Submission #897823

#	Time	Username	Problem	Language	Result	Execution time	Memory
897823		DAleksa	Chessboard (IZhO18_chessboard)	C++17	100 / 100	637 ms	4512 KiB

chessboard

#include <bits/stdc++.h>

using namespace std;

const int K = 1e5 + 10, SQ = 700;
int n, k;
int x1[K], Y1[K], x2[K], y2[K];
vector<int> divs;
long long sum[SQ], P;

long long get(int x, int y, int k) {
    if(x == 0 || y == 0) {
        return 0;
    }
    int X = (x / k) * k, Y = (y / k) * k;
    long long ans = ((X / k) * 1LL * (Y / k) + 1) / 2 * k * k;
//    cout << k << "\n";
//    cout << x << " " << y << "\n";
//    cout << X << " " << Y << "\n";
//    cout << ans << "\n";
    ans += (x - X) * 1LL * k * (((Y / k) + ((X / k) % 2 == 0)) / 2);
//    cout << ans << "\n";
    ans += (y - Y) * 1LL * k * (((X / k) + ((Y / k) % 2 == 0)) / 2);
//    cout << ans << "\n";
    if((X / k + Y / k) % 2 == 0) {
        ans += (x - X) * 1LL * (y - Y);
    }
    return ans;
}

long long get(int x1, int Y1, int x2, int y2, int k) {
    return get(x2, y2, k) - get(x2, Y1 - 1, k) - get(x1 - 1, y2, k) + get(x1 - 1, Y1 - 1, k);
}

int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(0);
    cin >> n >> k;
    for(int i = 0; i < k; i++) {
        cin >> x1[i] >> Y1[i] >> x2[i] >> y2[i];
        P += (x2[i] - x1[i] + 1) * 1LL * (y2[i] - Y1[i] + 1);
    }
    divs.push_back(1);
    for(int i = 2; i * i < n; i++) {
        if(n % i == 0) {
            divs.push_back(i);
            divs.push_back(n / i);
        }
    }
    if(n % (int)sqrt(n) == 0) {
        divs.push_back(sqrt(n));
    }
    sort(divs.begin(), divs.end());
    for(int i = 0; i < k; i++) {
        for(int d = 0; d < divs.size(); d++) {
            sum[d] += get(x1[i], Y1[i], x2[i], y2[i], divs[d]);
//            cout << x1[i] << " " << Y1[i] << " " << x2[i] << " " << y2[i] << " " << divs[d] << " " << get(x1[i], Y1[i], x2[i], y2[i], divs[d]) << "\n";
        }
    }
    long long ans = 1e18;
//    cout << P << "\n\n";
    for(int i = 0; i < divs.size(); i++) {
        long long all = (((n / divs[i]) * 1LL * (n / divs[i]) + 1) / 2) * divs[i] * divs[i];
        ans = min(ans, all + P - 2 * sum[i]);
//        cout << i << ": " << ans << "\n";
        all = ((n / divs[i]) * 1LL * (n / divs[i]) / 2) * divs[i] * divs[i];
        ans = min(ans, all - P + 2 * sum[i]);
//        cout << i << ": " << ans << "\n";
    }
    cout << ans;
    return 0;
}
/*

6 8
3 3 3 3
1 2 1 2
3 4 3 4
5 5 5 5
4 3 4 3
4 4 4 4
2 1 2 1
3 6 3 6


4 1
4 1 4 4

*/

Compilation message (stderr)

chessboard.cpp: In function 'int main()':
chessboard.cpp:55:26: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   55 |         for(int d = 0; d < divs.size(); d++) {
      |                        ~~^~~~~~~~~~~~~
chessboard.cpp:62:22: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   62 |     for(int i = 0; i < divs.size(); i++) {
      |                    ~~^~~~~~~~~~~~~

• Subtask 1: 8 / 8
• Subtask 2: 8 / 8
• Subtask 3: 15 / 15
• Subtask 4: 16 / 16
• Subtask 5: 23 / 23
• Subtask 6: 30 / 30