#Leetcode# 72. Edit Distance

Given two words word1 and word2, find the minimum number of operations required to convert word1 to word2.

You have the following 3 operations permitted on a word:

1. Insert a character
2. Delete a character
3. Replace a character

Example 1:

Input: word1 = "horse", word2 = "ros"
Output: 3
Explanation: 
horse -> rorse (replace 'h' with 'r')
rorse -> rose (remove 'r')
rose -> ros (remove 'e')

Example 2:

Input: word1 = "intention", word2 = "execution"
Output: 5
Explanation: 
intention -> inention (remove 't')
inention -> enention (replace 'i' with 'e')
enention -> exention (replace 'n' with 'x')
exention -> exection (replace 'n' with 'c')
exection -> execution (insert 'u')

代码：

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

　　字符串 dp