Matrix Chain Multiplication - The easy somewhat modern C++

mcm.cpp

#include<iostream>
#include<vector>
#include<climits>
#include<string>

// MCM
std::string make_exp(std::vector<std::vector<int>> &s, int i, int j) {
    if (i == j) {
        return std::string(1, 'A' + i - 1);
    }
    
    return "(" + make_exp(s, i, s[i][j]) + make_exp(s, s[i][j] + 1, j) + ")";
}

int main() {
    int n;
    std::cin >> n >> n;
    std::vector<int> p(n, 0);
    for (int i = 0; i < n; i++) std::cin >> p[i];
    // for (int k : p) std::cout << k;
    
    
    std::vector<std::vector<int>> c(n, std::vector<int>(n, 0));
    std::vector<std::vector<int>> s(n, std::vector<int>(n, 0));
    
    for (int l = 2; l < n; l++) {
        for (int i = 1; i <= n - l; i++) {
            int j = i + l - 1;
            int mk = -1;
            int m = INT_MAX;
            for (int k = i; k < j; k++) {
                int cost = p[i - 1] * p[k] * p[j] + c[i][k] + c[k + 1][j];
                if (cost < m) {
                    mk = k;
                    m = cost;
                }
            }
            c[i][j] = m;
            s[i][j] = mk;
        }
    }
    
    std::cout << c[1][n - 1] << '\n';
    std::cout << make_exp(s, 1, n-1);
    return 0;
}