LeetCode Edit Distance

题目：

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

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