Damerau-Levenshtein Distance
Edit distance allowing insertion, deletion, substitution, and transposition of adjacent characters.
Visualization
Interactive visualization for Damerau-Levenshtein Distance
Interactive visualization with step-by-step execution
Implementation
1function damerauLevenshtein(s1: string, s2: string): number {
2 const m = s1.length, n = s2.length;
3 const dp: number[][] = Array(m + 1).fill(0).map(() => Array(n + 1).fill(0));
4 for (let i = 0; i <= m; i++) dp[i][0] = i;
5 for (let j = 0; j <= n; j++) dp[0][j] = j;
6 for (let i = 1; i <= m; i++) {
7 for (let j = 1; j <= n; j++) {
8 const cost = s1[i - 1] === s2[j - 1] ? 0 : 1;
9 dp[i][j] = Math.min(
10 dp[i - 1][j] + 1,
11 dp[i][j - 1] + 1,
12 dp[i - 1][j - 1] + cost
13 );
14 if (i > 1 && j > 1 && s1[i - 1] === s2[j - 2] && s1[i - 2] === s2[j - 1]) {
15 dp[i][j] = Math.min(dp[i][j], dp[i - 2][j - 2] + 1);
16 }
17 }
18 }
19 return dp[m][n];
20}Deep Dive
Theoretical Foundation
Extension of Levenshtein allowing transpositions (swapping adjacent chars). More realistic for typos. dp[i][j] considers 4 operations.
Complexity
Time
O(n×m)
O(n×m)
O(n×m)
Space
O(n×m)
Applications
Industry Use
Spell checkers
OCR error correction
DNA sequence alignment
Use Cases
Related Algorithms
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Rabin-Karp Algorithm
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Boyer-Moore Algorithm
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