LeetCode 583. Delete Operation for Two Strings

Given two words word1 and word2, find the minimum number of steps required to make word1 and word2 the same, where in each step you can delete one character in either string.

idea:
this is the edit distance problem with only delete operation allowed.
2D array

this code is very much alike edit distance.

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 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]; //don't need to delete anything
                } else {
                    int min = Math.min(dp[i-1][j], dp[i][j-1]) + 1;
                    dp[i][j] = Math.min(min, dp[i-1][j-1]+2);
                }
            }
        }
        return dp[m][n];
        
    }
}