Edit Distance -- DP -- Leetcode

Question:

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

Answer:
DP!
public int minDistance(String word1, String word2) {
        int len1 = word1.length();
        int len2 = word2.length();
        if(len1==0)return len2;
        if(len2==0)return len1;
     
        int[][] dp = new int[len1+1][len2+1];
     
        for(int i=0;i<=len1;++i){
            dp[i][0] = i;
        }
        for(int i=1;i<=len2;++i){
            dp[0][i] = i;
        }
     
        for(int i=0;i<len1;++i){
            for(int j=0;j<len2;++j){
                // DP formular!
                if(word1.charAt(i) == word2.charAt(j)){
                    dp[i+1][j+1] = dp[i][j];
                }else{
                    dp[i+1][j+1] = minInThree(dp[i][j+1],  dp[i+1][j],  dp[i][j]) + 1;
                }
            }
        }
        return dp[len1][len2];
    }
 
    public int minInThree(int a, int b, int c){
        return Math.min(c, Math.min(a,b));
    }