Algorithm and programming technique list step by step

Bismillahir Rahmanir Rahim

Mathematics:

• Prime finding(sieve)
• Prime factorization
• GCD, LCM
• Factorial
• Fibonacci
• Counting, Permutation, combination
• Exponentiation
• Modular Arithmetic
• Euclid, Extended euclid

Data Structure:

• Stack
• Queue
• Priority Queue
• Linked list
• Heap
• Hash table
• Disjoint Set, Union Find
• Binary Search Tree
• Trie, Suffix Array
• Segmented Tree,Range minimum Query
• Binary Indexed Tree(BIT)
• Heavy light Decomposition

Sorting:

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

Searching:

• Linear Search
• Binary Search
• Ternary Search
• Map, HashMap

Dynamic Programming:

• Rod Cutting
• Maximum Sum (1D, 2D)
• Coin Change
• Longest Common Subsequence
• Longest Increasing subsequence, Longest Decreasing Subsequence
• Matrix Chain multiplication
• Edit Distance
• Knapsack problem, 0-1 Knapsack
• Bitmask DP
• Traveling Salesman problem
• Digit DP

Greedy Algorithm:

• Activity selection/Task scheduling problem
• Huffman coding

Graph Theory:

• Graph Representation(matrix, list/vector)
• Breadth First Search(BFS)
• Depth First Search(DFS)
• Topological Sort
• Strongly Connected Component(SCC)
• Minimum Spanning Tree(kruskal, prim)
• All pair's shortest path(Floyd Warshall)
• Djkastra algorithm
• Bellman Ford Algorithm
• Directed Acyclic Graph
• Bipartite Matching
• Max-Flow, Min-cost max-flow
• Cayley's Theorem
• Articulation Point, Bridge
• Euler tour/path
• Hamiltonian Cycle
• Stable Marriage problem
• Chinese Postman problem

Number Theory:

• Josephus Problem
• Farey Sequence
• Euler's phi
• Catalan numbers
• Burnside's lemma/circular permutation
• Modular inverse
• Probability
• Chinese Remainder Theorem
• Gaussian Elmination method
• Dilworth's Theorem
• Matrix Exponentiation
• Determinant of a matrix
• RSA public key crypto System
• GCD 
• LCM
• Euler Totient

Computational Geometry:

• Pick's Theorem
• Convex hull
• Line Intersection
• Point in a polygon
• Area of a polygon
• Line Sweeping
• Polygon intersection
• Closest Pair

Game Theory:

• Take Away game
• Nim
• Sprague-grundy Number

String:

• Naive String matching 
• Rabin karp Algo
• Finite Automata
• Knuth-Marris-Pratt Algo
• Manacher's Algo
• Aho korasick's Algo
• Boyer-Moore algo

Others:

• Recursion
• C++ Standard Template Library(STL)
• Backtracking
• Hungarian Algorithm

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