Sorting Algorithms

• Bubble Sort
• Selection Sort
• Insertion Sort
• Merge Sort
• Quick Sort
• Heap Sort
• Counting Sort
• Radix Sort
• Bucket Sort

Searching Algorithms

• Linear Search
• Binary Search
• Ternary Search

Mathematical Algorithms

• GCD / LCM
• Sieve of Eratosthenes
• Modular Arithmetic
• Fermat’s Theorem
• Euler’s Totient Function
• Fast Exponentiation

Graph Algorithms

• Breadth-First Search (BFS)
• Depth-First Search (DFS)
• Dijkstra’s Algorithm
• Bellman-Ford Algorithm
• Floyd-Warshall Algorithm
• Topological Sort
• Union-Find (DSU)
• Kruskal’s Algorithm
• Prim’s Algorithm
• Tarjan’s Algorithm
• Kosaraju’s Algorithm
• A* Search

Dynamic Programming

• 0/1 Knapsack
• Longest Common Subsequence (LCS)
• Longest Increasing Subsequence (LIS)
• Matrix Chain Multiplication
• DP on Trees
• Bitmask DP
• Knuth Optimization
• Convex Hull Trick
• Digit DP

String Algorithms

• KMP Algorithm
• Z-Algorithm
• Rabin-Karp
• Suffix Arrays
• Aho-Corasick
• Rolling Hashes
• Manacher’s Algorithm
• Edit Distance

Data Structure

• Treap

Backtracking

• N-Queens Problem
• Sudoku Solver
• Hamiltonian Path
• Subsets/Permutations

Greedy Algorithms

• Activity Selection
• Fractional Knapsack
• Huffman Coding

Bit Manipulation

• Bit Operations
• XOR Tricks
• Count Set Bits
• Bitmask Subsets

Geometry Algorithms

• Convex Hull
• Line Intersection
• Polygon Area

Advanced Techniques

• Mo’s Algorithm
• Heavy-Light Decomposition
• Centroid Decomposition
• Persistent Data Structures
• Sqrt Decomposition
• Monotonic Stack / Queue
• Sliding Window
• Two Pointers
• Two Heaps
• Meet in the Middle

Recurrence & Divide and Conquer

• Divide & Conquer
• Karatsuba Multiplication
• Binary Search on Answer
• Master Theorem
• Strassen’s Matrix Multiplication

Cryptographic Algorithms

• RSA
• Diffie-Hellman
• Hash Functions (MD5, SHA)

Core Problem Solving Skills

• Problem Decomposition
• Time/Space Complexity
• Mathematical Proof Techniques
• State Representation
• DP vs Greedy Decisions
• Modeling with Graphs & Trees