Edit Distance

Hard Dynamic Programming

Find the minimum number of single-character insertions, deletions or substitutions to turn one string into another (Levenshtein distance). 2-D DP.

Sample input

horse -> ros

Sample output

Solution

def edit_distance(a, b):
    m, n = len(a), len(b)
    dp = [[0] * (n + 1) for _ in range(m + 1)]
    for i in range(m + 1):
        dp[i][0] = i
    for j in range(n + 1):
        dp[0][j] = j
    for i in range(1, m + 1):
        for j in range(1, n + 1):
            if a[i - 1] == b[j - 1]:
                dp[i][j] = dp[i - 1][j - 1]
            else:
                dp[i][j] = 1 + min(dp[i - 1][j], dp[i][j - 1], dp[i - 1][j - 1])
    return dp[m][n]

print(edit_distance("horse", "ros"))

function editDistance(a, b) {
  const m = a.length, n = b.length;
  const dp = Array.from({ length: m + 1 }, () => new Array(n + 1).fill(0));
  for (let i = 0; i <= m; i++) dp[i][0] = i;
  for (let j = 0; j <= n; j++) dp[0][j] = j;
  for (let i = 1; i <= m; i++) {
    for (let j = 1; j <= n; j++) {
      if (a[i - 1] === b[j - 1]) {
        dp[i][j] = dp[i - 1][j - 1];
      } else {
        dp[i][j] = 1 + Math.min(dp[i - 1][j], dp[i][j - 1], dp[i - 1][j - 1]);
      }
    }
  }
  return dp[m][n];
}

console.log(editDistance("horse", "ros"));

public class Main {
    static int editDistance(String a, String b) {
        int m = a.length(), n = b.length();
        int[][] dp = new int[m + 1][n + 1];
        for (int i = 0; i <= m; i++) dp[i][0] = i;
        for (int j = 0; j <= n; j++) dp[0][j] = j;
        for (int i = 1; i <= m; i++) {
            for (int j = 1; j <= n; j++) {
                if (a.charAt(i - 1) == b.charAt(j - 1)) {
                    dp[i][j] = dp[i - 1][j - 1];
                } else {
                    dp[i][j] = 1 + Math.min(dp[i - 1][j - 1], Math.min(dp[i - 1][j], dp[i][j - 1]));
                }
            }
        }
        return dp[m][n];
    }

    public static void main(String[] args) {
        System.out.println(editDistance("horse", "ros"));
    }
}

fun editDistance(a: String, b: String): Int {
    val m = a.length
    val n = b.length
    val dp = Array(m + 1) { IntArray(n + 1) }
    for (i in 0..m) dp[i][0] = i
    for (j in 0..n) dp[0][j] = j
    for (i in 1..m) {
        for (j in 1..n) {
            if (a[i - 1] == b[j - 1]) {
                dp[i][j] = dp[i - 1][j - 1]
            } else {
                dp[i][j] = 1 + minOf(dp[i - 1][j], dp[i][j - 1], dp[i - 1][j - 1])
            }
        }
    }
    return dp[m][n]
}

fun main() {
    println(editDistance("horse", "ros"))
}

func editDistance(_ a: String, _ b: String) -> Int {
    let ac = Array(a), bc = Array(b)
    let m = ac.count, n = bc.count
    var dp = Array(repeating: Array(repeating: 0, count: n + 1), count: m + 1)
    for i in 0...m { dp[i][0] = i }
    for j in 0...n { dp[0][j] = j }
    if m >= 1 && n >= 1 {
        for i in 1...m {
            for j in 1...n {
                if ac[i - 1] == bc[j - 1] {
                    dp[i][j] = dp[i - 1][j - 1]
                } else {
                    dp[i][j] = 1 + min(dp[i - 1][j], dp[i][j - 1], dp[i - 1][j - 1])
                }
            }
        }
    }
    return dp[m][n]
}

print(editDistance("horse", "ros"))

int editDistance(String a, String b) {
  final m = a.length;
  final n = b.length;
  final dp = List.generate(m + 1, (_) => List.filled(n + 1, 0));
  for (var i = 0; i <= m; i++) dp[i][0] = i;
  for (var j = 0; j <= n; j++) dp[0][j] = j;
  for (var i = 1; i <= m; i++) {
    for (var j = 1; j <= n; j++) {
      if (a[i - 1] == b[j - 1]) {
        dp[i][j] = dp[i - 1][j - 1];
      } else {
        final del = dp[i - 1][j];
        final ins = dp[i][j - 1];
        final sub = dp[i - 1][j - 1];
        var best = del < ins ? del : ins;
        if (sub < best) best = sub;
        dp[i][j] = 1 + best;
      }
    }
  }
  return dp[m][n];
}

void main() {
  print(editDistance("horse", "ros"));
}

#include <iostream>
#include <vector>
#include <string>
#include <algorithm>
using namespace std;

int editDistance(const string& a, const string& b) {
    int m = a.size(), n = b.size();
    vector<vector<int>> dp(m + 1, vector<int>(n + 1, 0));
    for (int i = 0; i <= m; i++) dp[i][0] = i;
    for (int j = 0; j <= n; j++) dp[0][j] = j;
    for (int i = 1; i <= m; i++) {
        for (int j = 1; j <= n; j++) {
            if (a[i - 1] == b[j - 1]) {
                dp[i][j] = dp[i - 1][j - 1];
            } else {
                dp[i][j] = 1 + min({dp[i - 1][j], dp[i][j - 1], dp[i - 1][j - 1]});
            }
        }
    }
    return dp[m][n];
}

int main() {
    cout << editDistance("horse", "ros") << endl;
    return 0;
}

#include <stdio.h>
#include <string.h>

int minOf(int a, int b, int c) {
    int m = a < b ? a : b;
    return m < c ? m : c;
}

int editDistance(const char *a, const char *b) {
    int m = strlen(a), n = strlen(b);
    int dp[100][100];
    for (int i = 0; i <= m; i++) dp[i][0] = i;
    for (int j = 0; j <= n; j++) dp[0][j] = j;
    for (int i = 1; i <= m; i++) {
        for (int j = 1; j <= n; j++) {
            if (a[i - 1] == b[j - 1]) {
                dp[i][j] = dp[i - 1][j - 1];
            } else {
                dp[i][j] = 1 + minOf(dp[i - 1][j], dp[i][j - 1], dp[i - 1][j - 1]);
            }
        }
    }
    return dp[m][n];
}

int main() {
    printf("%d\n", editDistance("horse", "ros"));
    return 0;
}