This repository contains Python based examples of many popular algorithms and data structures.
☝ 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.
☝ Note: Still work in progress
Marked data structures and algorithms means they've been implemented already
A data structure is a particular way of organizing and storing data in a computer so that it can be accessed and modified efficiently. More precisely, a data structure is a collection of data values, the relationships among them, and the functions or operations that can be applied to the data.
B
- Beginner, A
- Advanced
B
ArraysB
Linked ListB
Doubly Linked ListB
QueueB
StackB
Hash MapB
Heap - max and min heap versionsB
Priority QueueA
TrieA
Tree
A
Binary Search TreeA
AVL TreeA
Red-Black TreeA
Segment Tree - with min/max/sum range queries examplesA
Fenwick Tree (Binary Indexed Tree)A
Graph (both directed and undirected)A
Disjoint SetA
Bloom FilterAn 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
B
Bit Manipulation - set/get/update/clear bits, multiplication/division by two, make negative etc.B
FactorialB
Fibonacci Number - classic and closed-form versionsB
Primality Test (trial division method)B
Euclidean Algorithm - calculate the Greatest Common Divisor (GCD)B
Least Common Multiple (LCM)B
Sieve of Eratosthenes - finding all prime numbers up to any given limitB
Is Power of Two - check if the number is power of two (naive and bitwise algorithms)B
Pascal's TriangleB
Complex Number - complex numbers and basic operations with themB
Radian & Degree - radians to degree and backwards conversionB
Fast PoweringA
Integer PartitionA
Square Root - Newton's methodA
Liu Hui π Algorithm - approximate π calculations based on N-gonsA
Discrete Fourier Transform - decompose a function of time (a signal) into the frequencies that make it upB
Cartesian Product - product of multiple setsB
Fisher–Yates Shuffle - random permutation of a finite sequenceA
Power Set - all subsets of a set (bitwise and backtracking solutions)A
Permutations (with and without repetitions)A
Combinations (with and without repetitions)A
Longest Common Subsequence (LCS)A
Longest Increasing SubsequenceA
Shortest Common Supersequence (SCS)A
Knapsack Problem - "0/1" and "Unbound" onesA
Maximum Subarray - "Brute Force" and "Dynamic Programming" (Kadane's) versionsA
Combination Sum - find all combinations that form specific sumB
Hamming Distance - number of positions at which the symbols are differentA
Levenshtein Distance - minimum edit distance between two sequencesA
Knuth–Morris–Pratt Algorithm (KMP Algorithm) - substring search (pattern matching)A
Z Algorithm - substring search (pattern matching)A
Rabin Karp Algorithm - substring searchA
Longest Common SubstringA
Regular Expression MatchingB
Linear SearchB
Jump Search (or Block Search) - search in sorted arrayB
Binary Search - search in sorted arrayB
Interpolation Search - search in uniformly distributed sorted arrayB
Bubble SortB
Selection SortB
Insertion SortB
Heap SortB
Merge SortB
Quicksort - in-place and non-in-place implementationsB
ShellsortB
Counting SortB
Radix SortB
Straight TraversalB
Reverse TraversalB
Depth-First Search (DFS)B
Breadth-First Search (BFS)B
Depth-First Search (DFS)B
Breadth-First Search (BFS)B
Kruskal’s Algorithm - finding Minimum Spanning Tree (MST) for weighted undirected graphA
Dijkstra Algorithm - finding shortest paths to all graph vertices from single vertexA
Bellman-Ford Algorithm - finding shortest paths to all graph vertices from single vertexA
Floyd-Warshall Algorithm - find shortest paths between all pairs of verticesA
Detect Cycle - for both directed and undirected graphs (DFS and Disjoint Set based versions)A
Prim’s Algorithm - finding Minimum Spanning Tree (MST) for weighted undirected graphA
Topological Sorting - DFS methodA
Articulation Points - Tarjan's algorithm (DFS based)A
Bridges - DFS based algorithmA
Eulerian Path and Eulerian Circuit - Fleury's algorithm - Visit every edge exactly onceA
Hamiltonian Cycle - Visit every vertex exactly onceA
Strongly Connected Components - Kosaraju's algorithmA
Travelling Salesman Problem - shortest possible route that visits each city and returns to the origin cityB
Polynomial Hash - rolling hash function based on polynomialB
Tower of HanoiB
Square Matrix Rotation - in-place algorithmB
Jump Game - backtracking, dynamic programming (top-down + bottom-up) and greedy examplesB
Unique Paths - backtracking, dynamic programming and Pascal's Triangle based examplesB
Rain Terraces - trapping rain water problem (dynamic programming and brute force versions)B
Recursive Staircase - count the number of ways to reach to the top (4 solutions)A
N-Queens ProblemA
Knight's TourAn 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.
B
Linear SearchB
Rain Terraces - trapping rain water problemB
Recursive Staircase - count the number of ways to reach to the topA
Maximum SubarrayA
Travelling Salesman Problem - shortest possible route that visits each city and returns to the origin cityA
Discrete Fourier Transform - decompose a function of time (a signal) into the frequencies that make it upB
Jump GameA
Unbound Knapsack ProblemA
Dijkstra Algorithm - finding shortest path to all graph verticesA
Prim’s Algorithm - finding Minimum Spanning Tree (MST) for weighted undirected graphA
Kruskal’s Algorithm - finding Minimum Spanning Tree (MST) for weighted undirected graphB
Binary SearchB
Tower of HanoiB
Pascal's TriangleB
Euclidean Algorithm - calculate the Greatest Common Divisor (GCD)B
Merge SortB
QuicksortB
Tree Depth-First Search (DFS)B
Graph Depth-First Search (DFS)B
Jump GameB
Fast PoweringA
Permutations (with and without repetitions)A
Combinations (with and without repetitions)B
Fibonacci NumberB
Jump GameB
Unique PathsB
Rain Terraces - trapping rain water problemB
Recursive Staircase - count the number of ways to reach to the topA
Levenshtein Distance - minimum edit distance between two sequencesA
Longest Common Subsequence (LCS)A
Longest Common SubstringA
Longest Increasing SubsequenceA
Shortest Common SupersequenceA
0/1 Knapsack ProblemA
Integer PartitionA
Maximum SubarrayA
Bellman-Ford Algorithm - finding shortest path to all graph verticesA
Floyd-Warshall Algorithm - find shortest paths between all pairs of verticesA
Regular Expression MatchingB
Jump GameB
Unique PathsB
Power Set - all subsets of a setA
Hamiltonian Cycle - Visit every vertex exactly onceA
N-Queens ProblemA
Knight's TourA
Combination Sum - find all combinations that form specific sum▶ Data Structures and Algorithms on YouTube
Big O notation is used to classify algorithms according to how their running time or space requirements grow as the input size grows. On the chart below you may find most common orders of growth of algorithms specified in Big O notation.
Source: Big O Cheat Sheet.
Below is the list of some of the most used Big O notations and their performance comparisons against different sizes of the input data.
Big O Notation | Computations for 10 elements | Computations for 100 elements | Computations for 1000 elements |
---|---|---|---|
O(1) | 1 | 1 | 1 |
O(log N) | 3 | 6 | 9 |
O(N) | 10 | 100 | 1000 |
O(N log N) | 30 | 600 | 9000 |
O(N^2) | 100 | 10000 | 1000000 |
O(2^N) | 1024 | 1.26e+29 | 1.07e+301 |
O(N!) | 3628800 | 9.3e+157 | 4.02e+2567 |
Data Structure | Access | Search | Insertion | Deletion | Comments |
---|---|---|---|---|---|
Array | 1 | n | n | n | |
Stack | n | n | 1 | 1 | |
Queue | n | n | 1 | 1 | |
Linked List | n | n | 1 | n | |
Hash Table | - | n | n | n | In case of perfect hash function costs would be O(1) |
Binary Search Tree | n | n | n | n | In case of balanced tree costs would be O(log(n)) |
B-Tree | log(n) | log(n) | log(n) | log(n) | |
Red-Black Tree | log(n) | log(n) | log(n) | log(n) | |
AVL Tree | log(n) | log(n) | log(n) | log(n) | |
Bloom Filter | - | 1 | 1 | - | False positives are possible while searching |
Name | Best | Average | Worst | Memory | Stable | Comments |
---|---|---|---|---|---|---|
Bubble sort | n | n2 | n2 | 1 | Yes | |
Insertion sort | n | n2 | n2 | 1 | Yes | |
Selection sort | n2 | n2 | n2 | 1 | No | |
Heap sort | n log(n) | n log(n) | n log(n) | 1 | No | |
Merge sort | n log(n) | n log(n) | n log(n) | n | Yes | |
Quick sort | n log(n) | n log(n) | n2 | log(n) | No | Quicksort is usually done in-place with O(log(n)) stack space |
Shell sort | n log(n) | depends on gap sequence | n (log(n))2 | 1 | No | |
Counting sort | n + r | n + r | n + r | n + r | Yes | r - biggest number in array |
Radix sort | n * k | n * k | n * k | n + k | Yes | k - length of longest key |