算法实现大全

The Archive of Interesting Code

The Archive of Interesting Code is an (ambitious) effort on my part to research, intuit, and code up every interesting algorithm and data structure ever invented. In doing so, I hope both to learn the mathematical techniques that power these technologies and to improve my skills as a programmer.

The examples on this site are in a variety of languages. I generally prefer to use C++ for algorithms, since the STL provides a great framework for expressing algorithms that work on a variety of data types. I code up most data structures in Java, both because theCollections framework allows them to be integrated in seamlessly with other applications and because automatic garbage collection simplifies some of the resource management. Every now and then I'll find an algorithm or data structure that is best represented in a different language like Haskell, in which case I'll forgo my usual language conventions.

In case you're curious what I'm someday hoping to having implemented on this page, you can check out my TODO list.

If you're interested in using any of this code in your applications, feel free to do so! You don't need to cite me or this website as a source, though I would appreciate it if you did. However, please don't plagiarize the code here by claiming authorship - that would just be dishonest. I also caution you that while I'm fairly confident that the code on this site is correct, I haven't mercilessly tested every line, and so there may be a lurking bug or two here.

Enjoy!

The Code

Name
Link
Date Added
Language
Description

Binomial Heap
(link)
7‑24‑2010
C++
An implementation of a binomial heap data structure for use as a priority queue.

Bounded Priority Queue
(link)
7‑24‑2010
C++
An implementation of a priority queue with a fixed upper limit to its size..

Matrix
(link)
7‑24‑2010
C++
A collection of classes for manipulating matrices.

VList
(link)
8‑16‑2010
Java
An implementation of the List abstraction backed by a VList.

Function Wrapper
(link)
8‑16‑2010
C++
A C++ wrapper class around unary functions.

String
(link)
8‑17‑2010
C++
An implementation of a string abstraction that uses the small string optimization.

nstream
(link)
8‑31‑2010
C++
An stream class that sends and receives data over a network.

Snake
(link)
8‑31‑2010
C++
An implementation of the game Snake with a rudimentary AI.

Mergesort
(link)
9‑14‑2010
C++
An implementation of the mergesort algorithm.

Next Permutation
(link)
10‑6‑2010
C++
An implementation of the next_permutation STL algorithm.

Interval Heap
(link)
10‑17‑2010
Java
An implementation of a double-ended priority queue using an interval heap.

Linear-Time Selection
(link)
10‑18‑2010
C++
A deterministic, linear-time selection algorithm using the median-of-medians algorithm.

Heapsort
(link)
10‑18‑2010
C++
An implementation of the heapsort algorithm.

Union-Find
(link)
10‑19‑2010
Java
An implementation of a disjoint-set data structure using a disjoint set forest.

Radix Sort
(link)
10‑19‑2010
C++
An implementation of the radix sort algorithm.

Rational
(link)
10‑23‑2010
C++
A data structure representing a rational number.

DPLL
(link)
10‑23‑2010
Haskell
An implementation of the DPLL algorithm for solving CNF-SAT.

Smoothsort
(link)
10‑27‑2010
C++
An implementation of the smoothsort algorithm, an adaptive heapsort variant.

Extendible Array
(link)
10‑28‑2010
Java
A dynamic array class with O(1) worst-case runtime lookup and append.

In-Place Merge
(link)
10‑29‑2010
C++
An implementation of a merge algorithm that runs in-place.

Random Shuffle
(link)
10‑29‑2010
C++
An algorithm for generating a random permutation of a set of elements.

Random Sample
(link)
10‑29‑2010
C++
An O(n) time, O(1) space algorithm for randomly choosing k elements out of a stream with uniform probability.

Natural Mergesort
(link)
10‑30‑2010
C++
An implementation of natural mergesort, an adaptive variant of mergesort.

Interpolation Search
(link)
10‑31‑2010
C++
An implementation of the interpolation search algorithm.

Introsort
(link)
10‑31‑2010
C++
An implementation of the introsort algorithm, a fast hybrid of quicksort, heapsort, and insertion sort.

Hashed Array Tree
(link)
11‑3‑2010
Java
An implementation of a dynamic array backed by a hashed array tree.

Recurrence Solver
(link)
11‑13‑2010
C++
A fast algorithm for generating terms of a sequence defined by a linear recurrence relation.

Fibonacci Heap
(link)
11‑15‑2010
Java
An implementation of a priority queue backed by a Fibonacci heap.

Dijkstra's Algorithm
(link)
11‑16‑2010
Java
An implementation of Dijkstra's algorithm for single-source shortest paths.

Prim's Algorithm
(link)
11‑17‑2010
Java
An implementation of Prim's algorithm for computing minimum spanning trees.

Kruskal's Algorithm
(link)
11‑17‑2010
Java
An implementation of Kruskal's algorithm for computing minimum spanning trees.

Majority Element
(link)
11‑17‑2010
C++
A fast, linear-time algorithm for finding the majority element of a data set.

Haar Transform
(link)
11‑17‑2010
C++
A set of functions to decompose a sequence of values into a sum of Haar wavelets.

Argmax
(link)
11‑19‑2010
C++
A pair of functions to compute the arg min or max of a function on some range.

Derivative
(link)
11‑19‑2010
C++
A function object that approximates the derivative of a function.

Levenshtein Distance
(link)
11‑19‑2010
C++
An algorithm for computing the Levenshtein distance between two sequences.

Skiplist
(link)
11‑20‑2010
C++
An implementation of a skip list, a randomized data structure for maintaining a sorted collection.

van Emde Boas Tree
(link)
11‑26‑2010
C++
An implementation of a sorted associative array backed by a van Emde Boas tree.

Cuckoo HashMap
(link)
11‑27‑2010
Java
An implementation of a hash table using cuckoo hashing.

Needleman-Wunsch Algorithm
(link)
11‑28‑2010
C++
An implementation of the Needleman-Wunsch algorithm for optimal string alignment.

Treap
(link)
11‑28‑2010
C++
An implementation of a sorted associative array backed by a treap.

Floyd-Warshall Algorithm
(link)
12‑10‑2010
Java
An implementation of the Floyd-Warshall algorithm for all-pairs shortest paths in a graph.

Power Iteration
(link)
12‑10‑2010
C++
An implementation of the power iteration algorithm for finding dominant eigenvectors.

Edmonds's Matching Algorithm
(link)
12‑15‑2010
Java
An implementation of Edmonds's matching algorithm for finding maximum matchings in undirected graphs.

Kosaraju's Algorithm
(link)
12‑15‑2010
Java
An implementation of Kosaraju's algorithm algorithm for finding strongly connected components of a directed graph.

2-SAT
(link)
12‑15‑2010
Java
A linear-time algorithm for solving 2-SAT.

Bellman-Ford Algorithm
(link)
12‑17‑2010
Java
An implementation of the Bellman-Ford algorithm for single-source shortest paths.

Topological Sort
(link)
12‑17‑2010
Java
An algorithm for computing a topological sort of a directed acyclic graph.

Graham Scan
(link)
12‑19‑2010
C++
An implementation of the Graham scan for finding convex hulls in 2D space.

Bipartite Testing
(link)
12‑19‑2010
Java
A linear-time algorithm for checking whether a directed graph is bipartite.

Johnson's Algorithm
(link)
12‑19‑2010
Java
An implementation of Johnson's algorithm for all-pairs shortest paths.

Strassen Algorithm
(link)
12‑20‑2010
C++
An implementation of the Strassen algorithm for fast matrix multiplication.

Cartesian Tree Sort
(link)
12‑21‑2010
C++
An implementation of Cartesian tree sort, an adaptive, out-of-place heapsort variant.

Ford-Fulkerson Algorithm
(link)
12‑21‑2010
Java
An implementation of the Ford-Fulkerson maximum-flow algorithm.

Scaling Ford-Fulkerson
(link)
12‑22‑2010
Java
An modification of the Ford-Fulkerson maximum-flow algorithm that uses scaling to achieve polynomial time..

Splay Tree
(link)
12‑27‑2010
C++
An implementation of a sorted associative array backed by a splay tree.

Ternary Search Tree
(link)
12‑28‑2010
C++
An implementation of a sorted set of strings backed by a ternary search tree.

Ring Buffer
(link)
12‑30‑2010
Java
An implementation of a FIFO queue using a ring buffer.

AVL Tree
(link)
12‑30‑2010
C++
A sorted associative container backed by an AVL tree.

Rabin-Karp Algorithm
(link)
1‑1‑2011
C++
An implementation of the Rabin-Karp algorithm for string matching.

RPN Evaluator
(link)
1‑18‑2011
C++ / strain
A library to tokenize and evaluate simple arithmetic expressions in reverse Polish notation.

Shunting-Yard Algorithm
(link)
1‑18‑2011
C++ / strain
An implementation of Dijkstra's shunting-yard algorithm for converting infix expressions to reverse-Polish notation.

Skew Binomial Heap
(link)
1‑20‑2011
C++
An implementation of a priority queue backed by a skew binomial heap.

2/3 Heap
(link)
3‑1‑2011
C++
An implementation of a priority queue whose branching factor alternates at different levels to maximize performance.

Zeckendorf Logarithm
(link)
3‑10‑2011
C++
An algorithm based on Zeckendorf representations that efficiently computes logarithms.

Factoradic Permutations
(link)
3‑17‑2011
C++
A set of algorithms for generating permutations using the factoradic number system.

Binary Cyclic Subsets
(link)
3‑20‑2011
C++
A set of algorithms for generating subsets in lexicographical order using binary numbers and cyclic shifts.

Fibonacci Iterator
(link)
3‑22‑2011
C++
An STL-style iterator for iterating over the Fibonacci numbers.

Fibonacci Search
(link)
3‑22‑2011
C++
An implementation of the Fibonacci search algorithm.

Euclid's Algorithm
(link)
4‑18‑2011
Haskell
An implementation of Euclid's algorithm and applications to continued fractions and the extended Euclidean algorithm.

Find Duplicate
(link)
4‑18‑2011
Python
An algorithm to find a repeated element in an array using Floyd's cycle-finding algorithm.

Permutation Generator
(link)
4‑19‑2011
Python
A generator for producing all permutations of a list of elements.

Matrix Find
(link)
4‑19‑2011
Python
A solution to the classic interview question of searching a sorted matrix for a particular value.

Binary GCD
(link)
4‑23‑2011
Scheme
An implementation of the binary GCD algorithm for computing greatest common divisors of nonnegative integers.

Knuth-Morris-Pratt Algorithm
(link)
5‑3‑2011
Python
An implementation of the Knuth-Morris-Pratt algorithm for fast string matching.

Kadane's Algorithm
(link)
5‑7‑2011
C++
An implementation of Kadane's algorithm for solving the maximum-weight subarray problem.

Karatsuba's Algorithm
(link)
8‑15‑2011
Python
An implementation of Karatsuba's algorithm for fast integer multiplication.

Min-Stack
(link)
8‑15‑2011
C++
An implementation of a LIFO stack that supports O(1) push, pop, and find-minimum.

Random Bag
(link)
8‑15‑2011
Python
A data structure that supports insertion and removal of a uniformly-random element.

Min-Queue
(link)
8‑15‑2011
C++
An implementation of a FIFO queue that supports O(1) push, pop, and find-minimum.

Lights-Out Solver
(link)
8‑29‑2011
C++
A solver for the game Lights Out using Gaussian elimination over GF(2).

Maximum Single-Sell Profit
(link)
11‑9‑2011
Python
Four algorithms for the maximum single-sell profit problem, each showing off a different algorithmic technique.

Generalized Kadane's Algorithm
(link)
11‑10‑2011
C++
A generalization of Kadane's algorithm for solving the maximum subarray problem subject to a length restriction.

Longest Range
(link)
11‑19‑2011
Java
An algorithm for solving the longest contiguous range problem.

Egyptian Fractions
(link)
11‑20‑2011
Python
An implementation of the greedy algorithm for finding Egyptian fractions.

LL(1) Parser Generator
(link)
11‑21‑2011
Java
An LL(1) parser generator.

LR(0) Parser Generator
(link)
11‑23‑2011
Java
An LR(0) parser generator.

Word Ladders
(link)
11‑27‑2011
JavaScript
A program for finding word ladders between two words.

88 Entries and Counting