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.

Example

Input: "sea", "eat"
Output: 2
Explanation: You need one step to make "sea" to "ea" and another step to make "eat" to "ea".

Note:
The length of given words won't exceed 500.
Characters in given words can only be lower-case letters.

思路：两字符串总长-2倍最长公共字串LCS 即为删除的最小步数

import org.junit.Test;

public class DeleteOperationForTwoStrings {
    public int minDistance(String word1, String word2) {
        int m = word1.length(), n = word2.length();
        int[][] dp = new int[m + 1][n + 1];
        for (int i = 1; i <= m; i++) {
            for (int j = 1; j <= n; j++) {
                dp[i][j] = word1.charAt(i - 1) == word2.charAt(j - 1) ?
                        dp[i - 1][j - 1] + 1 : Math.max(dp[i][j - 1], dp[i - 1][j]);
            }
        }
        return m + n - 2 * dp[m][n];
    }

    @Test
    public void test(){
        String w1="eat";
        String w2="sea";
        System.out.println(minDistance(w1,w2));
    }
}