This repository contains Python based examples of many popular algorithms and data structures.

Each algorithm and data structure has its own separate README with related explanations and links for further reading (sometimes including ones to YouTube videos).

☝ Note that this project is meant to be used for learning and researching purposes only and it is not meant to be used for production.

An algorithm is an unambiguous specification of how to solve a class of problems. It is a set of rules that precisely define a sequence of operations.

B - Beginner, A - Advanced

• Math
  • BBit Manipulation - set/get/update/clear bits, multiplication/division by two, make negative etc.
  • BFactorial
  • BFibonacci Number - classic and closed-form versions
  • BPrimality Test (trial division method)
  • BEuclidean Algorithm - calculate the Greatest Common Divisor (GCD)
  • BLeast Common Multiple (LCM)
  • BSieve of Eratosthenes - finding all prime numbers up to any given limit
  • BIs Power of Two - check if the number is power of two (naive and bitwise algorithms)
  • BPascal's Triangle
  • BComplex Number - complex numbers and basic operations with them
  • BRadian & Degree - radians to degree and backwards conversion
  • BFast Powering
  • AInteger Partition
  • ALiu Hui π Algorithm - approximate π calculations based on N-gons
  • ADiscrete Fourier Transform - decompose a function of time (a signal) into the frequencies that make it up
• Sets
  • BCartesian Product - product of multiple sets
  • BFisher–Yates Shuffle - random permutation of a finite sequence
  • APower Set - all subsets of a set (bitwise and backtracking solutions)
  • APermutations (with and without repetitions)
  • ACombinations (with and without repetitions)
  • ALongest Common Subsequence (LCS)
  • ALongest Increasing Subsequence
  • AShortest Common Supersequence (SCS)
  • AKnapsack Problem - "0/1" and "Unbound" ones
  • AMaximum Subarray - "Brute Force" and "Dynamic Programming" (Kadane's) versions
  • ACombination Sum - find all combinations that form specific sum
• Strings
  • BHamming Distance - number of positions at which the symbols are different
  • ALevenshtein Distance - minimum edit distance between two sequences
  • AKnuth–Morris–Pratt Algorithm (KMP Algorithm) - substring search (pattern matching)
  • AZ Algorithm - substring search (pattern matching)
  • ARabin Karp Algorithm - substring search
  • ALongest Common Substring
  • ARegular Expression Matching
• Searches
  • BLinear Search
  • BJump Search (or Block Search) - search in sorted array
  • BBinary Search - search in sorted array
  • BInterpolation Search - search in uniformly distributed sorted array
• Sorting
  • BBubble Sort
  • BSelection Sort
  • BInsertion Sort
  • BHeap Sort
  • BMerge Sort
  • BQuicksort - in-place and non-in-place implementations
  • BShellsort
  • BCounting Sort
  • BRadix Sort
• Linked Lists
  • BStraight Traversal
  • BReverse Traversal
• Trees
  • BDepth-First Search (DFS)
  • BBreadth-First Search (BFS)
• Graphs
  • BDepth-First Search (DFS)
  • BBreadth-First Search (BFS)
  • BKruskal’s Algorithm - finding Minimum Spanning Tree (MST) for weighted undirected graph
  • ADijkstra Algorithm - finding shortest paths to all graph vertices from single vertex
  • ABellman-Ford Algorithm - finding shortest paths to all graph vertices from single vertex
  • AFloyd-Warshall Algorithm - find shortest paths between all pairs of vertices
  • ADetect Cycle - for both directed and undirected graphs (DFS and Disjoint Set based versions)
  • APrim’s Algorithm - finding Minimum Spanning Tree (MST) for weighted undirected graph
  • ATopological Sorting - DFS method
  • AArticulation Points - Tarjan's algorithm (DFS based)
  • ABridges - DFS based algorithm
  • AEulerian Path and Eulerian Circuit - Fleury's algorithm - Visit every edge exactly once
  • AHamiltonian Cycle - Visit every vertex exactly once
  • AStrongly Connected Components - Kosaraju's algorithm
  • ATravelling Salesman Problem - shortest possible route that visits each city and returns to the origin city
• Cryptography
  • BPolynomial Hash - rolling hash function based on polynomial
• Uncategorized
  • BTower of Hanoi
  • BSquare Matrix Rotation - in-place algorithm
  • BJump Game - backtracking, dynamic programming (top-down + bottom-up) and greedy examples
  • BUnique Paths - backtracking, dynamic programming and Pascal's Triangle based examples
  • BRain Terraces - trapping rain water problem (dynamic programming and brute force versions)
  • AN-Queens Problem
  • AKnight's Tour

An algorithmic paradigm is a generic method or approach which underlies the design of a class of algorithms. It is an abstraction higher than the notion of an algorithm, just as an algorithm is an abstraction higher than a computer program.

• Brute Force - look at all the possibilities and selects the best solution
  • BLinear Search
  • BRain Terraces - trapping rain water problem
  • AMaximum Subarray
  • ATravelling Salesman Problem - shortest possible route that visits each city and returns to the origin city
  • ADiscrete Fourier Transform - decompose a function of time (a signal) into the frequencies that make it up
• Greedy - choose the best option at the current time, without any consideration for the future
  • BJump Game
  • AUnbound Knapsack Problem
  • ADijkstra Algorithm - finding shortest path to all graph vertices
  • APrim’s Algorithm - finding Minimum Spanning Tree (MST) for weighted undirected graph
  • AKruskal’s Algorithm - finding Minimum Spanning Tree (MST) for weighted undirected graph
• Divide and Conquer - divide the problem into smaller parts and then solve those parts
  • BBinary Search
  • BTower of Hanoi
  • BPascal's Triangle
  • BEuclidean Algorithm - calculate the Greatest Common Divisor (GCD)
  • BMerge Sort
  • BQuicksort
  • BTree Depth-First Search (DFS)
  • BGraph Depth-First Search (DFS)
  • BJump Game
  • BFast Powering
  • APermutations (with and without repetitions)
  • ACombinations (with and without repetitions)
• Dynamic Programming - build up a solution using previously found sub-solutions
  • BFibonacci Number
  • BJump Game
  • BUnique Paths
  • BRain Terraces - trapping rain water problem
  • ALevenshtein Distance - minimum edit distance between two sequences
  • ALongest Common Subsequence (LCS)
  • ALongest Common Substring
  • ALongest Increasing Subsequence
  • AShortest Common Supersequence
  • A0/1 Knapsack Problem
  • AInteger Partition
  • AMaximum Subarray
  • ABellman-Ford Algorithm - finding shortest path to all graph vertices
  • AFloyd-Warshall Algorithm - find shortest paths between all pairs of vertices
  • ARegular Expression Matching
• Backtracking - similarly to brute force, try to generate all possible solutions, but each time you generate next solution you test if it satisfies all conditions, and only then continue generating subsequent solutions. Otherwise, backtrack, and go on a different path of finding a solution. Normally the DFS traversal of state-space is being used.
  • BJump Game
  • BUnique Paths
  • BPower Set - all subsets of a set
  • AHamiltonian Cycle - Visit every vertex exactly once
  • AN-Queens Problem
  • AKnight's Tour
  • ACombination Sum - find all combinations that form specific sum
• Branch & Bound - remember the lowest-cost solution found at each stage of the backtracking search, and use the cost of the lowest-cost solution found so far as a lower bound on the cost of a least-cost solution to the problem, in order to discard partial solutions with costs larger than the lowest-cost solution found so far. Normally BFS traversal in combination with DFS traversal of state-space tree is being used.