Minimum Edit Distance

Given two wordsword1andword2, find the minimum number of steps required to convertword1toword2. (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

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 ++) {

                if(word1.charAt(i - 1) == word2.charAt(j - 1))
                    dp[i][j] = dp[i - 1][j - 1];
                else
                    dp[i][j] = Math.min(dp[i - 1][j - 1], Math.min(dp[i - 1][j], dp[i][j - 1])) + 1;
            }
        }    

        return dp[m][n];
    }
}