动态规划求最小编辑距离

//求最小编辑距离 
int editDistance(const string source, const string target)
{
        //step 1
        int len_source = source.length();
        int len_target = target.length();
        if (len_source == 0) return len_target;
        if (len_target == 0) return len_source;

        //Construct a matrix
        typedef vector< vector<int> >  Tmatrix;
        Tmatrix matrix(len_target + 1);
        for (int i = 0; i <= len_target; i++)  matrix[i].resize(len_source + 1);

        //step 2 Initialize
        for (int i = 1; i <= len_target; i++) matrix[i][0] = i;
        for (int i = 1; i <= len_source; i++) matrix[0][i] = i;

        //step 3
        for (int i = 1; i <= len_target; i++)
        {
                const char si = source[i - 1];
                //step 4
                for (int j = 1; j <= len_source; j++)
                {

                        const char tj = target[j - 1];
                        //step 5
                        int cost = si==tj ? 0:1;
                        //step 6
                        const int ins = matrix[i - 1][j] + 1;
                        const int del = matrix[i][j - 1] + 1;
                        const int replace = matrix[i - 1][j - 1] + cost;
                        matrix[i][j] = min(ins, min(del, replace));

                }
        }//step7
        return matrix[len_target][len_source];
}