Must know algorithms implemented in C++. These algorithms span over a wide range of data structures and complex concepts useful for competitive programming.

• [ ] (a) Number Theory

  1. Prime Number Generation (Sieve, Segmented Sieve)

  2. Euler Totient Theorem

  3. Fermat’s Theorem

  4. HCF & LCM (Euclid)

  5. Linear Diophantine Equations (Extended Euclid)

  6. Modulus Arithmetic (addition,multiplication,subtraction,modular Inverse)

  7. Cycle Finding (Floyd Algo and Brent Algo)

  8. Integer Factorization (Trial Division , Pollard Rho method)

  9. Lucas Theorem (Simple & Advance)

  10. Chinese Remainder Theorem

  11. Wilson Theorem

  12. Miller - Rabin Primality Testing

  13. Perfect Numbers

  14. Goldbach Conjecture

• [ ] (b) Probability

  1. Basic Probability and Conditional Probability

  2. Random Variables

  3. Probability Generating Functions

  4. Expectation

  5. Probability Distribution [Binomial, Poisson, Normal,Bernoulli]

• [ ] (c) Counting

  1. Pigeonhole principle

  2. Inclusion Exclusion

  3. Special Numbers [Stirling,Fibonacci,Catalan, Eulerian, Harmonic, Bernoulli]

  4. Polya Counting

  5. Burnside lemma

• [ ] (d) Permutation Cycles

• [ ] (e) Linear Algebra

  1. Addition And Subtraction Of Matrices

  2. Multiplication ( Strassen's algorithm ), Logarithmic exponentiation

  3. Matrix Transformations [ Transpose, Rotation Of Matrix, Representing Linear Transformations Using Matrix ]

  4. Determinant , Rank and Inverse Of Matrix [ Gaussian Elimination , Gauss Jordan Elimination]

  5. Solving System Of Linear Equations

  6. Matrix Exponentiation To Solve Recurrences

  7. Eigenvalues And Eigen vector

  8. Roots of a polynomial [ Prime factorization of a polynomial, Integer roots of a polynomial]

  9. Lagrange Interpolation

• [ ] (e) Game Theory

  1. Basic Concepts & Nim Game [Grundy Theorem , Grundy Number]

  2. Hackenbush

• [ ] (f) Group Theory

  1. Burnside Lemma

  2. Polya's Theorem

  Graphs:

• [ ] (a) Graph Representation

  1. Adjacency Matrix

  2. Adjacency List

  3. Incidence Matrix

  4. Edge List

• [ ] (b) Graph Types

  1. Directed

  2. Undirected

  3. Weighted

  4. Unweighted

  5. Planar

  6. Hamilton

  7. Euler

  8. Special Graphs

• [ ] (c) DFS & It’s Application

  1. Cycle Detection

  2. Articulation Points

  3. Bridges

  4. Strongly Connected Component

  5. Connected Component

  6. Path Finding

  7. Solving Maze

  8. Biconnectivity in Graph

  9. Topological Sorting

  10. Bipartite Checking

  11. Planarity Testing

  12. Flood-fill algorithm

• [ ] (d) BFS & It’s Application

  1. Shortest Path (No. Of Edges)

  2. Bipartite Checking

  3. Connected Components

• [ ] (d) Minimum Spanning Tree

  1. Prim’s Algorithm

  2. Kruskal Algorithm

• [ ] (d) Single Source Shortest-Path

  1. Dijkstra

  2. Bellman Ford

• [ ] (e) All pair Shortest Path

1. Floyd Warshall’s Algorithm

• [ ] (f) Euler Tour

• [ ] (g) Flow

  1. Ford-Fulkerson [PFS,DFS,BFS]

  2. Dinic's Algorithm

  3. Min Cost - Max Flow [Successive Shortest Path Algo,Cycle Cancelling Algorithm]

  4. Max Weighted BPM [Kuhn Munkres algorithm/Hungarian Method]

  5. Stoer Wagner Min-Cut Algo

  6. Hop-Kraft BPM

  7. Edmond Blossom Shrinking Algorithm

• [ ] (h) Other Important Topics On Graphs

  1. 2-SAT,

  2. LCA

  3. Maximum Cardinality Matching

  4. Application Flow

  5. Min Path Cover Over Dag

  6. Independent Edge Disjoint Path

  7. Minimum Vertex Cover

  8. Maximum Independent Set

• [ ] Data Structures

  1. Arrays

  2. Linked List

  3. Trees (Binary Tree And Binary Search Tree)

  4. Stacks

  5. Queues

  6. Heap

  7. Hash Tables

  8. Disjoint-Set Data Structures

  9. Trie

  10. Segment Tree

  11. Binary Index Tree

  12. Treap

• [ ] Searching And Sorting

  1. Linear Search

  2. Binary Search

  3. Ternary Search

  4. Selection Sort

  5. Bubble Sort

  6. Insertion Sort

  7. Merge Sort

  8. Quick Sort

  9. Quick Select

  10. Heap Sort

  11. Radix Sort

  12. Counting Sort

• [ ] Greedy

  1. Classical Problems of Greedy & Concept example : Fractional Knapsack

• [ ] Dynamic Programming Classical Problems

  1. Edit Distance

  2. Egg Dropping Puzzle

  3. Integer Knapsack

  4. Largest Independent Set

  5. Longest Biotonic Subsequence

  6. Longest Common Subsequence

  7. Longest Common Substring

  8. Longest Increasing Subsequence

  9. Longest Palindromic Subsequence

  10. Longest Palindromic Substring

  11. Longest Substring Without Repeating Character

  12. Matrix Chain Multiplication

  13. Max Size Square Submatrix With One

  14. Maximum Length Chain Pairs

  15. Maximum Sum Increasing Subsequence

  16. Optimal Binary Search Tree

  17. Palindrome Partition Problem

  18. Set Partition Problem

  19. Subset Sum

  20. Word Wrap Problem

• [ ] Dynamic Programming Advanced Techniques

  1. DP + Tree

  2. DP + Bit Masking

  3. DP + Binary Search

  4. DP + Graph

  5. DP + Matrix Exponentiation

  6. DP + Probability Space

  7. DP + Crack Recurrence

• [ ] Divide & Conquer

  1. Classical Problems & Concepts

  2. Merge Sort

  3. Closest Pair Points

• [ ] Other Algorithm Design Techniques

  1. BackTracking

  2. Man In Middle

  3. Newton-Raphson to reach the fixed point

  4. Brute Force

  5. Constructive Algo

  6. Sliding Window

  7. Pancake Sorting

• GNU GCC
• Make

make

./binary-name to run the program

👤 Chaitanya Rahalkar

• Twitter: @chairahalkar
• Github: @chaitanyarahalkar

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Copyright © 2019 Chaitanya Rahalkar.
This project is MIT licensed.