horse 改成 ros 要几步

每步可以插入、删除或替换一个字符。运行下面这段程序：

#include <algorithm>
#include <iostream>
#include <string>
#include <vector>
using namespace std;
using Item = pair<int, int>;   // (重量, 价值)

const vector<Item> ITEMS = {{3, 8}, {4, 9}, {5, 11}};

int edit(const string& a, const string& b) {
    int m = a.size(), n = b.size();
    vector<vector<int>> dp(m + 1, vector<int>(n + 1, 0));
    for (int i = 0; i <= m; i++) dp[i][0] = i;
    for (int j = 0; j <= n; j++) dp[0][j] = j;
    for (int i = 1; i <= m; i++) {
        for (int j = 1; j <= n; j++) {
            if (a[i - 1] == b[j - 1]) dp[i][j] = dp[i - 1][j - 1];
            else dp[i][j] = 1 + min({dp[i - 1][j - 1], dp[i - 1][j], dp[i][j - 1]});
        }
    }
    return dp[m][n];
}

int main() {
    cout << edit("horse", "ros") << endl;
}

（本题用 g++ -std=c++17 -O0 编译。）