Sleepy Cow Herding

#include <bits/stdc++.h>
using namespace std;
string info(vector<int> &herd, int &curr_cow, int &farthest_cow){
    string info = ", curr_cow: "  + to_string(curr_cow)  +"#H:"+to_string(herd[curr_cow])
         + ", farthest_cow: "+to_string(farthest_cow)+"#H: "+to_string(herd[farthest_cow]);
    return info;
}
int main() {
    freopen("herding.in", "r", stdin);

    int n;
    cin >> n;
    vector<int> herd(n);
    for (int i = 0; i < n; ++i) {
        cin >> herd[i];
    }
    sort(herd.begin(), herd.end());
    int min_moves = INT32_MAX;
    if (herd[n - 2] - herd[0] == n - 2 && herd[n - 1] - herd[n - 2] > 2) {
        min_moves = 2;
        cout << "min_moves#1" << endl;
    } else if (herd[n - 1] - herd[1] == n - 2 && herd[1] - herd[0] > 2) {
        min_moves = 2;
        cout << "min_moves#2" << endl;
    } else {
        // min is the patch of length n that has the least # of gaps
        int farthest_cow = 0;
        for (int curr_cow = 0; curr_cow < n; ++curr_cow) {
            cout << "[for] " +info(herd, curr_cow, farthest_cow)  << endl;
            while (
                farthest_cow + 1 < n
                && herd[farthest_cow + 1] - herd[curr_cow] < n
            ) {
                farthest_cow++;
                cout << "[while] " +info(herd, curr_cow, farthest_cow)  << endl;
            }
            min_moves = min(min_moves, n - (farthest_cow - curr_cow + 1));
            cout << "min_moves: "+to_string(min_moves) << endl;
        }
    }
    // calculate the number of empty cells
    int gap_num = 0;
    for (int i = 1; i < n; i++) {
        gap_num += herd[i] - herd[i - 1] - 1;
    }
    // max is the maximum of the total gap minus either the first or last gap
    int max_moves = max(
        gap_num - (herd[1] - herd[0] - 1),
        gap_num - (herd[n - 1] - herd[n - 2] - 1)
    );
    freopen("herding.out", "w", stdout);
    cout << min_moves << '\n' << max_moves << endl;
}