Why it matters

Edit distance is foundational. Spell-check, diff, DNA alignment use.

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The architecture

DP table dp[i][j].

Insert, delete, replace.

O(nm) time.

Edit distanceDP tabledp[i][j]Opsinsert, delete, replaceTimeO(nm)Levenshtein 1965; O(nm); Ukkonen O(nD) for small distance
Edit distance.
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How it works end to end

Levenshtein 1965.

Row-only O(min).

Ukkonen for small D.