DSA

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Data Structures and Algorithms (DSA) README

Introduction

• Objective: Understand core concepts of data structures and algorithms to solve computational problems efficiently.
• Pre-requisites: Basic understanding of a programming language and mathematical concepts like logarithms and modular arithmetic.

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1. Basics of DSA

Topics:

1. Time and Space Complexity

   • Big-O, Big-Θ, and Big-Ω Notations
   • Analyze iterative and recursive functions

2. Mathematics for DSA

   • Modular Arithmetic
   • GCD (Euclid’s Algorithm)
   • Exponentiation (Power functions, Modular Exponentiation)

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2. Arrays and Strings

Topics:

1. Arrays:

   • Traversal, Insertion, Deletion
   • Prefix Sums, Sliding Window
   • Kadane’s Algorithm (Maximum Subarray Sum)

2. Strings:

   • String Matching (KMP Algorithm, Rabin-Karp)
   • Anagrams, Palindromes
   • Z Algorithm

Practice:

• Two Sum Problem
• Longest Palindromic Substring

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3. Linked Lists

Topics:

1. Singly Linked List

   • Insertion, Deletion, Traversal
   • Detect Cycle (Floyd’s Cycle Detection)

2. Doubly Linked List

3. Circular Linked List

Practice:

• Reverse a Linked List
• Merge Two Sorted Linked Lists

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4. Stacks and Queues

Topics:

1. Stacks:

   • Next Greater Element
   • Evaluate Postfix/Prefix Expressions

2. Queues:

   • Circular Queue
   • Deque (Double-Ended Queue)

Practice:

• Implement Min Stack
• Sliding Window Maximum

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5. Trees

Topics:

1. Binary Tree:

   • Traversals (Inorder, Preorder, Postorder)
   • Diameter of a Tree
   • Lowest Common Ancestor (LCA)

2. Binary Search Tree (BST):

   • Insertion, Deletion, Search
   • Balanced BSTs (AVL Trees, Red-Black Trees)

3. Heaps:

   • Min-Heap and Max-Heap
   • Heap Sort

Practice:

• Convert Sorted Array to BST
• Binary Tree Level Order Traversal

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6. Graphs

Topics:

1. Representations: Adjacency Matrix, Adjacency List

2. Traversal Algorithms:

   • Depth First Search (DFS)
   • Breadth First Search (BFS)

3. Shortest Path Algorithms:

   • Dijkstra's Algorithm
   • Bellman-Ford

4. Minimum Spanning Tree (MST):

   • Kruskal’s Algorithm
   • Prim’s Algorithm

5. Topological Sorting

Practice:

• Detect Cycle in a Graph
• Clone a Graph

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7. Searching and Sorting Algorithms

Topics:

1. Sorting:

   • Bubble, Selection, Insertion Sort
   • Quick Sort, Merge Sort, Heap Sort

2. Searching:

   • Linear Search, Binary Search
   • Applications of Binary Search (First and Last Occurrence)

Practice:

• Search in Rotated Sorted Array
• Find Median in a Sorted Array

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8. Recursion and Backtracking

Topics:

1. Basics of Recursion

   • Factorial, Fibonacci, Power Functions

2. Backtracking:

   • N-Queens Problem
   • Rat in a Maze
   • Subset Sum

Practice:

• Generate Parentheses
• Word Search in a Grid

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9. Dynamic Programming (DP)

Topics:

1. Basics:

   • Recursion to DP Transition
   • 0/1 Knapsack, Subset Sum

2. Advanced DP:

   • Longest Common Subsequence (LCS)
   • Longest Increasing Subsequence (LIS)
   • Matrix Chain Multiplication

Practice:

• Edit Distance
• Minimum Path Sum

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10. Advanced Data Structures

Topics:

1. Tries:

   • Insert and Search
   • Longest Prefix Matching

2. Segment Trees:

   • Range Queries
   • Lazy Propagation

3. Fenwick Tree (Binary Indexed Tree)

Practice:

• Count Inversions using BIT
• Range Sum Queries

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11. Bit Manipulation

Topics:

1. Basics of Bits

   • AND, OR, XOR Operations
   • Bit Masking

2. Applications:

   • Subset Generation
   • Count Set Bits

Practice:

• Single Number Problem
• Power of Two

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12. Problem-Solving Strategies

Topics:

1. Divide and Conquer
2. Sliding Window Technique
3. Two Pointers

Practice:

• Maximum Product Subarray
• Container with Most Water

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Practice Platforms

1. LeetCode
2. GeeksforGeeks
3. Codeforces
4. HackerRank
5. CodeChef

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Learning Tips

1. Start small: Solve basic problems before tackling harder ones.
2. Debug efficiently: Use print statements or debugging tools to trace your logic.
3. Consistency: Practice daily to build strong problem-solving skills.

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