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：

动规

代码：

    int min(int a, int b){
        if(a < b)
            return a;
        return b;
    }
    int minDistance(string word1, string word2) {
        // Note: The Solution object is instantiated only once and is reused by each test case.
        int len1 = word1.length(), len2 = word2.length();
        if(len1 == 0)
            return len2;
        if(len2 == 0)
            return len1;
        vector<vector<int> > v(len1+1, vector<int>(len2+1));
        int i,j;
        for(i = 1; i <= len1; i++)
            v[i][0] = i;
        for(i = 1; i <= len2; i++)
            v[0][i] = i;
        for(i = 1; i <= len1; i++){
            for(j = 1; j <= len2; j++){
                if(word1[i-1] == word2[j-1])
                    v[i][j] = v[i-1][j-1];
                else
                    v[i][j] = min(v[i-1][j-1]+1,min(v[i-1][j]+1, v[i][j-1]+1));
            }
        }
        return v[len1][len2];
    }