README.md

Note:

Please don't take effort to create pull requests for new algorithms or data structures. This is just a curiosity-driven personal hobby and was originally not intended to be a library. Feel free fork and modify to fit your need if that's what you are looking for. You can however open issues or fix bugs with pull requests, I would be happy to take a look when I get time

Advanced Algorithms

Various important computer science algorithms generically implemented in C#.

Install by nuget

For beta releases on beta branch

Install-Package Advanced.Algorithms -Pre

For stable releases on stable branch

Install-Package Advanced.Algorithms

• API documentation

Supports

• .Net Standard 1.0 or above
• .Net Framework 4.0 or above

Development environment

Windows

• Visual Studio Code as IDE for .NET core
• Visual Studio 2017 as IDE for .NET framework/.NET core

Mac OS

• Visual Studio Code as IDE for .NET core
• Visual Studio 2017 as IDE for Mono

Linux

• Visual Studio Code as IDE for .NET core
• Mono develop as IDE for Mono

Data structures

List

• Array list (dynamic array) (implementation | tests)
• Skip list (implementation | tests)

HashSets

• HashSet (using separate chaining optionally with open address linear probing) (implementation | tests)
• Ordered HashSet (implementation | tests)

Dictionaries

• Dictionary (using separate chaining optionally with open address linear probing) (implementation | tests)
• Ordered Dictionary (implementation | tests)

Stack

• Stack (using dynamic array and optionally using singly linked list) (implementation | tests)

Queue

• Queue (using dynamic array and optionally using doubly linked list) (implementation | tests)
• Priority queue (implementation | tests)

Linked list

• Singly linked list (implementation | tests)
• Doubly linked list (implementation | tests)
• Circular linked list (implementation | tests)

Heap

• Binary heap (implementation | tests)
• d-ary heap (implementation | tests)
• Binomial heap (implementation | tests)
• Fibonacci heap (implementation | tests)
• Pairing heap (implementation | tests)

Note: It is observed that among the implementations here, in practice, with the exclusion of UpdateKey (decrement/increment) operation, regular Binary Heap & d-ary Heap outperforms other in theory superiors. Likely because it doesn't have pointer juggling overhead and hey arrays are faster!

Tree

• Tree (implementation | tests)
• Binary tree (implementation | tests)

Binary search trees

• Binary search tree (implementation | tests)
• AVL tree (implementation | tests)
• Red black tree (implementation | tests)
• Splay tree (implementation | tests)
• Treap tree (implementation | tests)

B trees (database trees)

• B-tree (implementation | tests)
• B+ tree (implementation | tests)

Queryable trees

• Segment tree (implementation | tests)
• Binary indexed tree (Fenwick tree) (implementation | tests)
• Multi-dimensional interval tree (implementation | tests) using nested red-black tree
• Multi-dimensional k-d tree (implementation | tests) for range and nearest neigbour queries
• Multi-dimensional range tree (implementation | tests) using nested red-black tree
• R-tree (implementation | tests)
• Quadtree (implementation | tests)

TODO: Support multi-dimentional segment tree & binary indexed tree.

Lookup trees

• Prefix tree (Trie) (implementation | tests)
• Suffix tree (implementation | tests)
• Ternary search tree (implementation | tests)

TODO: implement trie compression.

Set

• Disjoint set (implementation | tests)
• Sparse set (implementation | tests)
• Bloom filter (implementation | tests)

Graph

Adjacency list

• Graph (implementation | tests)
• Weighted Graph (implementation | tests)
• DiGraph (implementation | tests)
• Weighted DiGraph (implementation | tests)

Adjacency matrix

• Graph (implementation | tests)
• Weighted Graph (implementation | tests)
• DiGraph (implementation | tests)
• Weighted DiGraph (implementation | tests)

Algorithms

Graph algorithms

Articulation points

• Tarjan's articulation points finder (implementation | tests)

Bridges

• Tarjan's bridge finder (implementation | tests)

Connectivity

• Kosaraju's strongly connected component finder (implementation | tests)
• Tarjan's strongly connected component finder (implementation | tests)
• Tarjan's bi-connected graph tester (implementation | tests)

Coloring

• M-coloring (implementation | tests)

Cover

• Min vertex cover (implementation | tests)

Maximum flow

• Ford-Fulkerson algorithm (implementation | tests)
• Edmonds Karp's improvement (implementation | tests) on Ford-Fulkerson algorithm
• Push relabel algorithm (implementation | tests)

Shortest path

• Bellman-Ford algorithm (implementation | tests)
• Dijikstra's algorithm (implementation | tests) using Fibonacci heap.
• Floyd-Warshall algorithm (implementation | tests)
• Johnson's algorithm (implementation | tests)
• Travelling salesman path (implementation | tests)
• A* search algorithm (implementation | tests) using Fibonacci heap.

Matching

• Max bipartite matching (implementation | tests) using Edmonds Karp's improved Ford Fulkerson max flow algorithm
• Max bipartite matching (implementation | tests) using Hopcroft Karp algorithm

Cut

• Minimum cut (implementation | tests) using Edmonds Karp's improved Ford Fulkerson max flow algorithm

Cycle

• Cycle detection (implementation | tests)

Search

• Depth first (implementation | tests)
• Breadth first (implementation | tests)
• Bi-directional (implementation | tests)

Topological sort

• Depth first method (implementation | tests)
• Kahn's algorithm (implementation | tests)

Minimum spanning tree

• Kruskal's algorithm (implementation | tests) using merge sort and disjoint set
• Prim's algorithm (implementation | tests)

String

• Manacher's algorithm for linear time longest palindrome (implementation | tests)

Pattern matching

• Rabin-Karp string search (implementation | tests)
• Knuth–Morris–Pratt (KMP) string search (implementation | tests)
• Z algorithm for string search (implementation | tests)

Compression

• Huffman coding (implementation | tests)

Sorting and searching

• Binary search (implementation | tests)
• Quick select for kth smallest/largest in unordered collection using median of medians (implementation | tests)
• Majority element using Boyer-Moore voting algorithm (implementation | tests)

Sorting algorithms

• Bubble sort (implementation | tests)
• Insertion sort (implementation | tests)
• Selection sort (implementation | tests)
• Shell sort (implementation | tests)
• Tree sort (implementation | tests)
• Quick sort (implementation | tests)
• Heap sort (implementation | tests)
• Merge sort (implementation | tests)
• Bucket sort (implementation | tests)
• Radix sort (implementation | tests)
• Counting sort (implementation | tests)

Note: On a decent desktop, in given implementations here for +ive random input integers, the clear winner is counting sort (~0.1 seconds to sort 1 million integers) followed by Radix Sort (~0.4 seconds). Merge Sort, Heap Sort, Quick Sort & Bucket Sort are all winners for +ive & -ive random integer inputs. Tree sort has pointer juggling overhead on backing Red-Black Tree, so performs 8 times slower than Merge Sort in practice. Bubble Sort, Insertion Sort, Selection Sort & Shell Sort are among the worst for random input as observed from results.

Combinatorics

• Permutations (implementation | tests)
• Combinations (implementation | tests)
• Subsets (implementation | tests)

Distributed Systems

• Circular queue (ring buffer) (implementation | tests)
• Consistant hash (implementation | tests)
• LRU cache (implementation | tests)
• Asynchronous producer–consumer queue (implementation | tests)

Numerical methods

• Check primality (implementation | tests)
• Generate primes using sieve of Eratosthenes (implementation | tests)
• Fast exponentiation (implementation | tests)

Geometry (in 2D)

• Convex hull using gift wrapping algorithm (implementation | tests)
• Line intersection (implementation | tests)
• Closest point pair (implementation | tests)
• Check if given point inside polygon (implementation | tests)
• Rectangle intersection (implementation | tests)
• Point rotation (implementation | tests)
• Line interesections with Bentley-Ottmann sweep line algorithm using red-black tree and binary minimum heap (implementation | tests)

Bit manipulation

• Base conversion (implementation | tests)
• Calculate logarithm (base 2 & 10) (implementation | tests)
• GCD (implementation | tests)