【LeetCode 72】Edit Distance

Given two words word1 and word2, find the minimum number of steps required to convert word1 to word2. (each operation is counted as 1 step.)

You have the following 3 operations permitted on a word:

a) Insert a character
b) Delete a character
c) Replace a character

思路：

　　典型的动态规划题，递归要超时哦。状态转移方程：

     a[i][j] = min(

                       1. a[i-1][j] + 1,

                       2. a[i][j-1] + 1,

                       3. word1[i] == word2[j] ? a[i-1][j-1] : a[i-1][j-1] + 1

                      );

C++:

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