Edit Distance

Given two words word1 and word2, find the minimum number of steps required to convert word1 to word2. (each operation is counted as 1 step.)

You have the following 3 operations permitted on a word:

a) Insert a character b) Delete a character c) Replace a character

Solution:

public class Solution {
    public int minDistance(String word1, String word2) {
        int m = word1.length();
        int n = word2.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++){
                int step = word1.charAt(i-1)==word2.charAt(j-1) ? 0 : 1;
                dp[i][j] = Math.min(dp[i-1][j-1]+step, Math.min(dp[i-1][j], dp[i][j-1])+1);
            }
        }
        return dp[m][n];
    }
}