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

class Solution {
public:
    int minDistance(string word1, string word2) {
        int m = word1.size();
        int n = word2.size();
        
        vector> f(m+1,vector(n+1,0));
        for(int i=0;i<=m;i++)
            f[i][0] = i;
        for(int j=0;j<=n;j++)
            f[0][j] = j;
        //f[i][j]前i,j个字符所需要的次数
        for(int i=1;i