583 Delete Operation for Two Strings

583. Delete Operation for Two Strings

1. Question

Given two wordsword1andword2, find the minimum number of steps required to makeword1andword2the same, where in each step you can delete one character in either string.

Example 1:

Input: "sea", "eat"

Output: 2

Explanation:
You need one step to make "sea" to "ea" and another step to make "eat" to "ea".

Note:

1. The length of given words won't exceed 500.

2. Characters in given words can only be lower-case letters.

2. Implementation

(1) DP

思路: 找两个string之间的LCS，需要删除的操作就等于两个string的长度 - 2 * LCS

class Solution {
    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 = 0; i <= m; i++) {
            for (int j = 0; j <= n; j++) {
                if (i == 0 || j == 0) {
                    dp[i][j] = 0;
                }
                else if (word1.charAt(i - 1) == word2.charAt(j - 1)) {
                    dp[i][j] = dp[i - 1][j - 1] + 1;
                }
                else {
                    dp[i][j] = Math.max(dp[i - 1][j], dp[i][j - 1]);
                }
            }
        }
        return m + n - 2 * dp[m][n];
    }
}

3. Time & Space Complexity

DP: 时间复杂度: O(mn), 空间复杂度O(mn)