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The following outline is provided as an overview of and topical guide to algorithms:

An algorithm is a finite, well-defined sequence of instructions or rules for solving a problem or performing a computation.^[1] Algorithms are central to computer science, mathematics, operations research, artificial intelligence,^[2] cryptography, data compression, computer graphics, bioinformatics, and many other fields.^[3] The study of algorithms includes their design, proof of correctness, efficiency, computational complexity, and implementation in computer programs.^[4][5]

• Algorithm — finite sequence of instructions for solving a problem or performing a computation
• Computer program — implementation of algorithms and data-processing instructions in a programming language
• Data structure — organization of data used by algorithms
• Heuristic — practical problem-solving method that may not guarantee an optimal solution
• Pseudocode — informal notation for describing algorithms
• Specification — formal or informal statement of what an algorithm is intended to do
• State — stored information used during a computation
• Termination analysis — study of whether an algorithm eventually halts
• Turing machine — mathematical model of computation used in computability theory

• Euclidean algorithm — ancient algorithm for computing the greatest common divisor
• Muhammad ibn Musa al-Khwarizmi — mathematician whose Latinized name is associated with the word algorithm
• Algorithmic logic — logic-based study of programs and algorithms
• Computability theory — study of what can be computed
• Church–Turing thesis — thesis concerning the nature of effective computation
• Turing machine — model formalizing computation
• Lambda calculus — formal system used in the study of computation
• Von Neumann architecture — computer architecture influencing practical algorithm implementation

• Analysis of algorithms — study of the correctness and efficiency of algorithms
• Asymptotic analysis — analysis of algorithm behavior as input size grows
• Big O notation — upper-bound notation for growth rates
• Big Omega notation — lower-bound notation for growth rates
• Big Theta notation — tight-bound notation for growth rates
• Time complexity — amount of time an algorithm uses as input size changes
• Space complexity — amount of memory an algorithm uses as input size changes
• Best, worst and average case — common forms of algorithm-performance analysis
• Amortized analysis — analysis of average cost over a sequence of operations
• Competitive analysis (online algorithm) — analysis of online algorithms compared with optimal offline algorithms
• Correctness (computer science) — property that an algorithm satisfies its specification
• Loop invariant — condition used to prove correctness of iterative algorithms
• Recurrence relation — equation often used to analyze recursive algorithms
• Master theorem (analysis of algorithms) — theorem for solving many divide-and-conquer recurrences

• Brute-force search — method of exhaustively checking candidate solutions
• Divide-and-conquer algorithm — technique that divides a problem into smaller subproblems
• Decrease and conquer — technique that reduces a problem to a smaller instance
• Dynamic programming — technique for solving problems with overlapping subproblems and optimal substructure
• Greedy algorithm — algorithm that makes locally optimal choices
• Backtracking — search technique that abandons partial solutions that cannot lead to valid solutions
• Branch and bound — search technique using bounds to eliminate candidate solutions
• Randomized algorithm — algorithm using randomness as part of its logic
• Approximation algorithm — algorithm that finds near-optimal solutions for hard optimization problems
• Online algorithm — algorithm that receives input incrementally
• Parallel algorithm — algorithm designed for parallel computation
• Distributed algorithm — algorithm designed for distributed systems
• Streaming algorithm — algorithm for processing data streams with limited memory
• Quantum algorithm — algorithm designed for quantum computers^[6]

• Scheduling algorithms
• Round-robin scheduling
• Shortest job next
• Rate-monotonic scheduling
• Earliest deadline first scheduling
• Page replacement algorithm
• Least recently used
• Cache replacement policies

• Linear search
• Binary search algorithm
• Interpolation search
• Exponential search
• Jump search
• Depth-first search
• Breadth-first search
• Best-first search
• Beam search
• A* search algorithm
• Dijkstra's algorithm
• Iterative deepening depth-first search
• Monte Carlo tree search

• String-searching algorithm
• Knuth–Morris–Pratt algorithm
• Boyer–Moore string-search algorithm
• Rabin–Karp algorithm
• Aho–Corasick algorithm
• Levenshtein distance
• Edit distance
• Longest common subsequence
• Longest common substring
• Suffix tree
• Suffix array
• Burrows–Wheeler transform
• Regular expression
• Parsing
• Earley parser
• CYK algorithm

• Linear programming
• Simplex algorithm
• Interior-point method
• Integer programming
• Dynamic programming
• Gradient descent
• Stochastic gradient descent
• Newton's method
• Quasi-Newton method
• Broyden–Fletcher–Goldfarb–Shanno algorithm
• Lagrange multiplier
• Constraint satisfaction problem
• Local search (optimization)
• Hill climbing
• Tabu search
• Genetic algorithm
• Ant colony optimization algorithms
• Particle swarm optimization
• Evolutionary algorithm

• Convex hull algorithms
• Graham scan
• Gift wrapping algorithm
• Delaunay triangulation
• Voronoi diagram
• Line segment intersection
• Point location
• Closest pair of points problem
• Rotating calipers
• Sweep line algorithm

• Bresenham's line algorithm
• Flood fill
• Scanline rendering
• Z-buffering
• Ray casting
• Ray tracing (graphics)
• Path tracing
• Phong shading
• Texture mapping
• Bump mapping
• Normal mapping
• Marching cubes
• Canny edge detector
• Random sample consensus (RANSAC)
• Scale-invariant feature transform
• Hough transform
• Seam carving

• B-tree
• B+ tree
• Hash join
• Sort-merge join
• Query optimization
• PageRank
• Inverted index
• Tf–idf
• BM25
• Locality-sensitive hashing
• MapReduce
• Consistent hashing

• Needleman–Wunsch algorithm
• Smith–Waterman algorithm
• BLAST (biotechnology)
• Sequence alignment
• Hidden Markov model
• Viterbi algorithm
• Phylogenetic tree
• Molecular dynamics
• Finite element method
• Fast multipole method

• P (complexity)
• NP (complexity)
• NP-completeness
• NP-hardness
• EXPTIME
• PSPACE
• BPP (complexity)
• BQP
• Undecidable problem
• Halting problem
• Rice's theorem
• No free lunch theorem

• List of algorithms
• List of artificial intelligence algorithms
• List of combinatorial algorithms

• Algorithm engineering
• Outline of artificial intelligence
• Outline of computer science
• Procedure (computer science)
• List of data structures
• List of numerical analysis topics
• List of optimization software

• Cormen, Thomas H.; Leiserson, Charles E.; Rivest, Ronald L.; Stein, Clifford (2022). Introduction to Algorithms (4th ed.). MIT Press. ISBN 978-0-262-04630-5.
• Knuth, Donald E. (1968). The Art of Computer Programming. Addison-Wesley. ISBN 978-0-201-89683-1.
• Kleinberg, Jon; Tardos, Éva (2005). Algorithm Design. Pearson Education. ISBN 978-0-321-29535-4.
• Skiena, Steven S. (2020). The Algorithm Design Manual (3rd ed.). Springer. ISBN 978-3-030-54255-9.

• Media related to Algorithms at Wikimedia Commons
• Algorithms at Wikibooks
• Learning materials related to Algorithms at Wikiversity