Pe381 (#126)

* improving new_problem

* add solution for pe381

Author: KerimovEmil

solutions/PE381.py

@@ -0,0 +1,101 @@
+"""
+PROBLEM
+
+For a prime p let S(p) = (sum (p-k)!) mod p for 1 <= k <= 5.
+
+For example, if p=7,
+
+(7-1)! + (7-2)! + (7-3)! + (7-4)! + (7-5)! = 6! + 5! + 4! + 3! + 2! = 720+120+24+6+2 = 872.
+
+As 872 mod (7) = 4, S(7) = 4.
+
+It can be verified that sum S(p) = 480 for 5 <= p < 100.
+
+Find sum S(p) for 5 <= p < 10^8.
+
+ANSWER: 139602943319822
+Solve time: 3.661 seconds
+"""
+
+import unittest 
+from util.utils import timeit, primes_upto
+
+
+# with Wilson's theorem, we know that (p-1)! = -1 mod p
+# so we can rewrite the sum as:
+# S(p) = (\sum_{k=1}^{5} (p-k)!) mod p
+
+# (p-1)! = -1 mod p
+# (p-2)! = -1/(p-1) = -1/(-1) = 1 mod p
+# (p-3)! = 1/(p-2) = 1/(-2) = -1/2 mod p
+# (p-4)! = (-1/2)/(p-3) = (-1/2)/(-3) = 1/6 mod p
+# (p-5)! = (1/6)/(p-4) = (1/6)/(-4) = -1/24 mod p
+# so S(p) = (-1 + 1 - 1/2 + 1/6 - 1/24) mod p = (-12 + 4 - 1)/24 = -9/24 = -3/8 mod p
+
+# 1/(p-1) mod p = x such that x * (p-1) = 1 mod p
+# x * (-1) = 1 mod p
+# x = -1 mod p
+
+# 1/(p-2) mod p = x such that x * (p-2) = 1 mod p
+# x * (-2) = 1 mod p
+# x = -1/2 mod p
+
+# 1/(p-3) mod p = x such that x * (p-3) = 1 mod p
+# x * (-3) = 1 mod p
+# x = -1/3 mod p
+
+# 1/(p-4) mod p = x such that x * (p-4) = 1 mod p
+# x * (-4) = 1 mod p
+# x = -1/4 mod p
+
+# 1/(p-5) mod p = x such that x * (p-5) = 1 mod p
+# x * (-5) = 1 mod p
+# x = -1/5 mod p
+
+# We need to find the sum of S(p) for all primes 5 <= p < N
+# S(p) = -3/8 mod p
+
+# example N = 100
+# S(5) = -3/8 mod 5 = -3 * 2 mod 5 = -6 mod 5 = 4
+# S(7) = -3/8 mod 7 = -3 * 6 mod 7 = -18 mod 7 = 4
+# S(11) = -3/8 mod 11 = -3 * 7 mod 11 = -21 mod 11 = 1
+# S(13) = -3/8 mod 13 = -3 * 5 mod 13 = -15 mod 13 = 11
+# S(17) = -3/8 mod 17 = -3 * 15 mod 17 = -45 mod 17 = 11
+# S(19) = -3/8 mod 19 = -3 * 12 mod 19 = -36 mod 19 = 2
+# S(23) = -3/8 mod 23 = -3 * 14 mod 23 = -42 mod 23 = 4
+# S(29) = -3/8 mod 29 = -3 * 11 mod 29 = -33 mod 29 = 26
+# S(31) = -3/8 mod 31 = -3 * 27 mod 31 = -81 mod 31 = 13
+# S(37) = -3/8 mod 37 = -3 * 28 mod 37 = -84 mod 37 = 9
+
+
+
+class Problem381:
+    def __init__(self):
+        pass
+
+    @timeit
+    def solve(self, n):
+        primes = primes_upto(n)
+        total = 0
+        for p in primes[2:]:
+            total += self.S(int(p))
+        return total
+
+    @staticmethod
+    def S(p):
+        return (pow(-8, -1, p) * 3) % p
+
+
+class Solution381(unittest.TestCase):
+    def setUp(self):
+        self.problem = Problem381()
+
+    def test_small_n(self):
+        self.assertEqual(480, self.problem.solve(n=100))
+
+    def test_solution(self):
+        self.assertEqual(139602943319822, self.problem.solve(n=int(pow(10, 8))))
+
+
+if __name__ == '__main__':
+    unittest.main()

solutions/new_problem.py

@@ -1,9 +1,60 @@
 import os
 import argparse
 import sys
+import requests
+from bs4 import BeautifulSoup
+
+def get_problem_description(n):
+    url = f"https://projecteuler.net/problem={n}"
+    headers = {
+        'User-Agent': 'Mozilla/5.0 (Windows NT 10.0; Win64; x64) AppleWebKit/537.36 (KHTML, like Gecko) Chrome/120.0.0.0 Safari/537.36'
+    }
+    try:
+        response = requests.get(url, headers=headers, timeout=10)
+        if response.status_code == 200:
+            soup = BeautifulSoup(response.content, 'html.parser')
+            problem_content = soup.find('div', class_='problem_content')
+            if problem_content:
+                # Remove script and style tags
+                for script in problem_content(["script", "style"]):
+                    script.decompose()
+                
+                # Replace <br> with newlines
+                for br in problem_content.find_all('br'):
+                    br.replace_with('\n')
+                
+                # Replace <p> with newlines around content
+                for p in problem_content.find_all('p'):
+                    p.insert_before('\n')
+                    p.insert_after('\n')
+                
+                # Extract text
+                text = problem_content.get_text()
+                
+                # Clean up multiple newlines and spaces
+                lines = [line.strip() for line in text.split('\n')]
+                # Filter out multiple consecutive empty lines
+                cleaned_lines = []
+                for line in lines:
+                    if line or (cleaned_lines and cleaned_lines[-1] != ''):
+                        cleaned_lines.append(line)
+                
+                return '\n'.join(cleaned_lines).strip()
+    except Exception as e:
+        print(f"Warning: Could not fetch problem description: {e}")
+    return "PROBLEM DESCRIPTION COULD NOT BE AUTOMATICALLY RETRIEVED."
+
+TEMPLATE = """r\"\"\"
+PROBLEM
+
+{1}
+
+ANSWER: 
+Solve time: 
+\"\"\"
 
-TEMPLATE = """from util.utils import timeit
 import unittest
+from util.utils import timeit
 
 
 class Problem{0}:
@@ -26,7 +77,6 @@ def test_solution(self):
 
 if __name__ == '__main__':
     unittest.main()
-
 """
 
 if __name__ == '__main__':
@@ -42,7 +92,12 @@ def test_solution(self):
     if os.path.exists(f'./{fn}'):
         raise AssertionError(
             f'{fn} already exists! Just update the file you lazy bastard!')
-    with open(fn, 'w') as f:
-        f.write(TEMPLATE.format(args.p))
+    
+    print(f"Fetching problem {args.p} description...")
+    description = get_problem_description(args.p)
+    
+    with open(fn, 'w', encoding='utf-8') as f:
+        f.write(TEMPLATE.format(args.p, description))
 
+    print(f"Created {fn} with problem description.")
     sys.exit(0)