Algorithm¶

Version: v4 · 2026-10-17 · History
Prime #: 11
Domain group: Applied Sciences & Engineering
Origin domain: Computer Science & Software Engineering
Also from: Mathematics
Related primes: Function (Mapping)

Core Idea¶

Step-by-step procedure for solving a problem.

How would you explain it like I'm…

Step-by-Step Recipe

When you make a peanut butter sandwich, you do the same steps in the same order every time: get bread, open jar, spread, close. If you follow the steps just right, you always end up with a sandwich. A recipe like that, written so anyone can follow it, is an algorithm.

Recipe of Exact Steps

An algorithm is a list of steps that takes some starting stuff and turns it into a result. The steps have to be clear enough that anyone — or even a machine — could follow them without guessing. There must be a finite number of steps, each step must be unambiguous, and the procedure has to stop. A recipe, the long-division method, and instructions for tying your shoes are all algorithms. The point isn't just what answer you want; it's the exact, repeatable way of getting there.

Step-by-Step Procedure

An algorithm is a finite, definite, effective procedure for transforming inputs into outputs by a prescribed sequence of steps. The essential commitment is to *procedure*: not just what the answer is (that's a function) but the ordered, mechanically executable way of producing it. Every algorithm specifies its admissible inputs, a finite sequence of unambiguous steps, a termination condition it is guaranteed (or expected) to reach, and the result it produces at termination. The classical constraints — finiteness (it ends), definiteness (each step is unambiguous), and effectiveness (each step can actually be carried out) — together ensure the procedure can be executed without needing intelligence or judgment to fill in gaps.

An algorithm is a finite, definite, effective procedure for transforming inputs into outputs by a sequence of prescribed steps. The essential commitment is to *procedure*: not merely what the output should be — that is a function, a mathematical mapping — but the ordered, mechanically executable way of producing it. Every algorithm specifies four ingredients: (1) its admissible inputs, the class of objects it operates on; (2) a finite sequence of unambiguous steps; (3) a termination condition that the procedure is guaranteed (or in randomized cases, expected) to reach; and (4) a result it produces at termination. The classical constraints, articulated in Knuth's standard treatment, are finiteness (the procedure halts in a finite number of steps), definiteness (each step is precisely specified, with no ambiguity), and effectiveness (each step is sufficiently basic that it can in principle be carried out exactly by a person with paper and pencil). Together these constraints ensure the procedure can be executed without appeal to intelligence or judgment. The distinction between algorithm and function is structural: many distinct algorithms can compute the same function (e.g., several sorting algorithms all sort), and one algorithm's complexity profile and resource requirements can differ sharply from another's even when their outputs agree.

Broad Use¶

Guides reasoning in structured problem-solving (e.g., recipes, workflows, or business processes).

Clarity¶

Breaks processes into repeatable, structured steps, like recipes or sorting algorithms.

Manages Complexity¶

Standardizes problem-solving into repeatable steps.

Abstract Reasoning¶

Encourages structured, sequential reasoning and process optimization.

Knowledge Transfer¶

Found in computer science, logistics, and medicine (diagnostic protocols).

Example¶

A navigation app uses Dijkstra's algorithm to find the shortest path between two locations.

Relationships to Other Abstractions¶

Current abstraction Algorithm Prime

Parents (1) — outgoing typed relations

Algorithm presupposes, conditional Function (Mapping) Prime

An algorithm presupposes Function Mapping when its complete declared inputs determine one terminating output; unmodeled random choices or partial behavior fall outside this condition.

Condition / exception The procedure's extensional result is total and single-valued on a fully declared input domain; any random choices or relevant environment state are fixed as explicit inputs, and every admitted execution in that domain terminates with one result.

Children (80) — abstractions linked here by typed relations

AKS primality test Domain-specific is a kind of Algorithm

AKS is a deterministic finite procedure for deciding primality.
Alternating-Direction Implicit Method Domain-specific is a kind of Algorithm

Alternating implicit solves form a definite numerical procedure for a specified target.
Bisection Method Domain-specific is a kind of Algorithm

Algorithm is the strict parent because bisection prescribes finite executable steps, maintains a correctness invariant, terminates under a tolerance rule, and has an explicit evaluation bound.
Block walking Domain-specific is a kind of Algorithm

Block walking is a domain-specific kind of Algorithm: Block walking is a combinatorial proof technique that traverses structured blocks of a configuration according to local transition rules so a global counting, ordering, or existence result follows from the walk.
Bruun's FFT algorithm Domain-specific is a kind of Algorithm

It is a finite computational procedure for the DFT.

▸ Show 75 more

Chang–Roberts Algorithm Domain-specific is a kind of Algorithm
**`prime:algorithm`** is the broader abstraction this entry instantiates: Chang–Roberts is a finite rule system mapping admissible distributed executions to a selected leader.
Constant false alarm rate Domain-specific is a kind of Algorithm
CFAR is a strict Algorithm: finite reference-window inputs are transformed by an adaptive estimator and threshold rule into a terminating target/no-target decision.
Dadda multiplier Domain-specific is a kind of Algorithm
Dadda multiplier is a domain-specific kind of Algorithm: Hardware multiplier design.
Davis–Putnam Algorithm Domain-specific is a kind of Algorithm
**`prime:algorithm`** is the broader abstraction this entry instantiates.
DIIS Domain-specific is a kind of Algorithm
DIIS is an iterative residual-minimizing procedure for extrapolating improved solutions.
Direct Linear Transformation Domain-specific is a kind of Algorithm
**`prime:algorithm`** is the broader abstraction this entry instantiates.
Dispersive Flies Optimisation Domain-specific is a kind of Algorithm
DFO is a finite randomized input-to-output procedure with prescribed update steps and a stopping budget.
Division Algorithm Domain-specific is a kind of Algorithm
Division Algorithm is a strict specialization of `prime:algorithm`: it is a terminating, unambiguous procedure with defined inputs and outputs, but adds the arithmetic quotient–remainder contract.
Enumeration Algorithm Domain-specific is a kind of Algorithm
**`algorithm` — confirmed strict parent.** Every enumeration algorithm is an algorithm: it accepts an encoded input, executes definite effective steps, preserves correctness invariants, and has explicit termination and resource semantics.
Euler Method Domain-specific is a kind of Algorithm
**`prime:algorithm`** is the broader abstraction this entry instantiates.
Evolutionary Algorithm Domain-specific is a kind of Algorithm
**`prime:algorithm`** is the broader abstraction this entry instantiates.
Exponential Integrator Domain-specific is a kind of Algorithm
Exponential Integrator instantiates **Algorithm**: it is a terminating computational procedure for advancing a numerical state, and `prime:algorithm` is the broader abstraction this entry instantiates.
False position method Domain-specific is a kind of Algorithm
False-position methods are algorithms for solving a declared equation for an unknown.
Fast-and-Frugal Trees Domain-specific is a kind of Algorithm
A fast-and-frugal tree specializes Algorithm to finite ordered cue tests with one-sided early category exits.
Floyd's Cycle-Finding Algorithm Domain-specific is a kind of Algorithm
Floyd's two-speed successor procedure is a specific algorithm for deciding whether one reachable orbit repeats.
Forward–Backward Algorithm Domain-specific is a kind of Algorithm
Forward–Backward Algorithm is a strict specialization of prime:algorithm: it defines inputs, finite recursive steps, termination after two passes, and posterior-marginal outputs.
Fourier–Motzkin Elimination Domain-specific is a kind of Algorithm
**`prime:algorithm` (proposed primary parent, strict subsumption).** Fourier–Motzkin is a definite input-to-output procedure with correctness and resource semantics.
Frontal Solver Domain-specific is a kind of Algorithm
**Algorithm** is the strict parent because the frontal method is a terminating constructive procedure with specified inputs, output factorization, correctness, and time/storage bounds.
Gauss–Newton Algorithm Domain-specific is a kind of Algorithm
**prime:algorithm** is the broader abstraction this entry instantiates.
Greedy Randomized Adaptive Search Procedure Domain-specific is a kind of Algorithm
GRASP is a stepwise randomized construction and local-improvement procedure for combinatorial optimization.
Held–Karp algorithm Domain-specific is a kind of Algorithm
The method is a finite exact algorithm organized by dynamic-programming states.
Hunt–Szymanski Algorithm Domain-specific is a kind of Algorithm
**prime:algorithm** is the broader abstraction this entry instantiates.
Hybrid algorithm Domain-specific is a kind of Algorithm
The identity is a composite algorithmic strategy.
In-Place Algorithm Domain-specific is a kind of Algorithm
A strict in-place algorithm is an algorithm distinguished by same-buffer output and a constant counted auxiliary-unit budget.
Knuth–Eve Algorithm Domain-specific is a kind of Algorithm
Knuth–Eve instantiates **Algorithm** through a finite preprocessing procedure and a finite evaluator with a correctness invariant.
Knuth–Plass Line-Breaking Algorithm Domain-specific is a kind of Algorithm
**`prime:algorithm` — proposed strict subsumption parent.** For a finite paragraph and fixed parameter contract, it is a definite terminating procedure with admissible input, effective steps, a breakpoint/line output, and correctness relative.
Linear-quadratic regulator rapidly exploring random tree Domain-specific is a kind of Algorithm
Linear-quadratic regulator rapidly exploring random tree is a domain-specific instance of algorithm under its frozen identity. The complete catalog already supplies this broader identity.
Luhn Mod N Algorithm Domain-specific is a kind of Algorithm
Luhn Mod N specializes **Algorithm**: it is a finite deterministic generation/validation procedure with defined input, state, and output.
Markov algorithm Domain-specific is a kind of Algorithm
It is a finite rule-governed computational procedure.
Maze generation algorithm Domain-specific is a kind of Algorithm
It is an automated construction procedure.
Method of continued fractions Domain-specific is a kind of Algorithm
The continued-fractions method is a repeatable computational procedure for solving declared integral equations.
Nearest-Neighbor Chain Algorithm Domain-specific is a kind of Algorithm
**Algorithm** is the broader abstraction this entry instantiates: NN-chain is a strict algorithmic procedure with specified state, local-neighbor search, reciprocal-pair test, merge, and termination.
Network Simplex Algorithm Domain-specific is a kind of Algorithm
**`prime:algorithm` — strict subsumption.** Network simplex is a definite iterative procedure mapping a feasible minimum-cost-flow instance and starting-basis construction to an optimal flow or an infeasibility/unboundedness disposition under.
Newest Vertex Bisection Domain-specific is a kind of Algorithm
The labeled midpoint-split and conformity-completion rules specify a particular finite mesh-refinement algorithm under admissible initial labeling.
Non-Blocking Algorithm Domain-specific is a kind of Algorithm
A non-blocking algorithm is an executable concurrent procedure with an additional independent-progress condition.
Powerset Construction Domain-specific is a kind of Algorithm
Powerset construction is a finite effective conversion procedure that explores subset states and defines deterministic transitions and acceptance.
Pseudorandom Number Generator Domain-specific is a kind of Algorithm
PRNG is a specialization of `prime:algorithm`.
Pseudospectral time-domain method Domain-specific is a kind of Algorithm
The method is a numerical algorithm for wave evolution.
PTAS Reduction Domain-specific is a kind of Algorithm
**Algorithm** is the strict parent because the reduction certificate is a finite polynomial-time procedure for transforming an instance and tolerance and recovering a source solution with a proved postcondition.
QR Algorithm Domain-specific is a kind of Algorithm
QR Algorithm specializes `prime:algorithm`, the broader abstraction.
Random sample consensus Domain-specific is a kind of Algorithm
RANSAC is literally a repeatable randomized problem-solving procedure with explicit sampling, fitting, scoring, stopping, and refinement stages; What makes it its own entry: the random-minimal-hypothesis, thresholded-consensus, best-model, and refit loop, not robust estimation generally, random subsampling alone, or one software library.
Randomized Algorithm Domain-specific is a kind of Algorithm
A randomized algorithm is an algorithm whose internal random choices affect fixed-input behavior.
Reversible reference system propagation algorithm Domain-specific is a kind of Algorithm
r-RESPA is literally a repeatable state-update algorithm; its operator factorization and molecular-dynamics semantics form the DS residual.
Ridders' Method Domain-specific is a kind of Algorithm
Ridders' method is a specified iterative algorithm for finding a continuous real function's bracketed zero.
RNA22 Target-Prediction Algorithm Domain-specific is a kind of Algorithm
RNA22 strictly specializes **Algorithm**.
Search Algorithm Domain-specific is a kind of Algorithm
A search algorithm is an algorithm specialized to exploring a generated state space by a frontier strategy until a goal or stopping report is reached.
Self-organizing map Domain-specific is a kind of Algorithm
The SOM is literally a repeatable update algorithm with inputs, state, selection, neighborhood update, and stopping conditions; its topology-oriented competitive-learning rule supplies the DS specialization.
Sequential decoding Domain-specific is a kind of Algorithm
The method is a guided search algorithm over code paths.
Shinnar–Le Roux algorithm Domain-specific is a kind of Algorithm
Shinnar–Le Roux algorithm is a domain-specific kind of Algorithm: The Shinnar-Le Roux algorithm transforms between radio-frequency pulse parameters and a pair of polynomials so selective magnetic-resonance excitation profiles can be synthesized and analyzed through recursive filter-like operations.
Sorting Algorithm Domain-specific is a kind of Algorithm
A sorting algorithm is an algorithm specialized to rearranging a finite sequence into a key-defined total order under explicit resource bounds.
Stable Sort Domain-specific is a kind of Algorithm
Stable Sort is a domain-specific kind of algorithm under its frozen identity and differentia. Complete-catalog comparison found the corresponding live broader identity.
Steensgaard's algorithm Domain-specific is a kind of Algorithm
It is a specific scalable analysis algorithm.
Swedish Interactive Thresholding Algorithm Domain-specific is a kind of Algorithm
SITA is a strict specialization of **Algorithm**: it is a defined procedure mapping a perimetric test configuration and sequential patient responses to local threshold estimates and reliability information.
Tate's Algorithm Domain-specific is a kind of Algorithm
Tate's algorithm is an effective terminating local-arithmetic decision procedure with a finite resource account on its declared valid input domain.
Ternary search Domain-specific is a kind of Algorithm
It remains its own entry because its identity is fixed by the ordered domain, unimodality and strictness assumptions, minimization or maximization direction, probe placement, tie rule, discrete or continuous termination, evaluation precision, and complexity.
Thompson Sampling Domain-specific is a kind of Algorithm
Thompson Sampling is a domain-specific kind of algorithm under its frozen identity and differentia.
Topological Sorting Domain-specific is a kind of Algorithm
Topological sorting is an algorithm specialized to producing a linear extension of a precedence DAG or reporting a cycle in linear time.
Tournament sort Domain-specific is a kind of Algorithm
It is a sorting procedure organized as repeated tournament updates.
Tree Sort Domain-specific is a kind of Algorithm
The accepted reference-grade review places Tree Sort under Algorithm because the child instantiates or depends on the parent's broader structure while retaining its own constitutive identity.
Trellis quantization Domain-specific is a kind of Algorithm
The candidate is literally a finite dynamic-programming or shortest-path procedure over trellis states; its quantization and codec rate-distortion semantics supply the DS specialization.
Trial Division Domain-specific is a kind of Algorithm
Trial division is a finite exact-search algorithm over bounded proper-divisor candidates.
Truth-table reduction Domain-specific is a kind of Algorithm
A truth-table reduction is witnessed by a finite effective input-to-query-to-output procedure with a correctness contract.
Type Inference Domain-specific is a kind of Algorithm
Type inference is an algorithm specialized to generating and unifying typing constraints to return a principal type or a located type error.
Unicode Collation Algorithm Domain-specific is a kind of Algorithm
Unicode Collation Algorithm is a strict domain-specific instance of **`prime:algorithm`**.
Variable Elimination Domain-specific is a kind of Algorithm
Variable Elimination specializes `prime:algorithm`: inputs, ordered effective steps, exact output, termination, and resource bounds are explicit.
Verification-based message-passing algorithms in compressed sensing Domain-specific is a kind of Algorithm
Verification-based message-passing methods are algorithms for sparse-signal recovery.
Verlet Integration Domain-specific is a kind of Algorithm
Verlet Integration specializes `prime:algorithm`: it is a definite finite update procedure with inputs, outputs, accuracy, stability, and resource bounds.
Vincenty's formulae Domain-specific is a kind of Algorithm
Vincenty's formulae is a domain-specific instance of algorithm under its frozen identity. The complete catalog already supplies this broader identity.
Yannakakis Algorithm for Acyclic Joins Domain-specific is a kind of Algorithm
**`prime:algorithm` — proposed strict subsumption parent.** Yannakakis has a finite input, effective ordered steps, termination, correctness condition, output, and resource bound.
Yo-Yo Leader-Election Algorithm Domain-specific is a kind of Algorithm
The broader abstraction is `prime:algorithm`: Yo-Yo is a finite, specified procedure mapping an identified connected network to a leader designation, with correctness and termination obligations.
Ziggurat Algorithm Domain-specific is a kind of Algorithm
Ziggurat Algorithm is a strict specialization of `prime:algorithm`: it is a finite executable procedure with precomputation, random inputs, branching tests, and an output contract.
Bailey–Borwein–Plouffe Formula Domain-specific presupposes Algorithm
The broader abstraction is `prime:algorithm` by strict compositional presupposition.
Linear-on-the-Fly Testing Domain-specific includes Algorithm
An assembly algorithm is an internal constituent of each LOFT administration.
Quantum Computing Domain-specific presupposes Algorithm
Quantum Computing presupposes Algorithm: the parent's defining role is necessary to the child's frozen mechanism or criterion.
Computability Prime presupposes Algorithm
Per dossier and file: computability is 'the boundary/meta-level relation that algorithm presupposes' — the existence-question (does an effective procedure exist at all?) over algorithm's central object.

Hierarchy path (1) — routes to 1 parentless root

Algorithm → presupposes, conditional Function (Mapping)

Not to Be Confused With¶

Algorithm is not Transformation because transformation is a general mapping rule from inputs to outputs; an algorithm is a sequence of deterministic steps that, when executed, performs a computation or transformation—transformation is the abstract mapping; algorithm is the executable procedure.
Algorithm is not Recursion because recursion is the self-referential pattern where a function calls itself with reduced problem size; an algorithm may use recursion as a technique but can also use iteration or other control structures—recursion is a specific control pattern; algorithm is the broader executable procedure.
Algorithm is not Heuristic because a heuristic is a practical rule or shortcut that produces good (but not guaranteed optimal) results efficiently; an algorithm is a step-by-step procedure that is deterministic and guaranteed to terminate with a specified output—heuristic sacrifices optimality for efficiency; algorithm guarantees correctness.
Algorithm is not Iteration because iteration is the repetition of a process; an algorithm may use iteration but also uses other control structures (conditionals, recursion)—iteration is a control technique; algorithm is the full executable procedure.
Algorithm is not Sequencing because sequencing is the ordering of actions in time; an algorithm specifies not just the sequence but the logical control flow, conditionals, and data transformations—sequencing is the ordering; algorithm is the complete procedure with logic and data structures.