -0,0 +1,27 @@ +# Problem 41: Pandigital Prime +# +# What is the largest n-digit pandigital prime that exists? +# +# See https://projecteuler.net/problem=41 +from itertools import permutations +from sympy import isprime + + +def tuple2int(t: tuple[str, ...]) -> int: + return int("".join(t)) + + +def run(): + max_p = 0 + + # 8 and 9 digit pandigital numbers are divisible by 3, so they cannot be prime. + for permutation in permutations("7654321"): + p = tuple2int(permutation) + if isprime(p): + max_p = max(max_p, p) + + return max_p + + +def test_run(): + assert run() == 7652413 diff --git a/project_euler/42.py b/project_euler/42.py new file mode 100644 index 00000000..ad95c522 --- /dev/null +++ b/project_euler/42.py @@ -0,0 +1,38 @@ +# Problem 42: Coded Triangle Numbers +# +# How many are triangle words? +# +# See https://projecteuler.net/problem=42 +from pathlib import Path + + +def read_words() -> list[str]: + file = Path(__file__).parent / "data" / "42.txt" + return file.read_text().replace('"', "").strip().split(",") + + +def word_score(word: str) -> int: + return sum(ord(c) - ord("A") + 1 for c in word) + + +def triangle_numbers_up_to(limit: int) -> set[int]: + n = 1 + triangles: set[int] = set() + + while (t := n * (n + 1) // 2) <= limit: + triangles.add(t) + n += 1 + + return triangles + + +def run() -> int: + words = read_words() + scores = list(map(word_score, words)) + max_score = max(scores) + triangle_numbers = triangle_numbers_up_to(max_score) + return sum(1 for score in scores if score in triangle_numbers) + + +def test_run(): + assert run() == 162 diff --git a/project_euler/48.py b/project_euler/48.py new file mode 100644 index 00000000..3a2916fb --- /dev/null +++ b/project_euler/48.py @@ -0,0 +1,22 @@ +# Problem 48: Self powers. +# +# Computes the last ten digits of the series 1^1 + 2^2 + 3^3 + ... + 1000^1000. +# +# See https://projecteuler.net/problem=48 +from typing import cast +from toolz import curried, pipe + + +def run(n=1_000) -> int: + # This modulus will give us the last 10 digits. + m = 10**10 + result = pipe( + range(1, n + 1), + curried.map(lambda b: pow(b, b, m)), + curried.reduce(lambda a, b: (a + b) % m), + ) + return cast(int, result) + + +def test_run(): + assert run() == 9110846700 diff --git a/project_euler/5.py b/project_euler/5.py new file mode 100644 index 00000000..80d93524 --- /dev/null +++ b/project_euler/5.py @@ -0,0 +1,15 @@ +# Problem 5: Smallest Multiple +# +# Find the smallest positive number that is evenly divisible by all of the numbers from 1 to 20. +# +# See https://projecteuler.net/problem=5 +from functools import reduce +from math import lcm + + +def run(limit=20) -> int: + return reduce(lcm, range(1, limit + 1)) + + +def test_run(): + assert run() == 232792560 diff --git a/project_euler/52.py b/project_euler/52.py new file mode 100644 index 00000000..23f28eda --- /dev/null +++ b/project_euler/52.py @@ -0,0 +1,20 @@ +# Problem 52: Permuted Multiples +# +# Find the smallest positive integer, x, such that 2x, 3x, 4x, 5x, and 6x, contain the same digits. +# +# See https://projecteuler.net/problem=52 +def sort_digits(n: int) -> str: + return "".join(sorted(str(n))) + + +def run() -> int: + n = 1 + while True: + s = sort_digits(n) + if all(sort_digits(n * m) == s for m in range(2, 7)): + return n + n += 1 + + +def test_run(): + assert run() == 142857 diff --git a/project_euler/53.py b/project_euler/53.py new file mode 100644 index 00000000..3066fa53 --- /dev/null +++ b/project_euler/53.py @@ -0,0 +1,20 @@ +# Problem 53: Combinatoric Selections. +# +# Computes the number distinct values of (n choose r) for 1 ≤ n ≤ limit that are greater than 1_000_000. +# +# See {@link https://projecteuler.net/problem=53}. +import math + + +def run(limit=100) -> int: + count = 0 + for n in range(1, limit + 1): + for r in range(1, n): + c = math.comb(n, r) + if c > 1_000_000: + count += 1 + return count + + +def test_run(): + assert run() == 4075 diff --git a/project_euler/6.py b/project_euler/6.py new file mode 100644 index 00000000..5826baea --- /dev/null +++ b/project_euler/6.py @@ -0,0 +1,28 @@ +# Problem 6: Sum Square Difference +# +# Find the difference between the sum of the square of the first one hundred natural numbers and the square of the sum. +# +# See https://projecteuler.net/problem=6 +from typing import cast +from toolz import curried, pipe + + +def run() -> int: + a = pipe( + range(101), + curried.map(lambda n: n**2), + curried.reduce(lambda a, b: a + b), + ) + b = pipe( + range(101), + curried.reduce(lambda a, b: a + b), + lambda n: n**2, + ) + + a = cast(int, a) + b = cast(int, b) + return b - a + + +def test_run(): + assert run() == 25164150 diff --git a/project_euler/67.py b/project_euler/67.py new file mode 100644 index 00000000..2848ef22 --- /dev/null +++ b/project_euler/67.py @@ -0,0 +1,31 @@ +# Problem 67: Maximum Path Sum II +# +# Find the maximum total from top to bottom of the triangle. +# +# See https://projecteuler.net/problem=67 +from pathlib import Path + + +def create_row(line: str) -> list[int]: + return [int(s.strip()) for s in line.strip().split(" ")] + + +def create_triangle(): + input = Path(__file__).parent / "data" / "67.txt" + lines = input.read_text().strip().splitlines() + return [create_row(line) for line in lines] + + +def run(): + triangle = create_triangle() + + # See problem 18 for an explanation of this algorithm. + for i in range(len(triangle) - 2, -1, -1): + for j in range(len(triangle[i])): + triangle[i][j] += max(triangle[i + 1][j], triangle[i + 1][j + 1]) + + return triangle[0][0] + + +def test_run(): + assert run() == 7273 diff --git a/project_euler/69.py b/project_euler/69.py new file mode 100644 index 00000000..298986a0 --- /dev/null +++ b/project_euler/69.py @@ -0,0 +1,24 @@ +# Problem 69: Totient Maximum +# +# Find the value of n ≤ 1_000_000 for which n/φ(n) is a maximum. +# +# See https://projecteuler.net/problem=69 +from typing import cast +from sympy import primerange + + +def run(limit=1_000_000) -> int: + acc = 1 + + for x in primerange(2, limit): + p = cast(int, x) + n = acc * p + if n > limit: + return acc + acc = n + + raise ValueError("no solution") + + +def test_run(): + assert run() == 510510 diff --git a/project_euler/7.py b/project_euler/7.py new file mode 100644 index 00000000..dd40193d --- /dev/null +++ b/project_euler/7.py @@ -0,0 +1,14 @@ +# Problem 7: 10001st Prime +# +# What is the 10001st prime number? +# +# See https://projecteuler.net/problem=7 +from sympy import prime + + +def run(n=10_001) -> int: + return int(prime(n)) + + +def test_run(): + assert run() == 104743 diff --git a/project_euler/70.py b/project_euler/70.py new file mode 100644 index 00000000..41c4b74e --- /dev/null +++ b/project_euler/70.py @@ -0,0 +1,60 @@ +# Problem 70: Totient Permutation +# +# Find the value of n, 1 < n < 10^7, for which φ(n) is a permutation of n and the ratio n/φ(n) produces a minimum. +# +# See https://projecteuler.net/problem=70 +import math +from typing import cast +from sympy import primerange + + +# This is a special totient function that optimizes the computation of totient for a semi-prime whose factors are p +# and q. +# +# For a prime number, the totient is simply (sub1 p). Because the totient is a multiplicative function, +# totient(p * q) = totient(p) * totient(q). Therefore, the totient of a semi-prime is simply (p - 1) * (q - 1). +def totient(p: int, q: int) -> int: + return (p - 1) * (q - 1) + + +# Checks if two positive integers' digits are permutations of each other. +def is_permutation(m: int, n: int) -> bool: + return sorted(str(m)) == sorted(str(n)) + + +def semi_prime_pairs(limit: int) -> list[tuple[int, int]]: + n = 2 * (math.isqrt(limit) + 1) + ps = list(primerange(2, n)) + pairs: list[tuple[int, int]] = [] + + for i in range(len(ps)): + for j in range(i, len(ps)): + p = cast(int, ps[i]) + q = cast(int, ps[j]) + pairs.append((p, q)) + + return pairs + + +def run(limit=10_000_000) -> int: + pairs = semi_prime_pairs(limit) + result = 0 + min_ratio = math.inf + + for p, q in pairs: + n = p * q + if n >= limit: + continue + + phi = totient(p, q) + if is_permutation(n, phi): + ratio = n / phi + if ratio < min_ratio: + min_ratio = ratio + result = n + + return result + + +def test_run(): + assert run() == 8319823 diff --git a/project_euler/76.py b/project_euler/76.py new file mode 100644 index 00000000..73591866 --- /dev/null +++ b/project_euler/76.py @@ -0,0 +1,23 @@ +# Problem 76: Counting Summations +# +# How many different ways can one hundred be written as a sum of at least two positive integers? +# +# See https://projecteuler.net/problem=76 +from functools import cache + + +@cache +def partition(k: int, n: int) -> int: + if k > n: + return 0 + if k == n: + return 1 + return partition(k + 1, n) + partition(k, n - k) + + +def run(target=100) -> int: + return partition(1, target) - 1 + + +def test_run(): + assert run() == 190569291 diff --git a/project_euler/8.py b/project_euler/8.py new file mode 100644 index 00000000..a64281cd --- /dev/null +++ b/project_euler/8.py @@ -0,0 +1,59 @@ +# Problem 8: Largest Product in a Series +# +# Find the thirteen adjacent digits in the 1000 digit number that have the greatest product. What is the value of this +# product? +# +# See https://projecteuler.net/problem=8 +from pathlib import Path + + +def run(window=13) -> int: + file = Path(__file__).parent / "data" / "8.txt" + data = "".join(file.read_text().splitlines()) + + # Can be solved with a sliding window algorithm. We just have to take care to note the number of zeroes in the + # window; if a window has any zeroes in it, thet product of that window will be zero. At each step, we only compute + # the product if we have no zeroes in the window. + zeroes = 0 + max_product = 0 + product = 1 + + for i in range(len(data) - window): + # Create our window if we haven't seen enough elements. + if i < window: + digit = int(data[i]) + if digit == 0: + zeroes += 1 + continue + + product *= digit + if zeroes == 0: + max_product = max(max_product, product) + + continue + + # Otherwise, slide the window through the rest of the data. + incoming = data[i] + outgoing = data[i - window] + + # Multiply the product by the incoming digit if it's non-zero. + if incoming != "0": + product *= int(incoming) + else: + zeroes += 1 + + # Divide the product by the outgoing digit if it's non-zero. + if outgoing != "0": + product /= int(outgoing) + else: + zeroes -= 1 + + # Update max product only if there are no zeros in the current window. + if zeroes == 0: + max_product = max(max_product, product) + + return int(max_product) + + +def test_run(): + assert run() == 23514624000 diff --git a/project_euler/9.py b/project_euler/9.py new file mode 100644 index 00000000..c3e722f4 --- /dev/null +++ b/project_euler/9.py @@ -0,0 +1,22 @@ +# Problem 9: Special Pythagorean Triplet +# +# There exists exactly one Pythagorean triplet for which a + b + c = 1000. Find the product a * b * c. +# +# See https://projecteuler.net/problem=9 +def run(limit=1_000) -> int: + # Limit search space for a; since b and c are greater than a, the maximum value for a is 1/3 of the target. + a_max = limit // 3 + for a in range(1, a_max): + # Limit search space for b; since c is greater than b, the maximum value for b is half the remaining value. + b_max = (limit - a) // 2 + for b in range(a + 1, b_max): + c = limit - a - b + + if a * a + b * b == c * c: + return a * b * c + + raise ValueError("no triplet found") + + +def test_run(): + assert run() == 31875000 diff --git a/project_euler/__init__.py b/project_euler/__init__.py new file mode 100644 index 00000000..e69de29b diff --git a/project_euler/common/divisors.py b/project_euler/common/divisors.py new file mode 100644 index 00000000..c0f4fedb --- /dev/null +++ b/project_euler/common/divisors.py @@ -0,0 +1,25 @@ +from functools import cache +import math + + +@cache +def divisors(n: int) -> list[int]: + ds: set[int] = set() + + # Use trial division to find all divisors of n, up to sqrt(n). Only check up to sqrt(n) because you can't have a + # divisors greater than sqrt(n) that isn't paired with a divisor less than sqrt(n). + limit = int(math.sqrt(n)) + 1 + for i in range(1, limit): + if n % i == 0: + ds.add(i) + ds.add(n // i) + + return sorted(ds) + + +def sigma(n: int) -> int: + return sum(divisors(n)) + + +def tau(n: int) -> int: + return len(divisors(n)) diff --git a/project_euler/common/divisors_test.py b/project_euler/common/divisors_test.py new file mode 100644 index 00000000..5969f19e --- /dev/null +++ b/project_euler/common/divisors_test.py @@ -0,0 +1,22 @@ +from project_euler.common.divisors import divisors, sigma, tau + + +def test_divisors(): + assert divisors(1) == [1] + assert divisors(2) == [1, 2] + assert divisors(15) == [1, 3, 5, 15] + assert divisors(2015) == [1, 5, 13, 31, 65, 155, 403, 2015] + + +def test_sigma(): + assert sigma(1) == 1 + assert sigma(2) == 3 + assert sigma(15) == 24 + assert sigma(2015) == 2688 + + +def test_tau(): + assert tau(1) == 1 + assert tau(2) == 2 + assert tau(15) == 4 + assert tau(2015) == 8 diff --git a/project_euler/common/fibonacci_numbers.py b/project_euler/common/fibonacci_numbers.py new file mode 100644 index 00000000..6d826350 --- /dev/null +++ b/project_euler/common/fibonacci_numbers.py @@ -0,0 +1,5 @@ +def fibs(): + a, b = 0, 1 + while True: + yield a + a, b = b, a + b diff --git a/project_euler/common/modular_tetration.py b/project_euler/common/modular_tetration.py new file mode 100644 index 00000000..abe8de65 --- /dev/null +++ b/project_euler/common/modular_tetration.py @@ -0,0 +1,34 @@ +import math +from project_euler.common.order import ord +from project_euler.common.totient import totient + + +def _f(b: int, e: int, m: int) -> int: + o = ord(b, m) + t = hpow(b, e - 1, o) + return pow(b, t, m) + + +def _g(b: int, e: int, m: int, d: int) -> int: + n = m // d + t = hpow(b, e, n) + i = pow(b, totient(n) - 1, n) + u = (t * i) % n + return (b * u) % m + + +def hpow(b: int, e: int, m: int) -> int: + if m == 1: + return 0 + + if e == 1: + return b % m + + d = math.gcd(b, m) + if d == 1: + return _f(b, e, m) + + if d == m: + return 0 + + return _g(b, e, m, d) diff --git a/project_euler/common/modular_tetration_test.py b/project_euler/common/modular_tetration_test.py new file mode 100644 index 00000000..dc91ae11 --- /dev/null +++ b/project_euler/common/modular_tetration_test.py @@ -0,0 +1,10 @@ +from project_euler.common.modular_tetration import hpow + + +def test_modular_tetration(): + assert hpow(3, 1, 2) == 3**1 % 2 + assert hpow(3, 2, 20) == 3**3 % 20 + assert hpow(3, 3, 345) == 312 + assert hpow(5, 2, 7) == 5**5 % 7 + assert hpow(7, 4, 13) == 6 + assert hpow(10, 2, 6) == 10**10 % 6 diff --git a/project_euler/common/order.py b/project_euler/common/order.py new file mode 100644 index 00000000..ac33541d --- /dev/null +++ b/project_euler/common/order.py @@ -0,0 +1,19 @@ +from functools import cache +import math +from project_euler.common.divisors import divisors +from project_euler.common.totient import totient + + +@cache +def ord(b: int, m: int) -> int: + if math.gcd(b, m) != 1: + raise ValueError("b and m must be coprime") + + phi = totient(m) + ds = divisors(phi) + + for d in ds: + if pow(b, d, m) == 1: + return d + + raise ValueError("b and m must be coprime") diff --git a/project_euler/common/order_test.py b/project_euler/common/order_test.py new file mode 100644 index 00000000..b22f7919 --- /dev/null +++ b/project_euler/common/order_test.py @@ -0,0 +1,10 @@ +from project_euler.common.order import ord + + +def test_ord(): + assert ord(4, 7) == 3 + assert ord(10, 7) == 6 + assert ord(5, 3) == 2 + assert ord(13, 7) == 2 + assert ord(3, 20) == 4 + assert ord(3, 115) == 44 diff --git a/project_euler/common/prime_factors.py b/project_euler/common/prime_factors.py new file mode 100644 index 00000000..cc0140cb --- /dev/null +++ b/project_euler/common/prime_factors.py @@ -0,0 +1,10 @@ +from functools import cache +from sympy import isprime +from project_euler.common.divisors import divisors + + +@cache +def prime_factors(n: int) -> list[int]: + ds = divisors(n) + ps = [d for d in ds if d > 1 and isprime(d)] + return ps diff --git a/project_euler/common/prime_factors_test.py b/project_euler/common/prime_factors_test.py new file mode 100644 index 00000000..31ebe263 --- /dev/null +++ b/project_euler/common/prime_factors_test.py @@ -0,0 +1,10 @@ +from project_euler.common.prime_factors import prime_factors + + +def test_prime_factors(): + assert prime_factors(1) == [] + assert prime_factors(2) == [2] + assert prime_factors(27) == [3] + assert prime_factors(2015) == [5, 13, 31] + assert prime_factors(2310) == [2, 3, 5, 7, 11] + assert prime_factors(103243) == [7, 43] diff --git a/project_euler/common/totient.py b/project_euler/common/totient.py new file mode 100644 index 00000000..54bcc508 --- /dev/null +++ b/project_euler/common/totient.py @@ -0,0 +1,13 @@ +from functools import cache, reduce +import math +from project_euler.common.prime_factors import prime_factors + + +@cache +def totient(n: int) -> int: + if n == 1: + return 0 + + ps = prime_factors(n) + phi = reduce(lambda acc, p: acc * (1 - 1 / p), ps, n) + return math.floor(phi) diff --git a/project_euler/common/totient_test.py b/project_euler/common/totient_test.py new file mode 100644 index 00000000..1a980512 --- /dev/null +++ b/project_euler/common/totient_test.py @@ -0,0 +1,8 @@ +from project_euler.common.totient import totient + + +def test_totient(): + assert totient(1) == 0 + assert totient(7) == 6 + assert totient(15) == 8 + assert totient(2015) == 1440 diff --git a/data/107.txt b/project_euler/data/107.txt similarity index 100% rename from data/107.txt rename to project_euler/data/107.txt diff --git a/data/11.txt b/project_euler/data/11.txt similarity index 100% rename from data/11.txt rename to project_euler/data/11.txt diff --git a/data/13.txt b/project_euler/data/13.txt similarity index 100% rename from data/13.txt rename to project_euler/data/13.txt diff --git a/data/18.txt b/project_euler/data/18.txt similarity index 100% rename from data/18.txt rename to project_euler/data/18.txt diff --git a/data/22.txt b/project_euler/data/22.txt similarity index 100% rename from data/22.txt rename to project_euler/data/22.txt diff --git a/data/42.txt b/project_euler/data/42.txt similarity index 100% rename from data/42.txt rename to project_euler/data/42.txt diff --git a/data/67.txt b/project_euler/data/67.txt similarity index 100% rename from data/67.txt rename to project_euler/data/67.txt diff --git a/data/8.txt b/project_euler/data/8.txt similarity index 100% rename from data/8.txt rename to project_euler/data/8.txt diff --git a/data/primes.txt b/project_euler/data/primes.txt similarity index 60% rename from data/primes.txt rename to project_euler/data/primes.txt index 25faeafb..c73c7894 100644 --- a/data/primes.txt +++ b/project_euler/data/primes.txt @@ -216813,4 +216813,131701 @@ 2999933 2999951 2999957 -2999999 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"^2.2.4" +python = "^3.13" +sympy = "^1.13.3" +toolz = "^1.0.0" + +[tool.poetry.group.dev.dependencies] +black = "^25.1.0" +isort = "^6.0.1" +pyright = "^1.1.397" +pytest = "^8.3.4" +ruff = "^0.9.10" + +[tool.black] +line-length = 120 + +[tool.isort] +profile = "black" +force_sort_within_sections = true +lines_between_sections = 0 +lines_after_imports = 2 + +[tool.ruff] +line-length = 120 +lint.ignore = ["E722"] + +[tool.pytest.ini_options] +python_files = "*.py" + +[build-system] +requires = ["poetry-core"] +build-backend = "poetry.core.masonry.api" diff --git a/script/clean.mjs b/script/clean.mjs deleted file mode 100644 index 984b1c90..00000000 --- a/script/clean.mjs +++ /dev/null @@ -1,4 +0,0 @@ -import fse from 'fs-extra'; - -fse.emptyDirSync('build'); -fse.emptyDirSync('dist'); diff --git a/script/primes.mjs b/script/primes.mjs deleted file mode 100644 index b3169462..00000000 --- a/script/primes.mjs +++ /dev/null @@ -1,30 +0,0 @@ -import fs from 'fs'; -import path from 'path'; -import process from 'process'; - -// Implements of the Sieve of Eratosthenes algorithm up to a given limit. -// -// @remarks -// Writes the primes to a file for use in other problems. -// -// See {@link https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes}. -function sieve(n) { - const primes = new Array(n + 1).fill(true); - primes[0] = primes[1] = false; - - for (let i = 2; i * i <= n; i++) { - if (primes[i]) { - for (let j = i * i; j <= n; j += i) { - primes[j] = false; - } - } - } - - return primes.map((isPrime, i) => (isPrime ? i : -1)).filter(i => i !== -1); -} - -const limit = Number.parseInt(process.argv[2], 10 /* radix */); -const output = path.join('data', 'primes.txt'); -const primes = sieve(limit); - -fs.writeFileSync(output, primes.join('\n')); diff --git a/scripts.py b/scripts.py new file mode 100644 index 00000000..c4e92170 --- /dev/null +++ b/scripts.py @@ -0,0 +1,25 @@ +import subprocess + + +def run_cmd(cmd): + subprocess.run(cmd, shell=True, check=True) + + +def run_all(): + run_format() + run_lint() + run_tests() + + +def run_lint(): + run_cmd("poetry run ruff check --fix project_euler") + run_cmd("poetry run pyright project_euler") + + +def run_format(): + run_cmd("poetry run black project_euler") + run_cmd("poetry run isort project_euler") + + +def run_tests(): + run_cmd("poetry run pytest project_euler") diff --git a/src/1.ts b/src/1.ts deleted file mode 100644 index fb48de0a..00000000 --- a/src/1.ts +++ /dev/null @@ -1,10 +0,0 @@ -import _ from 'lodash'; - -// Computes the sum of all the multiples of 3 or 5 below the given limit. -// -// See {@link https://projecteuler.net/problem=1}. -export default function compute(limit: number) { - return _.range(limit) - .filter(n => n % 3 === 0 || n % 5 === 0) - .reduce((a, b) => a + b, 0); -} diff --git a/src/10.ts b/src/10.ts deleted file mode 100644 index 311291b5..00000000 --- a/src/10.ts +++ /dev/null @@ -1,10 +0,0 @@ -import primes from './core/primes'; - -// Computes the sum of all the prime numbers below the given limit. -// -// See {@link https://projecteuler.net/problem=10}. -export default function compute(limit: number) { - return primes() - .filter(p => p < limit) - .reduce((a, b) => a + b, 0); -} diff --git a/src/107.ts b/src/107.ts deleted file mode 100644 index 695975eb..00000000 --- a/src/107.ts +++ /dev/null @@ -1,137 +0,0 @@ -import _ from 'lodash'; -import slurp from './core/slurp'; - -type Graph = number[][]; -type Edge = [number, number]; - -// Computes the maximum savings that can be achieved by removing redundant edges from a network graph. -// -// @remarks -// Uses Prim's algorithm to construct a minimum spanning tree. -// -// See {@link https://en.wikipedia.org/wiki/Prim%27s_algorithm}. -// See {@link https://projecteuler.net/problem=107}. -export default function compute() { - const graph = parse(); - - // This is the total cost of the network, computed by summing all edge weights. - const weight1 = getWeightOfAllEdges(graph); - - // This is a set of edges that form a minimum spanning tree of the network. - const edges = getMinimumSpanningTree(graph); - - // This is the total cost of the minimum spanning tree. - const weight2 = getWeightOfEdges(graph, edges); // Calculate MST cost - - // The delta between the total weight and the MST weight is our savings. - return Math.floor(weight1 - weight2); -} - -function parse(): Graph { - return slurp('107.txt') - .trim() - .split('\n') - .map(line => { - return line.split(',').map(value => (value === '-' ? Infinity : _.toNumber(value))); - }); -} - -function getWeightOfAllEdges(graph: Graph) { - let total = 0; - - for (const row of graph) { - total += row.reduce((sum, value) => { - if (value === Infinity) { - return sum; - } - - return sum + value; - }, 0); - } - - return total / 2; -} - -function getWeightOfEdges(graph: Graph, edges: Set): number { - let total = 0; - - for (const edge of edges) { - total += getWeight(graph, edge); - } - - return total; -} - -function getWeight(graph: Graph, edge: Edge) { - const [u, v] = edge; - return graph[u][v]; -} - -function getNeighbors(graph: Graph, u: number) { - const n = graph.length; - const result = new Set(); - - for (let v = 0; v < n; v++) { - if (graph[u][v] !== Infinity) { - result.add(v); - } - } - - return result; -} - -function getFrontierNodes(graph: Graph, nodes: Set): Set { - const edges = new Set(); - - for (const u of nodes) { - for (const v of getNeighbors(graph, u)) { - if (!nodes.has(v)) { - edges.add([u, v]); - } - } - } - - return edges; -} - -function getCheapestEdge(graph: Graph, vertices: Set, excluded: Set): Edge { - let minEdge: Edge = [-1, -1]; - let minCost = Infinity; - - for (const edge of getFrontierNodes(graph, vertices)) { - const [u, v] = edge; - const key = `${u}-${v}`; - - if (!excluded.has(key)) { - const edgeCost = getWeight(graph, edge); - if (edgeCost < minCost) { - minCost = edgeCost; - minEdge = edge; - } - } - } - - return minEdge; -} - -function getMinimumSpanningTree(graph: Graph): Set { - const nodes = new Set([0]); - const mst = new Set(); - const excluded = new Set(); - - while (nodes.size < graph.length) { - const edge = getCheapestEdge(graph, nodes, excluded); - if (edge[0] === -1) { - break; - } - - nodes.add(edge[0]); - nodes.add(edge[1]); - mst.add(edge); - - excluded.add(`${edge[0]}-${edge[1]}`); - excluded.add(`${edge[1]}-${edge[0]}`); - } - - return mst; -} diff --git a/src/11.ts b/src/11.ts deleted file mode 100644 index b1034792..00000000 --- a/src/11.ts +++ /dev/null @@ -1,65 +0,0 @@ -import _ from 'lodash'; -import slurp from './core/slurp'; - -// Computes the greatest product of 4 adjacent numbers in the same direction in the grid defined by `11.txt`. -// -// See {@link https://projecteuler.net/problem=11}. -export default function compute() { - const m = slurp('11.txt') - .trim() - .split('\n') - .map(line => { - return line - .split(' ') - .map(s => s.trim()) - .map(_.toNumber); - }); - - const rows = m.length; - const columns = m[0].length; - let result = 0; - for (let i = 0; i < rows; i++) { - for (let j = 0; j < columns; j++) { - result = Math.max( - result, - product(m, i, j, Direction.UP), - product(m, i, j, Direction.RIGHT), - product(m, i, j, Direction.UP_RIGHT), - product(m, i, j, Direction.DOWN_RIGHT) - ); - } - } - - return result; -} - -const Direction = { - UP: [-1, 0], - RIGHT: [0, 1], - UP_RIGHT: [-1, 1], - DOWN_RIGHT: [1, 1] -} as const; - -// Safely compute the product of the four elements in the matrix starting at position (i, j) and moving in the direction -// indicated by (di, dj). -// -// @remarks -// If the product is NaN or if we get an out-of-bounds error, we return 0. -function product(m: number[][], i: number, j: number, direction: readonly [number, number]): number { - try { - const [di, dj] = direction; - let p = 1; - - for (let k = 0; k < 4; k++) { - p *= m[i + k * di][j + k * dj]; - } - - if (Number.isNaN(p)) { - return 0; - } - - return p; - } catch { - return 0; - } -} diff --git a/src/12.ts b/src/12.ts deleted file mode 100644 index 4174c2fa..00000000 --- a/src/12.ts +++ /dev/null @@ -1,16 +0,0 @@ -import tau from './core/tau'; - -// Computes the value of the first triangle number to have over the given number of divisors. -// -// See {@link https://projecteuler.net/problem=12}. -export default function compute(limit: number): number { - let n = 0; - let i = 1; - - while (tau(n) <= limit) { - n += i; - i += 1; - } - - return n; -} diff --git a/src/120.ts b/src/120.ts deleted file mode 100644 index 70293194..00000000 --- a/src/120.ts +++ /dev/null @@ -1,29 +0,0 @@ -import _ from 'lodash'; - -// Computes the sum of the maximum remainders of (a - 1)^n + (a + 1)^n for 3 ≤ a ≤ 1000. -// -// See {@link https://projecteuler.net/problem=120}. -export default function compute(): number { - return _.range(3, 1001) - .map(f) - .reduce((a, b) => a + b, 0); -} - -function f(a: number) { - function g(n: number) { - if (n === 1) { - return 2 * a; - } - - if (n % 2 === 0) { - return 2; - } - - return 2 * n * a; - } - - return _.range(1, 2 * a + 1) - .map(g) - .map(n => n % (a * a)) - .reduce((a, b) => Math.max(a, b), 0); -} diff --git a/src/123.ts b/src/123.ts deleted file mode 100644 index a55a54be..00000000 --- a/src/123.ts +++ /dev/null @@ -1,31 +0,0 @@ -import primes from './core/primes'; - -// Finds the least value of n for which the remainder described in the problem first exceeds 1e10. -// -// See {@link https://projecteuler.net/problem=123}. -export default function compute(limit: number) { - return find(primes(), limit); -} - -function r(p: number, n: number) { - if (n % 2 === 0) { - return 2; - } - - return p * n * 2; -} - -function find(ps: number[], limit: number): number { - let n = 1; - - for (let i = 0; i < ps.length; i++) { - const p = ps[i]; - if (r(p, n) >= limit) { - return n; - } - - n++; - } - - throw new Error('not enough primes'); -} diff --git a/src/13.ts b/src/13.ts deleted file mode 100644 index 8bf39c7f..00000000 --- a/src/13.ts +++ /dev/null @@ -1,12 +0,0 @@ -import _ from 'lodash'; -import slurp from './core/slurp'; - -// Compute the first ten digits of the sum of the one-hundred 50-digit numbers defined by `13.txt`. -// -// See {@link https://projecteuler.net/problem=13}. -export default function compute() { - const numbers = slurp('13.txt').split('\n').map(BigInt); - const sum = numbers.reduce((a, b) => a + b, 0n); - const text = sum.toString().slice(0, 10); - return _.toNumber(text); -} diff --git a/src/14.ts b/src/14.ts deleted file mode 100644 index 71ea55a4..00000000 --- a/src/14.ts +++ /dev/null @@ -1,35 +0,0 @@ -// Computes the number that produces the longest Collatz chain under a given limit. -// -// See {@link https://projecteuler.net/problem=14}. -export default function compute(limit: number) { - let max = 0; - let result = 0; - - for (let i = 1; i < limit; i++) { - const current = collatzLength(i); - if (current > max) { - max = current; - result = i; - } - } - - return result; -} - -const memo = new Map(); - -function collatzLength(n: number): number { - if (n === 1) { - return 0; - } - - if (memo.has(n)) { - return memo.get(n)!; - } - - const next = n % 2 === 0 ? n / 2 : 3 * n + 1; - const result = 1 + collatzLength(next); - - memo.set(n, result); - return result; -} diff --git a/src/15.ts b/src/15.ts deleted file mode 100644 index 89b6cbb0..00000000 --- a/src/15.ts +++ /dev/null @@ -1,22 +0,0 @@ -import factorial from './core/factorial'; - -// Computes the number of routes from the upper left to the bottom right of a lattice grid. -// -// @remarks -// It's not necessary to actually generate the routes; we can count them directly. Starting at the upper left, one must -// move down exactly 20 times, and right exactly 20 times in order to reach the bottom right. Represent the downward -// movement as a 'D' and the rightward movement as an 'R', then the number of routes to the bottom right is equal to the -// number of permutations of a 'word' with 20 D's and 20 R's. -// -// This can be viewed as a multiset permutation whose cardinality is the -// multinomial coefficient. -// -// See {@link https://en.wikipedia.org/wiki/Permutation#Permutations_of_multisets}. -// See {@link https://projecteuler.net/problem=15}. -export default function compute() { - const k = factorial(20); - const n = factorial(20 + 20); - const d = k * k; - - return n / d; -} diff --git a/src/16.ts b/src/16.ts deleted file mode 100644 index 05f2ac62..00000000 --- a/src/16.ts +++ /dev/null @@ -1,9 +0,0 @@ -import _ from 'lodash'; - -// Computes the sum of the digits of the given number raised to the given power. -// -// See {@link https://projecteuler.net/problem=16}. -export default function compute(k: number, e: number) { - const s = BigInt(Math.pow(k, e)).toString(); - return s.split('').reduce((a, b) => a + _.toNumber(b), 0); -} diff --git a/src/17.ts b/src/17.ts deleted file mode 100644 index e7e289bf..00000000 --- a/src/17.ts +++ /dev/null @@ -1,59 +0,0 @@ -// Compute the number of letters used to write out the numbers from 1 to 1000. -// -// See {@link https://projecteuler.net/problem=17}. -export default function compute() { - const map = new Map([ - [1, 'one'], - [2, 'two'], - [3, 'three'], - [4, 'four'], - [5, 'five'], - [6, 'six'], - [7, 'seven'], - [8, 'eight'], - [9, 'nine'], - [10, 'ten'], - [11, 'eleven'], - [12, 'twelve'], - [13, 'thirteen'], - [14, 'fourteen'], - [15, 'fifteen'], - [16, 'sixteen'], - [17, 'seventeen'], - [18, 'eighteen'], - [19, 'nineteen'], - [20, 'twenty'], - [30, 'thirty'], - [40, 'forty'], - [50, 'fifty'], - [60, 'sixty'], - [70, 'seventy'], - [80, 'eighty'], - [90, 'ninety'] - ]); - - function say(n: number): string { - if (n === 1000) { - return 'one thousand'; - } else if (n >= 100 && n % 100 !== 0) { - const key = Math.floor(n / 100); - return `${map.get(key)} hundred and ${say(n % 100)}`; - } else if (n >= 100) { - const key = Math.floor(n / 100); - return `${map.get(key)} hundred`; - } else if (n >= 20 && n % 10 !== 0) { - const key = n - (n % 10); - return `${map.get(key)} ${say(n % 10)}`; - } else if (n >= 20) { - return map.get(n)!; - } else { - return map.get(n)!; - } - } - - let sum = 0; - for (let i = 1; i <= 1000; i++) { - sum += say(i).replace(/\s+/g, '').length; - } - return sum; -} diff --git a/src/18.ts b/src/18.ts deleted file mode 100644 index 315b388d..00000000 --- a/src/18.ts +++ /dev/null @@ -1,57 +0,0 @@ -// Compute the maximum total from top to bottom of the triangle below. -// -// @remarks -// -// Rather than calculating the path sums going down, look at the bottom row and -// the row above it. -// -// For example, assume that the tree has height 4 and that these are the last 2 -// rows: -// -// 17 47 82 -// 18 35 87 10 -// -// At 17, you will never take the left path containing 18, because 35 + 17 is -// greater. At 47, you will never take the left path for 35, because 47 + 87 is -// greater, and so on. -// -// Therefore, these last 2 rows can be reduced to a single row once the optimal -// path is taken: -// -// 52 134 169 -// -// Once this reduction is done, compare this newly constructed row to the one -// above it and perform the same reduction until only one row remains with one -// value. -// -// See {@link https://projecteuler.net/problem=18}. -export default function compute() { - const input = ` - 75 - 95 64 - 17 47 82 - 18 35 87 10 - 20 04 82 47 65 - 19 01 23 75 03 34 - 88 02 77 73 07 63 67 - 99 65 04 28 06 16 70 92 - 41 41 26 56 83 40 80 70 33 - 41 48 72 33 47 32 37 16 94 29 - 53 71 44 65 25 43 91 52 97 51 14 - 70 11 33 28 77 73 17 78 39 68 17 57 - 91 71 52 38 17 14 91 43 58 50 27 29 48 - 63 66 04 68 89 53 67 30 73 16 69 87 40 31 - 04 62 98 27 23 09 70 98 73 93 38 53 60 04 23`; - const triangle = input - .trim() - .split('\n') - .map(row => row.trim().split(' ').map(Number)); - - for (let i = triangle.length - 2; i >= 0; i--) { - for (let j = 0; j < triangle[i].length; j++) { - triangle[i][j] += Math.max(triangle[i + 1][j], triangle[i + 1][j + 1]); - } - } - - return triangle[0][0]; -} diff --git a/src/188.ts b/src/188.ts deleted file mode 100644 index 0ec66f9f..00000000 --- a/src/188.ts +++ /dev/null @@ -1,5 +0,0 @@ -import mtetn from './core/modular-tetration'; - -export default function compute() { - return mtetn(1777, 1855, 1e8); -} diff --git a/src/19.ts b/src/19.ts deleted file mode 100644 index 5630315d..00000000 --- a/src/19.ts +++ /dev/null @@ -1,35 +0,0 @@ -// Compute the number of Sundays that fell on the first of the month during the twentieth century (1 Jan 1901 to -// 31 Dec 2000). -// -// See {@link https://projecteuler.net/problem=19}. -export default function compute() { - // Days per month, considering February as 28 days. - const daysPerMonth = [31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31]; - - // Computes days in a month, taking into account leap years. - function daysInMonth(month: number, year: number): number { - let days = daysPerMonth[month]; - if (month === 1 && year % 4 === 0 && (year % 100 !== 0 || year % 400 === 0)) { - days += 1; - } - - return days; - } - - // Start on 1 Jan 1901, a Tuesday (day 2). - let days = 2; - - // Compute the number of Sundays on the first of the month from 1901 to 2000. - let result = 0; - for (let year = 1901; year <= 2000; year++) { - for (let month = 0; month < 12; month++) { - if (days % 7 === 0) { - result += 1; - } - - days += daysInMonth(month, year); - } - } - - return result; -} diff --git a/src/2.ts b/src/2.ts deleted file mode 100644 index e3592af8..00000000 --- a/src/2.ts +++ /dev/null @@ -1,10 +0,0 @@ -import fibs from './core/fibs'; - -// Computes the sum of all the even Fibonacci numbers below the given limit. -// -// See {@link https://projecteuler.net/problem=2}. -export default function compute(limit: number) { - return fibs(limit) - .filter(n => n % 2 === 0) - .reduce((a, b) => a + b, 0); -} diff --git a/src/20.ts b/src/20.ts deleted file mode 100644 index f6af5284..00000000 --- a/src/20.ts +++ /dev/null @@ -1,16 +0,0 @@ -import _ from 'lodash'; -import factorial from './core/factorial'; - -// Computes the sum of the digits of the factorial of a given number. -// -// See {@link https://projecteuler.net/problem=20}. -export default function compute(limit: number) { - const text = _.toString(factorial(limit)); - - let sum = 0; - for (let i = 0; i < text.length; i++) { - sum += _.toNumber(text[i]); - } - - return sum; -} diff --git a/src/21.ts b/src/21.ts deleted file mode 100644 index 6b496611..00000000 --- a/src/21.ts +++ /dev/null @@ -1,18 +0,0 @@ -import _ from 'lodash'; -import sigma from './core/sigma'; - -// Computes the sum of all amicable numbers under `limit`. -// -// See {@link https://projecteuler.net/problem=21} -export default function compute(limit: number) { - let sum = 0; - - for (const a of _.range(2, limit + 1)) { - const b = sigma(a) - a; - if (a > b && sigma(b) - b === a) { - sum += a + b; - } - } - - return sum; -} diff --git a/src/22.ts b/src/22.ts deleted file mode 100644 index 5c6aea12..00000000 --- a/src/22.ts +++ /dev/null @@ -1,36 +0,0 @@ -// Computes name scores based on the names in the text file. -// -// See {@link https://projecteuler.net/problem=22} -import _ from 'lodash'; -import slurp from './core/slurp'; - -function getNames() { - return slurp('22.txt') - .split(',') - .map(line => line.slice(1, -1)) - .sort((a, b) => a.localeCompare(b)); -} - -function getScores() { - const codes = _.range('A'.charCodeAt(0), 'Z'.charCodeAt(0) + 1).map(c => String.fromCharCode(c)); - const values = _.range(1, 27); - return new Map(_.zip(codes, values) as [[string, number]]); -} - -function getScore(name: string, scores: Map) { - return name.split('').reduce((a, b) => a + scores.get(b)!, 0); -} - -export default function compute() { - const scores = getScores(); - const names = getNames(); - - let result = 0; - for (let i = 0; i < names.length; i++) { - const name = names[i]; - const score = getScore(name, scores); - result += (i + 1) * score; - } - - return result; -} diff --git a/src/23.ts b/src/23.ts deleted file mode 100644 index 7db3f51a..00000000 --- a/src/23.ts +++ /dev/null @@ -1,23 +0,0 @@ -import _ from 'lodash'; -import sigma from './core/sigma'; - -// Computes the sum of all the positive integers which cannot be written as the sum of two abundant numbers. -// -// See {@link https://projecteuler.net/problem=23} -export default function compute(limit: number) { - const abundants = _.range(1, limit + 1).filter(n => sigma(n) - n > n); - const numbers = _.range(0, limit + 1); - - for (let i = 0; i < abundants.length; i++) { - for (let j = i; j < abundants.length; j++) { - const sum = abundants[i] + abundants[j]; - if (sum <= limit) { - numbers[sum] = 0; - } else { - break; - } - } - } - - return numbers.reduce((a, b) => a + b, 0); -} diff --git a/src/24.rkt b/src/24.rkt deleted file mode 100644 index 329c6b34..00000000 --- a/src/24.rkt +++ /dev/null @@ -1,20 +0,0 @@ -#lang racket -(require rackunit) - - -(define (list->number lst) - ((compose string->number - (curry apply string-append) - (curry map number->string)) - lst)) - -(define result - ((compose (curryr vector-ref (sub1 1000000)) - list->vector - (curryr sort <) - (curry map list->number) - permutations) - (range 10))) - -(displayln result) -(check-equal? result 2783915460) diff --git a/src/25.rkt b/src/25.rkt deleted file mode 100644 index 48bb7f53..00000000 --- a/src/25.rkt +++ /dev/null @@ -1,14 +0,0 @@ -#lang racket -(require rackunit) -(require "lib/core.rkt") -(require "lib/number-theory.rkt") - - -(define result - (for/last ((i (in-naturals)) - (n fibs) - #:break (>= (count-digits n) 1000)) - (add1 i))) - -(displayln result) -(check-equal? result 4782) diff --git a/src/26.rkt b/src/26.rkt deleted file mode 100644 index 085ab622..00000000 --- a/src/26.rkt +++ /dev/null @@ -1,23 +0,0 @@ -#lang racket -(require (only-in rackunit check-equal?)) -(require (only-in "lib/number-theory.rkt" divides? ord)) - - -(define numbers - (filter (lambda (n) (and (not (divides? 2 n)) (not (divides? 5 n)))) - (range 999 1 -1))) - -(define (max-period best numbers) - (if (empty? numbers) - best - (let* ((n (first numbers)) - (t (ord 10 n))) - (cond ((= t (sub1 n)) (cons n t)) - ((> t (cdr best)) (max-period (cons n t) (rest numbers))) - (else (max-period best (rest numbers))))))) - -(define result - (car (max-period (cons 0 0) numbers))) - -(displayln result) -(check-equal? result 983) diff --git a/src/27.rkt b/src/27.rkt deleted file mode 100644 index 2f49d0a5..00000000 --- a/src/27.rkt +++ /dev/null @@ -1,27 +0,0 @@ -#lang racket -(require rackunit) -(require "lib/core.rkt") -(require "lib/number-theory.rkt") - - -(define ps - (filter prime? (range 1000))) - -(define (f n a b) - (+ (* n n) (* a n) b)) - -(define (primes-count a b) - (length (takef (range b) (compose prime? (curryr f a b))))) - -(define m - (for*/hash ((b (append ps (map (curry * -1) ps))) - (a (range -1000 1001))) - (let ((c (primes-count a b))) - (values c (cons a b))))) - -(define result - (let ((v (hash-ref m (apply max (hash-keys m))))) - (* (car v) (cdr v)))) - -(displayln result) -(check-equal? result -59231) diff --git a/src/28.rkt b/src/28.rkt deleted file mode 100644 index 67c31b32..00000000 --- a/src/28.rkt +++ /dev/null @@ -1,48 +0,0 @@ -#lang racket -(require rackunit) -(require "lib/2darray.rkt") - - -(define (turn heading) - (match heading - ('right 'down) - ('down 'left) - ('left 'up) - ('up 'right))) - -(define (next i j heading) - (match heading - ('right (cons (add1 i) j)) - ('down (cons i (sub1 j))) - ('left (cons (sub1 i) j)) - ('up (cons i (add1 j))))) - -(define (make-spiral n) - (define (loop m p heading n) - (let ((i (car p)) - (j (cdr p))) - (when (2darray-in-bounds? m i j) - (let* ((heading* (turn heading)) - (p* (next i j heading*)) - (i* (car p*)) - (j* (cdr p*))) - (2darray-set! m i j n) - (if (= (2darray-ref m i* j*) 0) - (loop m p* heading* (add1 n)) - (loop m (next i j heading) heading (add1 n))))))) - (let ((m (make-2darray n n))) - (loop m (cons (quotient n 2) (quotient n 2)) 'up 1) - m)) - -(define limit 1001) - -(define spiral (make-spiral limit)) - -(define result - (sub1 - (for*/sum ((i (in-range limit))) - (+ (2darray-ref spiral i i) - (2darray-ref spiral i (- (2darray-num-cols spiral) i 1)))))) - -(displayln result) -(check-equal? result 669171001) diff --git a/src/29.rkt b/src/29.rkt deleted file mode 100644 index b8a7043f..00000000 --- a/src/29.rkt +++ /dev/null @@ -1,13 +0,0 @@ -#lang racket -(require rackunit) -(require "lib/set.rkt") - - -(define result - (set-length - (for*/set ((a (in-range 2 101)) - (b (in-range 2 101))) - (expt a b)))) - -(displayln result) -(check-equal? result 9183) diff --git a/src/3.ts b/src/3.ts deleted file mode 100644 index ab9dc53a..00000000 --- a/src/3.ts +++ /dev/null @@ -1,8 +0,0 @@ -import primeFactors from './core/prime-factors'; - -// Computes the largest prime factor of a given number. -// -// See {@link https://projecteuler.net/problem=3}. -export default function compute(n: number) { - return Math.max(...primeFactors(n)); -} diff --git a/src/30.rkt b/src/30.rkt deleted file mode 100644 index 53a1f8b0..00000000 --- a/src/30.rkt +++ /dev/null @@ -1,23 +0,0 @@ -#lang racket -(require rackunit) -(require srfi/41) -(require "lib/core.rkt") - - -(define (digital-sum-5 n) - (for/sum ((c (string->list (number->string n)))) - (expt (char->integer* c) 5))) - -(define limit - (let* ((x (expt 9 5)) - (s (stream-take-while (lambda (n) (<= (expt 10 (sub1 n)) x)) - (stream-from 0)))) - (* (stream-length s) x))) - -(define result - (for/sum ((i (range 10 limit)) - #:when (= i (digital-sum-5 i))) - i)) - -(displayln result) -(check-equal? result 443839) diff --git a/src/31.rkt b/src/31.rkt deleted file mode 100644 index 6d77ed46..00000000 --- a/src/31.rkt +++ /dev/null @@ -1,43 +0,0 @@ -#lang racket -(require rackunit) -(require (for-syntax racket/function)) -(require (for-syntax racket/syntax)) - - -(begin-for-syntax - (define (make-id stx id-fragment) - ((compose (curry datum->syntax stx) - string->symbol - (curry format "p~a") - syntax->datum) id-fragment))) - -(define-syntax (define-p stx) - (syntax-case stx () - ((_ x y) - (with-syntax ((px (make-id stx #'x)) - (py (make-id stx #'y))) - #'(define (px n) - (if (>= n 0) - (+ (px (- n x)) (py n)) - 0)))))) - -(define (p1 n) 1) - -(define-p 2 1) - -(define-p 5 2) - -(define-p 10 5) - -(define-p 20 10) - -(define-p 50 20) - -(define-p 100 50) - -(define-p 200 100) - -(define result (p200 200)) - -(displayln result) -(check-equal? result 73682) diff --git a/src/32.rkt b/src/32.rkt deleted file mode 100644 index 206cac0d..00000000 --- a/src/32.rkt +++ /dev/null @@ -1,43 +0,0 @@ -#lang racket -(require rackunit) -(require "lib/core.rkt") - - -(define pandigital-products (make-hash)) - -(define (pandigital-product-values n i j) - (let*-values (((lst) (integer->char-list n)) - ((a rst) (split-at lst i)) - ((b c) (split-at rst j)) - ((a*) (char-list->integer a)) - ((b*) (char-list->integer b)) - ((c*) (char-list->integer c))) - (list a* b* c*))) - -(define (check-pandigital-product a b c) - ; If abc forms a pandigital product, then bac forms one as well. - (let ((p1 (list->integer (list a b c))) - (p2 (list->integer (list b a c)))) - (when (and (not (hash-has-key? pandigital-products p1)) - (= c (* a b))) - (hash-set! pandigital-products p1 c) - (hash-set! pandigital-products p2 c)))) - -(define result 0) - -(begin - (for ((p (permutations (range 1 10)))) - (let ((n (list->integer p))) - ; Check for products formed by a * bcde = fghi or abcd * e = fghi. - (apply check-pandigital-product (pandigital-product-values n 1 4)) - ; Check for products formed by ab * cde = fghi or abc * de = fghi. - ; It's impossible to have a product with 5 digits because: - ; (* 9 876) and (* 98 76) don't have 5 digits, but those are the max - ; products you can get with the 4 remaining digits. - (apply check-pandigital-product (pandigital-product-values n 2 3)))) - (set! result - (for/sum ((i (distinct (hash-values pandigital-products)))) - i))) - -(displayln result) -(check-equal? result 45228) diff --git a/src/33.rkt b/src/33.rkt deleted file mode 100644 index a08f5676..00000000 --- a/src/33.rkt +++ /dev/null @@ -1,41 +0,0 @@ -#lang racket -(require rackunit) -(require "lib/core.rkt") - - -(define (denominators n) - (define (denominators* digit start) - (flatten - (for/list ((i (in-range start 10))) - (list (list->integer (list i digit)) - (list->integer (list digit i)))))) - (let* ((lst (integer->list n)) - (a (car lst)) - (b (cadr lst))) - (filter (curryr > n) - (distinct (append (denominators* a a) (denominators* b a)))))) - -(define (cancellable? m n) - (let* ((m* (integer->list m)) - (n* (integer->list n)) - (v (/ m n)) - (a (car m*)) - (b (cadr m*)) - (c (car n*)) - (d (cadr n*))) - (cond ((ormap zero? (list a b c d)) #f) - ((= a c) (= v (/ b d))) - ((= a d) (= v (/ b c))) - ((= b c) (= v (/ a d))) - ((= b d) (= v (/ a c))) - (else #f)))) - -(define result - (denominator - (for*/product ((m (range 11 99)) - (n (denominators m)) - #:when (cancellable? m n)) - (/ m n)))) - -(displayln result) -(check-equal? result 100) diff --git a/src/34.rkt b/src/34.rkt deleted file mode 100644 index d7f6edea..00000000 --- a/src/34.rkt +++ /dev/null @@ -1,26 +0,0 @@ -#lang racket -(require rackunit) -(require "lib/core.rkt") -(require "lib/number-theory.rkt") - - -(define limit (for/sum ((i (in-range 1 10))) - (log10 i))) - -(define max-digits - (letrec ((loop (lambda (d) - (if (< (- d 1 (log10 d)) limit) - (loop (add1 d)) - (sub1 d))))) - (loop 1))) - -(define max-factorion - (* (factorial 9) max-digits)) - -(define result - (for/sum ((n (range 3 (add1 max-factorion))) - #:when (factorion? n)) - n)) - -(displayln result) -(check-equal? result 40730) diff --git a/src/35.rkt b/src/35.rkt deleted file mode 100644 index fd19d6e8..00000000 --- a/src/35.rkt +++ /dev/null @@ -1,28 +0,0 @@ -#lang racket -(require rackunit) -(require "lib/core.rkt") -(require "lib/number-theory.rkt") - - -(define primes - (filter (curryr < 1000000) (file->list "/data/primes.txt"))) - -(define (rotate lst) - (append (cdr lst) (list (car lst)))) - -(define (rotations n) - (define (loop lst acc) - (let ((lst* (rotate lst)) - (acc* (if (empty? acc) (list lst) acc))) - (if (= (length lst*) (length acc*)) - acc* - (loop lst* (append acc* (list lst*)))))) - (map list->integer (loop (integer->list n) empty))) - -(define (circular? p) - (andmap prime? (rotations p))) - -(define result (length (filter circular? primes))) - -(displayln result) -(check-equal? result 55) diff --git a/src/36.rkt b/src/36.rkt deleted file mode 100644 index 69028a87..00000000 --- a/src/36.rkt +++ /dev/null @@ -1,18 +0,0 @@ -#lang racket -(require rackunit) - - -(define (palindrome? x) - (if (string? x) - (let ((lst (string->list x))) - (equal? lst (reverse lst))) - (and (palindrome? (number->string x 2)) - (palindrome? (number->string x 10))))) - -(define result - (for/sum ((n (in-range 1000000)) - #:when (palindrome? n)) - n)) - -(displayln result) -(check-equal? result 872187) diff --git a/src/37.rkt b/src/37.rkt deleted file mode 100644 index f63aa898..00000000 --- a/src/37.rkt +++ /dev/null @@ -1,41 +0,0 @@ -#lang racket -(require rackunit) -(require "lib/core.rkt") -(require "lib/string.rkt") -(require "lib/number-theory.rkt") - -(define primes - (filter (curryr < 1000000) (file->list "/data/primes.txt"))) - -(define limit 11) - -(define (truncate* n direction) - (let* ((s (number->string n)) - (k (if (symbol=? direction 'left) - (string-drop 1 s) - (string-take (sub1 (string-length s)) s)))) - (string->number k))) - -(define truncatable? - (case-lambda - ((n) (and (truncatable? n 'left) (truncatable? n 'right))) - ((n direction) (and (prime? n) - (or (< n 10) - (truncatable? (truncate* n direction) - direction)))))) - -(define find-primes - (case-lambda - ((ps) (find-primes ps '())) - ((ps ts) (let ((p (car ps))) - (cond ((< p limit) (find-primes (cdr ps) ts)) - ((= (length ts) limit) ts) - (else (if (truncatable? p) - (find-primes (cdr ps) (cons p ts)) - (find-primes (cdr ps) ts)))))))) - -(define result - (for/sum ((p (find-primes primes))) p)) - -(displayln result) -(check-equal? result 748317) diff --git a/src/38.rkt b/src/38.rkt deleted file mode 100644 index 54d26689..00000000 --- a/src/38.rkt +++ /dev/null @@ -1,33 +0,0 @@ -#lang racket -(require rackunit) -(require "lib/core.rkt") - -(define pandigitals - (list->set (map list->integer (permutations (range 1 10))))) - -(define (pandigital? n) - (set-member? pandigitals n)) - -(define (string-append* s n) - (string-append s (number->string n))) - -; Creates a 1 to 9 pandigital from consecutive digits starting from 2. -; The problem does not make it especially clear that the pandigital -; product must have exactly 9 digits and 'trivial' products like -; 1 * 987654321 are not permitted." -(define pandigital-product - (case-lambda - ((n) (pandigital-product n "" 1)) - ((n s i) (cond - ((= (string-length s) 9) (if (= i 1) "" s)) - ((> (string-length s) 9) "") - (else (pandigital-product n (string-append* s (* n i)) (add1 i))))))) - -(define result - (let* ((xs (range 1 99999)) - (ys (map (compose string->number pandigital-product) xs)) - (zs (filter pandigital? ys))) - (apply max zs))) - -(displayln result) -(check-equal? result 932718654) diff --git a/src/4.ts b/src/4.ts deleted file mode 100644 index f4fd8ac1..00000000 --- a/src/4.ts +++ /dev/null @@ -1,26 +0,0 @@ -import _ from 'lodash'; - -// Finds the largest palindrome made from the product of two 3-digit numbers. -// -// See {@link https://projecteuler.net/problem=4}. -export default function compute() { - let max = 0; - - // To speed up the search, we can limit the search space and search backwards. We want to find the largest - // palindrome, so we start with the largest numbers first. - for (let i = 999; i > 99; i--) { - for (let j = 999; j > 99; j--) { - const n = i * j; - if (isPalindrome(n) && n > max) { - max = n; - } - } - } - - return max; -} - -function isPalindrome(n: number) { - const s = _.toString(n); - return s === s.split('').reverse().join(''); -} diff --git a/src/40.ts b/src/40.ts deleted file mode 100644 index bc040785..00000000 --- a/src/40.ts +++ /dev/null @@ -1,31 +0,0 @@ -import _ from 'lodash'; - -// Computes the product of the digits of the 1st, 10th, 100th, 1000th, 10000th, 100000th, and 1000000th digits of the -// Champernowne constant. -// -// See {@link https://en.wikipedia.org/wiki/Champernowne_constant}. -// See {@link https://projecteuler.net/problem=40}. -export default function compute(): number { - const s = generateChampernowneConstant(); - - let result = 1; - for (let i = 1; i <= 1_000_000; i *= 10) { - const c = s.charAt(i - 1); - const j = _.toNumber(c); - result *= j; - } - - return result; -} - -function generateChampernowneConstant(): string { - let s = ''; - let num = 1; - - while (s.length < 1_000_000) { - s += num.toString(); - num++; - } - - return s; -} diff --git a/src/41.rkt b/src/41.rkt deleted file mode 100644 index abe02e31..00000000 --- a/src/41.rkt +++ /dev/null @@ -1,13 +0,0 @@ -#lang racket -(require rackunit) -(require "lib/core.rkt") -(require "lib/number-theory.rkt") - -(define xs - (map list->integer (permutations (range 1 8)))) - -(define result - (apply max (filter prime? xs))) - -(displayln result) -(check-equal? result 7652413) diff --git a/src/42.rkt b/src/42.rkt deleted file mode 100644 index 6d252ba0..00000000 --- a/src/42.rkt +++ /dev/null @@ -1,49 +0,0 @@ -#lang racket -(require rackunit) -(require srfi/1) -(require srfi/41) -(require "lib/core.rkt") - -(define charmap - (zipmap - (map integer->char (range (char->integer #\A) (add1 (char->integer #\Z)))) - (range 1 (add1 26)))) - -(define words - ((compose (curryr string-split ",") - (curryr string-replace "\"" "") - file->string) - "../data/42.txt")) - -(define (word-score w) - ((compose (curry apply +) - (curry map (curry hash-ref charmap)) - string->list) - w)) - -(define longest-word-length - (apply max (map string-length words))) - -(define largest-word-score - (* longest-word-length 26)) - -(define (triangle n) - (quotient (* n (add1 n)) 2)) - -(define triangles - (stream-map triangle (stream-from 0))) - -(define triangle-word-scores - ((compose list->set - stream->list - (curry stream-take-while (curryr <= largest-word-score))) - triangles)) - -(define (triangle? n) - (set-member? triangle-word-scores n)) - -(define result - (length (filter triangle? (map word-score words)))) - -(displayln result) -(check-equal? result 162) diff --git a/src/48.ts b/src/48.ts deleted file mode 100644 index 0156e6a4..00000000 --- a/src/48.ts +++ /dev/null @@ -1,14 +0,0 @@ -import _ from 'lodash'; -import mexpt from './core/modular-exponentiation-bigint'; - -// Computes the last ten digits of the series 1^1 + 2^2 + 3^3 + ... + 1000^1000. -// -// See {@link https://projecteuler.net/problem=48}. -export default function compute(): bigint { - // This modulus will give use the last 10 digits. - const mod = BigInt(10 ** 10); - return _.range(1, 1001) - .map(BigInt) - .map(b => mexpt(b, b, mod)) - .reduce((a, b) => (a + b) % mod, 0n); -} diff --git a/src/5.ts b/src/5.ts deleted file mode 100644 index 6acb2197..00000000 --- a/src/5.ts +++ /dev/null @@ -1,9 +0,0 @@ -import _ from 'lodash'; -import lcm from './core/lcm'; - -// Computes the smallest number that can be divided by each of the numbers from 1 to n without any remainder. -// -// See {@link https://projecteuler.net/problem=5}. -export default function compute(n: number) { - return _.range(1, n + 1).reduce(lcm, 1); -} diff --git a/src/52.ts b/src/52.ts deleted file mode 100644 index 8f6846f9..00000000 --- a/src/52.ts +++ /dev/null @@ -1,23 +0,0 @@ -// Computes the smallest positive integer x such that 2x, 3x, 4x, 5x, and 6x, contain the same digits. -// -// See {@link https://projecteuler.net/problem=52} -export default function compute() { - let x = 1; - - while (true) { - const s = sort(x); - const isValid = [2, 3, 4, 5, 6].every(m => { - return sort(x * m) === s; - }); - - if (isValid) { - return x; - } - - x++; - } -} - -function sort(x: number): string { - return x.toString().split('').sort().join(''); -} diff --git a/src/53.ts b/src/53.ts deleted file mode 100644 index aa41e3b6..00000000 --- a/src/53.ts +++ /dev/null @@ -1,20 +0,0 @@ -import _ from 'lodash'; -import combinations from './core/combinations'; - -// Computes the number distinct values of (n choose r) for 1 ≤ n ≤ limit that are greater than 1_000_000. -// -// See {@link https://projecteuler.net/problem=53}. -export default function compute(limit: number) { - let count = 0; - - for (const n of _.range(1, limit + 1)) { - for (const r of _.range(1, n - 1)) { - const c = combinations(n, r); - if (c > 1_000_000) { - count++; - } - } - } - - return count; -} diff --git a/src/6.ts b/src/6.ts deleted file mode 100644 index 2ba9a3d9..00000000 --- a/src/6.ts +++ /dev/null @@ -1,13 +0,0 @@ -import _ from 'lodash'; - -// Computes the difference between the sum of the squares of the first n natural numbers and the square of the sum of -// the first n natural numbers. -// -// See {@link https://projecteuler.net/problem=6}. -export default function compute(limit: number) { - const a = _.range(limit + 1) - .map(n => n ** 2) - .reduce((a, b) => a + b, 0); - const b = _.range(limit + 1).reduce((a, b) => a + b, 0) ** 2; - return b - a; -} diff --git a/src/67.ts b/src/67.ts deleted file mode 100644 index 39de4c06..00000000 --- a/src/67.ts +++ /dev/null @@ -1,19 +0,0 @@ -import slurp from './core/slurp'; - -// Computes the maximum path sum from the top to the bottom of a triangle. -// -// See {@link https://projecteuler.net/problem=67} -export default function compute() { - const triangle = slurp('67.txt') - .trim() - .split('\n') - .map(row => row.trim().split(' ').map(Number)); - - for (let i = triangle.length - 2; i >= 0; i--) { - for (let j = 0; j < triangle[i].length; j++) { - triangle[i][j] += Math.max(triangle[i + 1][j], triangle[i + 1][j + 1]); - } - } - - return triangle[0][0]; -} diff --git a/src/69.ts b/src/69.ts deleted file mode 100644 index ad350fbc..00000000 --- a/src/69.ts +++ /dev/null @@ -1,26 +0,0 @@ -import primes from './core/primes'; - -// Computes the value of n for which n/φ(n) is maximized. -// -// @remarks -// It's not necessary to actually compute the totient function for each number. The ratio will be largest with the -// denominator is as small as possible. This will occur when n has many prime divisors. -// -// See {@link docs/problem-69.md}. -// See {@link https://projecteuler.net/problem=69}. -export default function compute(limit: number) { - let ps = primes(); - let acc = 1; - - while (ps.length > 0) { - const n = acc * ps[0]; - if (n > limit) { - return acc; - } - - acc = n; - ps = ps.slice(1); - } - - throw new Error('not enough primes'); -} diff --git a/src/7.ts b/src/7.ts deleted file mode 100644 index 9c13001f..00000000 --- a/src/7.ts +++ /dev/null @@ -1,12 +0,0 @@ -import primes from './core/primes'; - -// Computes the nth prime number. -// -// @remarks -// -// Problem cheats. Just uses a precomputed list of prime numbers. -// -// See {@link https://projecteuler.net/problem=7}. -export function compute(n: number) { - return primes()[n - 1]; -} diff --git a/src/70.ts b/src/70.ts deleted file mode 100644 index 8e414105..00000000 --- a/src/70.ts +++ /dev/null @@ -1,69 +0,0 @@ -import primes from './core/primes'; - -// Computes the value of n for which φ((n) is a permutation of n and the ratio n/φ(n) produces a minimum. -// -// See {@link https://projecteuler.net/problem=70} -export default function compute(limit: number) { - const pairs = getSemiPrimePairs(getLimit(limit)) - .map(pair => transformPair(pair)) - .filter(pair => isWithinLimit(pair, limit)) - .filter(pair => isPermutation(pair)); - - let minRatio = limit; - let result = 0; - - for (const [phi, n] of pairs) { - const ratio = n / phi; - if (ratio < minRatio) { - minRatio = ratio; - result = n; - } - } - - return result; -} - -// This is a special totient function that optimizes the computation of totient for a semi-prime whose factors are p -// and q. -// -// For a prime number, the totient is simply (sub1 p). Because the totient is a multiplicative function, -// totient(p * q) = totient(p) * totient(q). Therefore, the totient of a semi-prime is simply (p - 1) * (q - 1). -function totient(p: number, q: number): number { - return (p - 1) * (q - 1); -} - -// Checks if two positive integers' digits are permutations of each other. -function isPermutation(pair: [number, number]): boolean { - const [m, n] = pair; - return m.toString().split('').sort().join('') === n.toString().split('').sort().join(''); -} - -function getLimit(limit: number): number { - return 2 * (Math.floor(Math.sqrt(limit)) + 1); -} - -function isWithinLimit(pair: [number, number], limit: number): boolean { - return pair[1] < limit; -} - -function getSemiPrimePairs(limit: number): [number, number][] { - const ps = primes().filter(p => p < limit); - const pairs: [number, number][] = []; - - for (let i = 0; i < ps.length; i++) { - for (let j = i; j < ps.length; j++) { - const p = ps[i]; - const q = ps[j]; - pairs.push([p, q]); - } - } - - return pairs; -} - -// Creates totient to semi-prime pairs. -function transformPair(factors: [number, number]): [number, number] { - const [p, q] = factors; - const n = p * q; - return [totient(p, q), n]; -} diff --git a/src/76.ts b/src/76.ts deleted file mode 100644 index 86117ef8..00000000 --- a/src/76.ts +++ /dev/null @@ -1,27 +0,0 @@ -// Computes the number of ways `target` can be written as a sum of at least two positive integers. -// -// See {@link https://projecteuler.net/problem=76} -export default function compute(target: number) { - return partition(1, target) - 1; -} - -const map = new Map(); - -function partition(k: number, n: number): number { - if (k > n) { - return 0; - } - - if (k === n) { - return 1; - } - - const key = `${k},${n}`; - if (map.has(key)) { - return map.get(key)!; - } - - const value = partition(k + 1, n) + partition(k, n - k); - map.set(key, value); - return value; -} diff --git a/src/8.ts b/src/8.ts deleted file mode 100644 index d452cccf..00000000 --- a/src/8.ts +++ /dev/null @@ -1,63 +0,0 @@ -import _ from 'lodash'; -import slurp from './core/slurp'; - -// Compute the largest product of of `window` consecutive digits in the given data. -// -// @remarks -// -// Can be solved with a sliding window algorithm. We just have to take care to note the number of zeroes in the window; -// if a window has any zeroes in it, thet product of that window will be zero. At each step, we only compute the -// product if we have no zeroes in the window. -// -// See {@link https://projecteuler.net/problem=8}. -export default function compute(window: number): number { - const data = slurp('8.txt').split('\n').join(''); - - // Keep a running tally of zeroes encountered in the window. Every time an incoming digit is a zero, we'll increment - // the count. Every time an outgoing digit is a zero, we'll decrement the count. - let zeroes = 0; - let max = 0; - let product = 1; - - // Create the initial window and update the product. - for (let i = 0; i < window; i++) { - const digit = _.toNumber(data[i]); - if (digit === 0) { - zeroes++; - continue; - } - - product *= digit; - } - - if (zeroes === 0) { - max = product; - } - - // Slide the window through the rest of the data. - for (let i = window; i < data.length; i++) { - const incoming = _.toNumber(data[i]); - const outgoing = _.toNumber(data[i - window]); - - // Multiply the product by the incoming digit if it's non-zero. - if (incoming !== 0) { - product *= incoming; - } else { - zeroes++; - } - - // Divide the product by the outgoing digit if it's non-zero. - if (outgoing !== 0) { - product /= outgoing; - } else { - zeroes--; - } - - // Update max product only if there are no zeros in the current window. - if (zeroes === 0) { - max = Math.max(max, product); - } - } - - return max; -} diff --git a/src/9.ts b/src/9.ts deleted file mode 100644 index d2a3faaf..00000000 --- a/src/9.ts +++ /dev/null @@ -1,23 +0,0 @@ -// Compute the product of the Pythagorean triplet for which a + b + c = target. -// -// See {@link https://projecteuler.net/problem=9}. -export default function compute(target: number) { - let result = 0; - - // Limit search space for a; since b and c are greater than a, the maximum value for a is 1/3 of the target. - const amax = Math.floor(target / 3); - for (let a = 1; a <= amax; a++) { - // Limit search space for b; since c is greater than b, the maximum value for b is half the remaining value. - const bmax = Math.floor((target - a) / 2); - for (let b = a + 1; b < bmax; b++) { - const c = target - a - b; - - if (a * a + b * b === c * c) { - result = a * b * c; - break; - } - } - } - - return result; -} diff --git a/src/core/combinations.ts b/src/core/combinations.ts deleted file mode 100644 index 49b25d53..00000000 --- a/src/core/combinations.ts +++ /dev/null @@ -1,22 +0,0 @@ -// Computes the number of combinations of n items taken r at a time. -// -// See {@link https://en.wikipedia.org/wiki/Combination}. -// See {@link https://en.wikipedia.org/wiki/Binomial_coefficient}. -export default function combinations(n: number, r: number): number { - if (r > n || n < 0 || r < 0) { - return 0; - } - - // Note that C(n, r) = C(n, n - r). - if (r > n - r) { - r = n - r; - } - - let result = 1; - for (let i = 0; i < r; i++) { - result *= n - i; - result /= i + 1; - } - - return result; -} diff --git a/src/core/divisors.ts b/src/core/divisors.ts deleted file mode 100644 index 07493476..00000000 --- a/src/core/divisors.ts +++ /dev/null @@ -1,31 +0,0 @@ -const memo = new Map(); - -// Computes the divisors of a given number. -// -// @remarks -// Uses a simple algorithm of trial division and memoizes the results. -// -// @returns The divisors in ascending order. -export default function divisors(n: number): number[] { - if (memo.has(n)) { - return memo.get(n)!; - } - - const set = new Set(); - const limit = Math.floor(Math.sqrt(n)); - - // We only need to go up to the square root of the number to find all of its divisors; divisors always occur in pairs, - // and you can't get divisors larger than the square root. - for (let i = 1; i <= limit; i++) { - if (n % i === 0) { - set.add(i); - set.add(n / i); - } - } - - const ds = Array.from(set); - ds.sort((a, b) => a - b); - - memo.set(n, ds); - return ds; -} diff --git a/src/core/factorial.ts b/src/core/factorial.ts deleted file mode 100644 index 6e8db775..00000000 --- a/src/core/factorial.ts +++ /dev/null @@ -1,20 +0,0 @@ -// Computes the factorial of a non-negative integer n. -// -// @remarks -// These numbers get big fast, so we return a bigint. -export default function factorial(n: number): bigint { - if (n < 0) { - throw new Error('n must be non-negative'); - } - - if (n === 0 || n === 1) { - return 1n; - } - - let product = 2n; - for (let i = 3n; i <= n; i++) { - product *= i; - } - - return product; -} diff --git a/src/core/fibs.ts b/src/core/fibs.ts deleted file mode 100644 index 604e97a1..00000000 --- a/src/core/fibs.ts +++ /dev/null @@ -1,26 +0,0 @@ -// Computes the Fibonacci numbers up to the given limit. -// -// @remarks -// Uses an iterative algorithm, does not memoize the results, and is not suitable for generating them. -export default function fibs(limit: number): number[] { - if (limit < 1) { - return []; - } - - if (limit === 1) { - return [0]; - } - - const fibs: number[] = [0, 1]; - - while (true) { - const next = fibs[fibs.length - 1] + fibs[fibs.length - 2]; - if (next >= limit) { - break; - } - - fibs.push(next); - } - - return fibs; -} diff --git a/src/core/gcd.ts b/src/core/gcd.ts deleted file mode 100644 index 5895e28f..00000000 --- a/src/core/gcd.ts +++ /dev/null @@ -1,14 +0,0 @@ -// Computes the greatest common divisor of two numbers. -// -// See {@link https://en.wikipedia.org/wiki/Greatest_common_divisor}. -export default function gcd(m: number, n: number): number { - if (m < 0 || n < 0) { - throw new Error('m and n must be non-negative.'); - } - - while (n !== 0) { - [m, n] = [n, m % n]; - } - - return m; -} diff --git a/src/core/lcm.ts b/src/core/lcm.ts deleted file mode 100644 index 3e94b761..00000000 --- a/src/core/lcm.ts +++ /dev/null @@ -1,8 +0,0 @@ -import gcd from './gcd'; - -// Computes the least common multiple of two numbers. -// -// See {@link https://en.wikipedia.org/wiki/Least_common_multiple}. -export default function lcm(m: number, n: number): number { - return Math.abs(m * n) / gcd(m, n); -} diff --git a/src/core/modular-exponentiation-bigint.ts b/src/core/modular-exponentiation-bigint.ts deleted file mode 100644 index daa7da6a..00000000 --- a/src/core/modular-exponentiation-bigint.ts +++ /dev/null @@ -1,21 +0,0 @@ -// Computes b ** e modulo m. -// -// @remarks -// Works with bigints. -// -// See {@link https://en.wikipedia.org/wiki/Modular_exponentiation}. -// See {@link https://en.wikipedia.org/wiki/Exponentiation_by_squaring}. -export default function mexpt(b: bigint, e: bigint, m: bigint): bigint { - let a = 1n; - - while (e > 0) { - if (e % 2n === 1n) { - a = (a * b) % m; - } - - b = (b * b) % m; - e /= 2n; - } - - return a; -} diff --git a/src/core/modular-exponentiation.ts b/src/core/modular-exponentiation.ts deleted file mode 100644 index 203e21c5..00000000 --- a/src/core/modular-exponentiation.ts +++ /dev/null @@ -1,21 +0,0 @@ -// Computes b ** e modulo m. -// -// @remarks -// Uses the left-to-right binary method for modular exponentiation. -// -// See {@link https://en.wikipedia.org/wiki/Modular_exponentiation}. -// See {@link https://en.wikipedia.org/wiki/Exponentiation_by_squaring}. -export default function mexpt(b: number, e: number, m: number): number { - let a = 1; - - while (e > 0) { - if (e & 1) { - a = (a * b) % m; - } - - b = (b * b) % m; - e >>= 1; - } - - return a; -} diff --git a/src/core/modular-tetration.ts b/src/core/modular-tetration.ts deleted file mode 100644 index ac512c2e..00000000 --- a/src/core/modular-tetration.ts +++ /dev/null @@ -1,42 +0,0 @@ -import gcd from './gcd'; -import mexpt from './modular-exponentiation'; -import ord from './order'; -import totient from './totient'; - -// Computes the modular tetration of b to the power of e modulo m. -// -// See {@link https://en.wikipedia.org/wiki/Tetration}. -export default function mtetn(b: number, e: number, m: number): number { - function f(b: number, e: number, m: number): number { - const o = ord(b, m); - const t = mtetn(b, e - 1, o); - return mexpt(b, t, m); - } - - function g(b: number, e: number, m: number, d: number): number { - const n = Math.floor(m / d); - const t = mtetn(b, e, n); - const i = mexpt(b, totient(n) - 1, n); - const u = (t * i) % n; - return (b * u) % m; - } - - if (m === 1) { - return 0; - } - - if (e === 1) { - return b % m; - } - - const d = gcd(b, m); - if (d === 1) { - return f(b, e, m); - } - - if (d === m) { - return 0; - } - - return g(b, e, m, d); -} diff --git a/src/core/order.ts b/src/core/order.ts deleted file mode 100644 index de37a90b..00000000 --- a/src/core/order.ts +++ /dev/null @@ -1,37 +0,0 @@ -import gcd from './gcd'; -import divisors from './divisors'; -import mexpt from './modular-exponentiation'; -import totient from './totient'; - -const memo = new Map(); - -// Computes the multiplicative order of b modulo m. -// -// @remarks -// The multiplicative order of b modulo m is the smallest positive integer d such that b ** d ≡ 1 (mod m). -// -// See {@link https://en.wikipedia.org/wiki/Multiplicative_order}. -export default function ord(b: number, m: number): number { - if (gcd(b, m) !== 1) { - throw new Error('b and m must be coprime'); - } - - // We'd like to memoize based on both b and m, so we concatenate them into a single string. - const key = `${b},${m}`; - if (memo.has(key)) { - return memo.get(key)!; - } - - const phi = totient(m); - const ds = divisors(phi); - - for (const d of ds) { - if (mexpt(b, d, m) === 1) { - memo.set(key, d); - return d; - } - } - - // This shouldn't happen if b and m are coprime. - throw new Error('could not compute ord(b, m)'); -} diff --git a/src/core/prime-factors.ts b/src/core/prime-factors.ts deleted file mode 100644 index e35984dd..00000000 --- a/src/core/prime-factors.ts +++ /dev/null @@ -1,27 +0,0 @@ -import divisors from './divisors'; - -const memo = new Map(); - -// Computes the prime factors of a given number. -// -// @remarks -// Checks all divisors for the number and returns the ones that are prime. Memoizes the results. -// -// @returns The prime factors in ascending order. -export default function primeFactors(n: number): number[] { - if (memo.has(n)) { - return memo.get(n)!; - } - - const ds = divisors(n); - const primes: number[] = []; - - for (const d of ds) { - if (d > 1 && divisors(d).length === 2) { - primes.push(d); - } - } - - memo.set(n, primes); - return primes; -} diff --git a/src/core/primes.ts b/src/core/primes.ts deleted file mode 100644 index 4c7591f2..00000000 --- a/src/core/primes.ts +++ /dev/null @@ -1,10 +0,0 @@ -import _ from 'lodash'; -import slurp from './slurp'; - -// Returns the list of prime numbers. -// -// @remarks -// Cheats. Uses a precomputed list of primes from {@link script/primes.mjs}. -export default function primes(): number[] { - return slurp('primes.txt').split('\n').map(_.toNumber); -} diff --git a/src/core/sigma.ts b/src/core/sigma.ts deleted file mode 100644 index fea3ed6f..00000000 --- a/src/core/sigma.ts +++ /dev/null @@ -1,8 +0,0 @@ -import divisors from './divisors'; - -// Computes the sum of the divisors of a given number. -// -// See {@link https://en.wikipedia.org/wiki/Divisor_function} -export default function sigma(n: number): number { - return divisors(n).reduce((a, b) => a + b, 0); -} diff --git a/src/core/slurp.ts b/src/core/slurp.ts deleted file mode 100644 index 2d22f3a1..00000000 --- a/src/core/slurp.ts +++ /dev/null @@ -1,7 +0,0 @@ -import fs from 'fs'; -import path from 'path'; - -export default function slurp(name: string): string { - const file = path.join('data', name); - return fs.readFileSync(file, 'utf8').toString(); -} diff --git a/src/core/tau.ts b/src/core/tau.ts deleted file mode 100644 index 2d32388e..00000000 --- a/src/core/tau.ts +++ /dev/null @@ -1,12 +0,0 @@ -import divisors from './divisors'; - -// Compute the number of divisors of a number. -// -// @remarks -// Includes the number itself. -// -// See {@link https://en.wikipedia.org/wiki/Tau_function}. -// See {@link https://en.wikipedia.org/wiki/Divisor_function}. -export default function tau(n: number): number { - return divisors(n).length; -} diff --git a/src/core/totient.ts b/src/core/totient.ts deleted file mode 100644 index f144ba6b..00000000 --- a/src/core/totient.ts +++ /dev/null @@ -1,29 +0,0 @@ -import primeFactors from './prime-factors'; - -const memo = new Map(); - -// Computes the totient of a given number. -// -// @remarks -// The totient of a number n is the number of positive integers less than n that are coprime to n. We can compute this -// directly using the number's distinct prime factors. -// -// See {@link https://en.wikipedia.org/wiki/Euler's_totient_function}. -export default function totient(n: number): number { - if (memo.has(n)) { - return memo.get(n)!; - } - - if (n === 1) { - return 0; - } - - const phi = Math.floor( - primeFactors(n) - .map(p => 1 - 1 / p) - .reduce((a, b) => a * b, n) - ); - - memo.set(n, phi); - return phi; -} diff --git a/test/1.test.ts b/test/1.test.ts deleted file mode 100644 index 0a6649b9..00000000 --- a/test/1.test.ts +++ /dev/null @@ -1,7 +0,0 @@ -import compute from '../src/1'; - -describe('multiples of 3 or 5', () => { - test('problem 1', async () => { - expect(compute(1000)).toBe(233168); - }); -}); diff --git a/test/10.test.ts b/test/10.test.ts deleted file mode 100644 index 68abf0e2..00000000 --- a/test/10.test.ts +++ /dev/null @@ -1,7 +0,0 @@ -import compute from '../src/10'; - -describe('summation of primes', () => { - test('problem 10', async () => { - expect(compute(2_000_000)).toBe(142913828922); - }); -}); diff --git a/test/107.test.ts b/test/107.test.ts deleted file mode 100644 index 7493b6ed..00000000 --- a/test/107.test.ts +++ /dev/null @@ -1,7 +0,0 @@ -import compute from '../src/107'; - -describe('minimal network', () => { - test('problem 107', async () => { - expect(compute()).toBe(259679); - }); -}); diff --git a/test/11.test.ts b/test/11.test.ts deleted file mode 100644 index c87cddbd..00000000 --- a/test/11.test.ts +++ /dev/null @@ -1,7 +0,0 @@ -import compute from '../src/11'; - -describe('largest product in a grid', () => { - test('problem 11', async () => { - expect(compute()).toBe(70600674); - }); -}); diff --git a/test/12.test.ts b/test/12.test.ts deleted file mode 100644 index a9e552b1..00000000 --- a/test/12.test.ts +++ /dev/null @@ -1,7 +0,0 @@ -import compute from '../src/12'; - -describe('highly divisible triangular number', () => { - test('problem 12', async () => { - expect(compute(500)).toBe(76576500); - }); -}); diff --git a/test/120.test.ts b/test/120.test.ts deleted file mode 100644 index b73688e3..00000000 --- a/test/120.test.ts +++ /dev/null @@ -1,7 +0,0 @@ -import compute from '../src/120'; - -describe('square remainders', () => { - test('problem 120', async () => { - expect(compute()).toBe(333082500); - }); -}); diff --git a/test/123.test.ts b/test/123.test.ts deleted file mode 100644 index 5b2ef7f1..00000000 --- a/test/123.test.ts +++ /dev/null @@ -1,7 +0,0 @@ -import compute from '../src/123'; - -describe('prime square remainders', () => { - test('problem 123', async () => { - expect(compute(1e10)).toBe(21035); - }); -}); diff --git a/test/13.test.ts b/test/13.test.ts deleted file mode 100644 index 90f414f5..00000000 --- a/test/13.test.ts +++ /dev/null @@ -1,7 +0,0 @@ -import compute from '../src/13'; - -describe('large sum', () => { - test('problem 13', async () => { - expect(compute()).toBe(5537376230); - }); -}); diff --git a/test/14.test.ts b/test/14.test.ts deleted file mode 100644 index b4875efd..00000000 --- a/test/14.test.ts +++ /dev/null @@ -1,7 +0,0 @@ -import compute from '../src/14'; - -describe('longest collatz sequence', () => { - test('problem 14', async () => { - expect(compute(1_000_000)).toBe(837799); - }); -}); diff --git a/test/15.test.ts b/test/15.test.ts deleted file mode 100644 index e3e0bc6e..00000000 --- a/test/15.test.ts +++ /dev/null @@ -1,10 +0,0 @@ -import _ from 'lodash'; -import compute from '../src/15'; - -describe('lattice paths', () => { - test('problem 15', async () => { - // Jest cannot compare bigints very well, so we have to convert them to strings. - const value = _.toString(compute()); - expect(value).toBe('137846528820'); - }); -}); diff --git a/test/16.test.ts b/test/16.test.ts deleted file mode 100644 index 83e7bf49..00000000 --- a/test/16.test.ts +++ /dev/null @@ -1,7 +0,0 @@ -import compute from '../src/16'; - -describe('power digit sum', () => { - test('problem 16', async () => { - expect(compute(2, 1000)).toBe(1366); - }); -}); diff --git a/test/17.test.ts b/test/17.test.ts deleted file mode 100644 index 1abebecb..00000000 --- a/test/17.test.ts +++ /dev/null @@ -1,7 +0,0 @@ -import compute from '../src/17'; - -describe('number letter counts', () => { - test('problem 17', async () => { - expect(compute()).toBe(21124); - }); -}); diff --git a/test/18.test.ts b/test/18.test.ts deleted file mode 100644 index 3f9e12a5..00000000 --- a/test/18.test.ts +++ /dev/null @@ -1,7 +0,0 @@ -import compute from '../src/18'; - -describe('maximum path sum i', () => { - test('problem 18', async () => { - expect(compute()).toBe(1074); - }); -}); diff --git a/test/188.test.ts b/test/188.test.ts deleted file mode 100644 index 6a691dae..00000000 --- a/test/188.test.ts +++ /dev/null @@ -1,7 +0,0 @@ -import compute from '../src/188'; - -describe('hyperexponentiation', () => { - test('problem 188', async () => { - expect(compute()).toBe(95962097); - }); -}); diff --git a/test/19.test.ts b/test/19.test.ts deleted file mode 100644 index 9dddb611..00000000 --- a/test/19.test.ts +++ /dev/null @@ -1,7 +0,0 @@ -import compute from '../src/19'; - -describe('counting sundays', () => { - test('problem 19', async () => { - expect(compute()).toBe(171); - }); -}); diff --git a/test/2.test.ts b/test/2.test.ts deleted file mode 100644 index 4e14a694..00000000 --- a/test/2.test.ts +++ /dev/null @@ -1,7 +0,0 @@ -import compute from '../src/2'; - -describe('even fibonacci numbers', () => { - test('problem 2', async () => { - expect(compute(4_000_000)).toBe(4613732); - }); -}); diff --git a/test/20.test.ts b/test/20.test.ts deleted file mode 100644 index 85c930c7..00000000 --- a/test/20.test.ts +++ /dev/null @@ -1,7 +0,0 @@ -import compute from '../src/20'; - -describe('factorial digit sum', () => { - test('problem 20', async () => { - expect(compute(100)).toBe(648); - }); -}); diff --git a/test/21.test.ts b/test/21.test.ts deleted file mode 100644 index 2ab1c3fc..00000000 --- a/test/21.test.ts +++ /dev/null @@ -1,7 +0,0 @@ -import compute from '../src/21'; - -describe('amicable numbers', () => { - test('problem 21', async () => { - expect(compute(10_000)).toBe(31626); - }); -}); diff --git a/test/22.test.ts b/test/22.test.ts deleted file mode 100644 index 9df60adc..00000000 --- a/test/22.test.ts +++ /dev/null @@ -1,7 +0,0 @@ -import compute from '../src/22'; - -describe('name scores', () => { - test('problem 22', async () => { - expect(compute()).toBe(871198282); - }); -}); diff --git a/test/23.test.ts b/test/23.test.ts deleted file mode 100644 index cce81cd2..00000000 --- a/test/23.test.ts +++ /dev/null @@ -1,7 +0,0 @@ -import compute from '../src/23'; - -describe('non-abundant sums', () => { - test('problem 23', async () => { - expect(compute(28123)).toBe(4179871); - }); -}); diff --git a/test/3.test.ts b/test/3.test.ts deleted file mode 100644 index c4d7cf53..00000000 --- a/test/3.test.ts +++ /dev/null @@ -1,7 +0,0 @@ -import compute from '../src/3'; - -describe('largest prime factor', () => { - test('problem 3', async () => { - expect(compute(600851475143)).toBe(6857); - }); -}); diff --git a/test/4.test.ts b/test/4.test.ts deleted file mode 100644 index 0ffbd99e..00000000 --- a/test/4.test.ts +++ /dev/null @@ -1,7 +0,0 @@ -import compute from '../src/4'; - -describe('largest palindrome product', () => { - test('problem 4', async () => { - expect(compute()).toBe(906609); - }); -}); diff --git a/test/40.test.ts b/test/40.test.ts deleted file mode 100644 index 10b63472..00000000 --- a/test/40.test.ts +++ /dev/null @@ -1,7 +0,0 @@ -import compute from '../src/40'; - -describe("champernowne's constant", () => { - test('problem 40', async () => { - expect(compute()).toBe(210); - }); -}); diff --git a/test/48.test.ts b/test/48.test.ts deleted file mode 100644 index f717ca78..00000000 --- a/test/48.test.ts +++ /dev/null @@ -1,9 +0,0 @@ -import _ from 'lodash'; -import compute from '../src/48'; - -describe('self powers', () => { - test('problem 48', async () => { - const value = compute(); - expect(_.toString(value)).toBe('9110846700'); - }); -}); diff --git a/test/5.test.ts b/test/5.test.ts deleted file mode 100644 index 5fdbe677..00000000 --- a/test/5.test.ts +++ /dev/null @@ -1,7 +0,0 @@ -import compute from '../src/5'; - -describe('smallest multiple', () => { - test('problem 5', async () => { - expect(compute(20)).toBe(232792560); - }); -}); diff --git a/test/52.test.ts b/test/52.test.ts deleted file mode 100644 index a0b23a16..00000000 --- a/test/52.test.ts +++ /dev/null @@ -1,7 +0,0 @@ -import compute from '../src/52'; - -describe('permuted multiples', () => { - test('problem 52', async () => { - expect(compute()).toBe(142857); - }); -}); diff --git a/test/53.test.ts b/test/53.test.ts deleted file mode 100644 index 9c1c4a1e..00000000 --- a/test/53.test.ts +++ /dev/null @@ -1,7 +0,0 @@ -import compute from '../src/53'; - -describe('combinatoric selections', () => { - test('problem 53', async () => { - expect(compute(100)).toBe(4075); - }); -}); diff --git a/test/6.test.ts b/test/6.test.ts deleted file mode 100644 index b641aa21..00000000 --- a/test/6.test.ts +++ /dev/null @@ -1,7 +0,0 @@ -import compute from '../src/6'; - -describe('sum square difference', () => { - test('problem 6', async () => { - expect(compute(100)).toBe(25164150); - }); -}); diff --git a/test/67.test.ts b/test/67.test.ts deleted file mode 100644 index f91e4ec0..00000000 --- a/test/67.test.ts +++ /dev/null @@ -1,7 +0,0 @@ -import compute from '../src/67'; - -describe('maximum path sum ii', () => { - test('problem 67', async () => { - expect(compute()).toBe(7273); - }); -}); diff --git a/test/69.test.ts b/test/69.test.ts deleted file mode 100644 index fed49a38..00000000 --- a/test/69.test.ts +++ /dev/null @@ -1,7 +0,0 @@ -import compute from '../src/69'; - -describe('totient maximum', () => { - test('problem 69', async () => { - expect(compute(1_000_000)).toBe(510510); - }); -}); diff --git a/test/7.test.ts b/test/7.test.ts deleted file mode 100644 index e601755f..00000000 --- a/test/7.test.ts +++ /dev/null @@ -1,7 +0,0 @@ -import { compute } from '../src/7'; - -describe('10001st prime', () => { - test('problem 7', async () => { - expect(compute(10001)).toBe(104743); - }); -}); diff --git a/test/70.test.ts b/test/70.test.ts deleted file mode 100644 index 3f1febc7..00000000 --- a/test/70.test.ts +++ /dev/null @@ -1,7 +0,0 @@ -import compute from '../src/70'; - -describe('totient permutation', () => { - test('problem 70', async () => { - expect(compute(1e7)).toBe(8319823); - }); -}); diff --git a/test/76.test.ts b/test/76.test.ts deleted file mode 100644 index 86b7a8b6..00000000 --- a/test/76.test.ts +++ /dev/null @@ -1,7 +0,0 @@ -import compute from '../src/76'; - -describe('counting summations', () => { - test('problem 76', async () => { - expect(compute(100)).toBe(190569291); - }); -}); diff --git a/test/8.test.ts b/test/8.test.ts deleted file mode 100644 index f0db558f..00000000 --- a/test/8.test.ts +++ /dev/null @@ -1,7 +0,0 @@ -import compute from '../src/8'; - -describe('largest product in a series', () => { - test('problem 8', async () => { - expect(compute(13)).toBe(23514624000); - }); -}); diff --git a/test/9.test.ts b/test/9.test.ts deleted file mode 100644 index badb47c0..00000000 --- a/test/9.test.ts +++ /dev/null @@ -1,7 +0,0 @@ -import compute from '../src/9'; - -describe('special pythagorean triplet', () => { - test('problem 9', async () => { - expect(compute(1000)).toBe(31875000); - }); -}); diff --git a/test/core/combinations.test.ts b/test/core/combinations.test.ts deleted file mode 100644 index 8d5f3e56..00000000 --- a/test/core/combinations.test.ts +++ /dev/null @@ -1,11 +0,0 @@ -import combinations from '../../src/core/combinations'; - -describe('combinations', () => { - test('combinations', async () => { - expect(combinations(0, 0)).toBe(1); - expect(combinations(100, 0)).toBe(1); - expect(combinations(100, 100)).toBe(1); - expect(combinations(5, 2)).toBe(10); - expect(combinations(10, 3)).toBe(120); - }); -}); diff --git a/test/core/divisors.test.ts b/test/core/divisors.test.ts deleted file mode 100644 index afb1cd04..00000000 --- a/test/core/divisors.test.ts +++ /dev/null @@ -1,10 +0,0 @@ -import divisors from '../../src/core/divisors'; - -describe('divisors', () => { - test('divisors', async () => { - expect(divisors(1)).toStrictEqual([1]); - expect(divisors(2)).toStrictEqual([1, 2]); - expect(divisors(15)).toStrictEqual([1, 3, 5, 15]); - expect(divisors(2015)).toStrictEqual([1, 5, 13, 31, 65, 155, 403, 2015]); - }); -}); diff --git a/test/core/factorial.test.ts b/test/core/factorial.test.ts deleted file mode 100644 index 3269fa5f..00000000 --- a/test/core/factorial.test.ts +++ /dev/null @@ -1,16 +0,0 @@ -import _ from 'lodash'; -import factorial from '../../src/core/factorial'; - -describe('factorial', () => { - // Jest can't compare bigints very well, so we have to convert them to strings. - test('factorial', async () => { - expect(_factorial(0)).toBe('1'); - expect(_factorial(1)).toBe('1'); - expect(_factorial(5)).toBe('120'); - expect(_factorial(10)).toBe('3628800'); - }); - - function _factorial(n: number): string { - return _.toString(factorial(n)); - } -}); diff --git a/test/core/fibs.test.ts b/test/core/fibs.test.ts deleted file mode 100644 index 944a2603..00000000 --- a/test/core/fibs.test.ts +++ /dev/null @@ -1,9 +0,0 @@ -import fibs from '../../src/core/fibs'; - -describe('fibs', () => { - test('fibs', async () => { - expect(fibs(0)).toStrictEqual([]); - expect(fibs(1)).toStrictEqual([0]); - expect(fibs(10)).toStrictEqual([0, 1, 1, 2, 3, 5, 8]); - }); -}); diff --git a/test/core/gcd.test.ts b/test/core/gcd.test.ts deleted file mode 100644 index a2e4c5cc..00000000 --- a/test/core/gcd.test.ts +++ /dev/null @@ -1,16 +0,0 @@ -import gcd from '../../src/core/gcd'; - -describe('greatest common divisor', () => { - test('gcd', async () => { - expect(gcd(48, 18)).toBe(6); - expect(gcd(101, 103)).toBe(1); - expect(gcd(56, 98)).toBe(14); - expect(gcd(270, 192)).toBe(6); - expect(gcd(0, 5)).toBe(5); - expect(gcd(5, 0)).toBe(5); - expect(gcd(0, 0)).toBe(0); - expect(gcd(3, 20)).toBe(1); - expect(gcd(3, 345)).toBe(3); - expect(gcd(3, 115)).toBe(1); - }); -}); diff --git a/test/core/lcm.test.ts b/test/core/lcm.test.ts deleted file mode 100644 index 34317e19..00000000 --- a/test/core/lcm.test.ts +++ /dev/null @@ -1,7 +0,0 @@ -import lcm from '../../src/core/lcm'; - -describe('least common multiple', () => { - test('lcm', async () => { - expect(lcm(12, 18)).toBe(36); - }); -}); diff --git a/test/core/modular-exponentiation-bigint.test.ts b/test/core/modular-exponentiation-bigint.test.ts deleted file mode 100644 index 3329363e..00000000 --- a/test/core/modular-exponentiation-bigint.test.ts +++ /dev/null @@ -1,11 +0,0 @@ -import _ from 'lodash'; -import mexpt from '../../src/core/modular-exponentiation-bigint'; - -describe('modular exponentiation with bigint', () => { - test('mexpt', async () => { - expect(_.toString(mexpt(3n, 1n, 2n))).toBe('1'); - expect(_.toString(mexpt(3n, 0n, 9n))).toBe('1'); - expect(_.toString(mexpt(5n, 3n, 13n))).toBe('8'); - expect(_.toString(mexpt(4n, 13n, 497n))).toBe('445'); - }); -}); diff --git a/test/core/modular-exponentiation.test.ts b/test/core/modular-exponentiation.test.ts deleted file mode 100644 index 24fe06bb..00000000 --- a/test/core/modular-exponentiation.test.ts +++ /dev/null @@ -1,10 +0,0 @@ -import mexpt from '../../src/core/modular-exponentiation'; - -describe('modular exponentiation', () => { - test('mexpt', async () => { - expect(mexpt(3, 1, 2)).toBe(1); - expect(mexpt(3, 0, 9)).toBe(1); - expect(mexpt(5, 3, 13)).toBe(8); - expect(mexpt(4, 13, 497)).toBe(445); - }); -}); diff --git a/test/core/modular-tetration.test.ts b/test/core/modular-tetration.test.ts deleted file mode 100644 index 7c34d7cc..00000000 --- a/test/core/modular-tetration.test.ts +++ /dev/null @@ -1,12 +0,0 @@ -import mtetn from '../../src/core/modular-tetration'; - -describe('modular tetration', () => { - test('mtetn', async () => { - expect(mtetn(3, 1, 2)).toBe(3 ** 1 % 2); - expect(mtetn(3, 2, 20)).toBe(3 ** 3 % 20); - expect(mtetn(3, 3, 345)).toBe(312); - expect(mtetn(5, 2, 7)).toBe(5 ** 5 % 7); - expect(mtetn(7, 4, 13)).toBe(6); - expect(mtetn(10, 2, 6)).toBe(10 ** 10 % 6); - }); -}); diff --git a/test/core/order.test.ts b/test/core/order.test.ts deleted file mode 100644 index 5a80753b..00000000 --- a/test/core/order.test.ts +++ /dev/null @@ -1,12 +0,0 @@ -import ord from '../../src/core/order'; - -describe('multiplicative order', () => { - test('order modulo m', async () => { - expect(ord(4, 7)).toBe(3); - expect(ord(10, 7)).toBe(6); - expect(ord(5, 3)).toBe(2); - expect(ord(13, 7)).toBe(2); - expect(ord(3, 20)).toBe(4); - expect(ord(3, 115)).toBe(44); - }); -}); diff --git a/test/core/prime-factors.test.ts b/test/core/prime-factors.test.ts deleted file mode 100644 index 067ca39d..00000000 --- a/test/core/prime-factors.test.ts +++ /dev/null @@ -1,10 +0,0 @@ -import primeFactors from '../../src/core/prime-factors'; - -describe('prime factors', () => { - test('primeFactors', async () => { - expect(primeFactors(1)).toStrictEqual([]); - expect(primeFactors(2)).toStrictEqual([2]); - expect(primeFactors(27)).toStrictEqual([3]); - expect(primeFactors(103243)).toStrictEqual([7, 43]); - }); -}); diff --git a/test/core/sigma.test.ts b/test/core/sigma.test.ts deleted file mode 100644 index d81ab19c..00000000 --- a/test/core/sigma.test.ts +++ /dev/null @@ -1,10 +0,0 @@ -import sigma from '../../src/core/sigma'; - -describe('sum of divisors', () => { - test('sigma', async () => { - expect(sigma(1)).toBe(1); - expect(sigma(2)).toBe(3); - expect(sigma(15)).toBe(24); - expect(sigma(2015)).toBe(2688); - }); -}); diff --git a/test/core/tau.test.ts b/test/core/tau.test.ts deleted file mode 100644 index b5691846..00000000 --- a/test/core/tau.test.ts +++ /dev/null @@ -1,10 +0,0 @@ -import tau from '../../src/core/tau'; - -describe('number of divisors', () => { - test('tau', async () => { - expect(tau(1)).toBe(1); - expect(tau(2)).toBe(2); - expect(tau(15)).toBe(4); - expect(tau(2015)).toBe(8); - }); -}); diff --git a/test/core/totient.test.ts b/test/core/totient.test.ts deleted file mode 100644 index 0a9a4d5c..00000000 --- a/test/core/totient.test.ts +++ /dev/null @@ -1,10 +0,0 @@ -import totient from '../../src/core/totient'; - -describe('totient', () => { - test('totient', async () => { - expect(totient(1)).toBe(0); - expect(totient(7)).toBe(6); - expect(totient(15)).toBe(8); - expect(totient(2015)).toBe(1440); - }); -}); diff --git a/test/jest.config.mjs b/test/jest.config.mjs deleted file mode 100644 index a5c55685..00000000 --- a/test/jest.config.mjs +++ /dev/null @@ -1,12 +0,0 @@ -export default { - clearMocks: true, - moduleFileExtensions: ['js', 'ts'], - modulePaths: [''], - testEnvironment: 'node', - testMatch: ['**/*.test.ts'], - testTimeout: 1000, - transform: { - '^.+\\.ts$': 'ts-jest' - }, - verbose: true -}; diff --git a/tsconfig.json b/tsconfig.json deleted file mode 100644 index 2f75948a..00000000 --- a/tsconfig.json +++ /dev/null @@ -1,19 +0,0 @@ -{ - // See https://github.com/tsconfig/bases/blob/main/bases/recommended.json - "extends": "@tsconfig/recommended/tsconfig.json", - "compilerOptions": { - "declaration": true, - "declarationMap": true, - "esModuleInterop": true, - "module": "ESNext", - "moduleResolution": "node", - "outDir": "./build", - "sourceMap": true, - "strict": true, - "target": "ES2024", - "typeRoots": ["node_modules/@types"], - "types": ["jest", "node"] - }, - "include": ["script", "src", "test"], - "exclude": ["build", "dist", "node_modules"] -}