Algorithms, topic by topic

An algorithm is a recipe a computer can follow: exact steps that turn an input into the answer. This site goes through the classic ones a topic at a time. Every page says what the algorithm does, how it works in plain words, gives working code in Python, Java and C++, and then opens up, if you want, into a worked example, the math of why it is correct and how fast it is, and an animation you can step through.

The picture above is one of them at work: nine real places on Mars joined by roads as long as the true distances between them, and the shortest route from Erebus Montes to Gale crater found by Dijkstra's algorithm.

Topics

Topic	What is in it
Foundations	How we measure speed (Big-O) and how recursion works: the two ideas every other page uses
Sorting	Eight ways to put a list in order, from bubble sort to radix sort, and when each one wins
Searching	Binary search and its cousins: halving the answer, two pointers and the sliding window
Data structures	Stacks, queues, hash tables, heaps, search trees, union-find, Fenwick and segment trees, tries
Graphs	Breadth- and depth-first search, topological order, shortest paths, spanning trees, strongly connected parts
Dynamic programming	Solving a big problem by remembering the answers to its smaller ones: coins, knapsacks, subsequences, edit distance
Greedy	Taking the best-looking step every time, and how to prove that it works: scheduling and Huffman codes
Strings	Finding a pattern in a text fast: KMP, Rabin-Karp and the Z-algorithm
Number theory	Greatest common divisors, primes by the sieve, and powers in \(O(\log n)\) steps
Backtracking	Trying every choice, but giving up early on dead ends: subsets, permutations, N-Queens

New to this? Start with How to read this site, then Big-O, then sorting.