72. 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

DP

public class Solution {
    public int minDistance(String word1, String word2) {
        if(word1 == null && word2 == null) return 0;
        if(word1 == null || word2 == null) return word1 == null ? word2.length() : word1.length();
        if(word1.length() == 0 || word2.length() == 0) return word1.length() == 0 ? word2.length() : word1.length();

        int m = word1.length()+1;
        int n = word2.length()+1;
        int[][] dp = new int[m][n];
        for(int i=0; i<m;i++) dp[i][0] = i;
        for(int i=0;i<n; i++) dp[0][i] = i;
        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], Math.min(dp[i-1][j-1], dp[i][j-1])) + 1;
                }
            }
        }

        return dp[m-1][n-1];

    }
}