Delete Operation for Two Strings

题目描述：

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 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.

思路：

问题可以转化为求两个字符串的最长公共子序列（注意不是子字符串）

代码：

class Solution {
public:
    int minDistance(string word1, string word2) {
        int m=word1.size();
        int n=word2.size();
        if (m==0)
            return n;
        if (n==0)
            return m;
        vector<vector<int>> dp(m+1,vector<int>(n+1,0));
        for (int i=1; i<=m; ++i)
            for (int j=1; j<=n; ++j)
            {
                if (word1[i-1]==word2[j-1])
                    dp[i][j]=dp[i-1][j-1]+1;
                else
                    dp[i][j]=max(dp[i-1][j],dp[i][j-1]);
            }
        int maxlen=dp[m][n];
        return (m-maxlen)+(n-maxlen);
    }
};