Algorithms & Data Structures
the bound is a claim, and it is checkable
Concept

Index — where it appears

A structure built once over a text so that later queries need not scan it, worth its construction cost only when enough queries follow to divide it by. It is worth its construction cost only once enough queries follow to divide it by, and its own size is the thing this collection measured at zero for four phases.

Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.

Also named here as state machine — the same set of essays touches all of them, so they are one junction rather than several.

roothseirhesssolid: a transition on a character · dashed: a suffix or failure link10 states for 12 pattern characters

One pass for every pattern at once

Sixty-four patterns, one text, twenty thousand characters read. Running this site's KMP once per pattern reads 1,595,445 — and an implementation missing one kind of link finds fewer occurrences, reads exactly as much, and looks better on every counter.

text · Automaton —1234152abcbcbccbsolid: a transition on a character · dashed: a suffix or failure link8 states ≤ 9, 9 transitions ≤ 11

Every substring, in fewer states than substrings

A text of 512 characters has 129,416 distinct substrings. A machine that recognises every one of them, and nothing else, needs 831 states — and the bound it is under, 2n − 1, is reached exactly by a string one line long.

structures · Automaton

Named alongside it

The objects these essays reach for when they reach for this one.

AlphabetAmortised analysisAutomatonMeasured countState machineString matchingSuffix automatonAho-corasickAuxiliary spaceCharacter comparisonFailure functionKmp

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