#include <iostream>
#include <cassert>
#define int long long int
#define ericxiao ios_base::sync_with_stdio(0);cin.tie(0);
using namespace std;
const int maxN = 1e5 + 326;
struct Rect{
int l, r, d, u, A;
Rect(){}
Rect(int l, int r, int d, int u): l(l), r(r), d(d), u(u){
A = (r - l + 1) * (u - d + 1);
}
} rects[maxN];
inline bool onDiag(int x, int y, int d){
return (((x % (2 * d)) < d) == ((y % (2 * d)) < d));
}
inline int id(int x, int y, int d){
return x / d * maxN + y / d;
}
inline int getArea(int a, int b){
if(a < 0 || b < 0) return 0;
return a * b;
}
inline int Area(int l, int r, int d, int u, int div){
if(l > r || d > u) return 0;
if(div == 1){
if(((r - l + 1) & 1) && ((u - d + 1) & 1)) return ((r - l + 1) * (u - d + 1) + 1)/ 2;
return ((r - l + 1) * (u - d + 1))/ 2;
}
//cout << "running: " << l << " " << r << " " << d << " " << u << " " << div << endl;
int _l = (l + div - 1) / div * div, _r = r / div * div, _u = u / div * div, _d = (d + div - 1) / div * div, res = 0;
if((l / div == r / div) && (u / div == d / div)){
return (u - d + 1) * (r - l + 1) * onDiag(l, u, div);
}
if(l / div == r / div){
int k = 0;
k += (u - _u + 1) * onDiag(l, u, div);
k += (_d - d) * onDiag(l, d, div);
if(onDiag(l, _d, div) && ((_u - _d) / div) & 1) k += ((_u - _d) / div / 2 + 1) * d;
else k += ((_u - _d) / div / 2) * d;
return k * (r - l + 1);
}
if(u / div == d / div){
int k = 0;
k += (_l - l) * onDiag(l, u, div);
k += (r - _r + 1) * onDiag(r, u, div);
if(onDiag(_l, u, div) && ((_r - _l) / div) & 1) k += ((_r - _l) / div / 2 + 1) * d;
else k += ((_r - _l) / div / 2) * d;
return k * (u - d + 1);
}
res = (_r - _l) / div * (_u - _d) / div;
if(onDiag(_l, _d, div) && (res & 1)) res = (res + 1) / 2;
else res = res / 2;
res *= div * div;
if(onDiag(l, u, div)){
res += getArea((_l - l), (u - _u + 1));
}
if(onDiag(r, u, div)){
res += getArea((r - _r + 1), (u - _u + 1));
}
if(onDiag(r, d, div)){
res += getArea((r - _r + 1), (_d - d));
}
if(onDiag(l, d, div)){
res += getArea((_l - l), (_d - d));
}
res += Area(_l, _r - 1, _u, u, div);
res += Area(_l, _r - 1, d, _d - 1, div);
res += Area(l, _l - 1, _d, _u - 1, div);
res += Area(_r, r, _d, _u - 1, div);
//cout << l << " " << r << " " << d << " " << u << " " << div << ", res = " << res << endl;
return res;
}
int N, K;
inline int check(int d){
//top left is black
//cout << "d = " << d << endl;
int _ans = maxN * maxN, tmp = ((N / d) * (N / d) + 1) / 2 * (d * d), tmp2 = ((N / d) * (N / d)) / 2 * (d * d);
//cout << "1tmp = " << tmp << endl;
for(int i = 0; i < K; i++){
int A = Area(rects[i].l, rects[i].r, rects[i].d, rects[i].u, d), B = rects[i].A - A;
tmp += B - A;
tmp2 += A - B;
}
return min(tmp, tmp2);
//top right is black
}
signed main(){
ericxiao;
cin >> N >> K;
int l, r, d, u;
for(int i = 0; i < K; i++){
cin >> l >> d >> r >> u;
l--; d--; r--; u--;
rects[i] = Rect(l, r, d, u);
//cout << "rects[i] a = " << rects[i].A << endl;
}
int ans = maxN * maxN;
for(int div = 1; div * div <= N; div++){
if(!(N % div)){
ans = min(ans, check(div));
if(div != 1) ans = min(ans, check(N / div));
}
}
cout << ans << endl;
}
/*
*
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
*/
Compilation message
chessboard.cpp: In function 'long long int check(long long int)':
chessboard.cpp:87:6: warning: unused variable '_ans' [-Wunused-variable]
87 | int _ans = maxN * maxN, tmp = ((N / d) * (N / d) + 1) / 2 * (d * d), tmp2 = ((N / d) * (N / d)) / 2 * (d * d);
| ^~~~
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
364 KB |
Output is correct |
| 2 |
Correct |
1 ms |
364 KB |
Output is correct |
| 3 |
Correct |
1 ms |
364 KB |
Output is correct |
| 4 |
Correct |
1 ms |
364 KB |
Output is correct |
| 5 |
Correct |
1 ms |
364 KB |
Output is correct |
| 6 |
Correct |
1 ms |
364 KB |
Output is correct |
| 7 |
Correct |
1 ms |
364 KB |
Output is correct |
| 8 |
Correct |
1 ms |
364 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Incorrect |
24 ms |
2796 KB |
Output isn't correct |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
364 KB |
Output is correct |
| 2 |
Correct |
1 ms |
364 KB |
Output is correct |
| 3 |
Incorrect |
1 ms |
364 KB |
Output isn't correct |
| 4 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
364 KB |
Output is correct |
| 2 |
Correct |
1 ms |
364 KB |
Output is correct |
| 3 |
Incorrect |
1 ms |
364 KB |
Output isn't correct |
| 4 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Incorrect |
24 ms |
2796 KB |
Output isn't correct |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
1 ms |
364 KB |
Output is correct |
| 2 |
Correct |
1 ms |
364 KB |
Output is correct |
| 3 |
Correct |
1 ms |
364 KB |
Output is correct |
| 4 |
Correct |
1 ms |
364 KB |
Output is correct |
| 5 |
Correct |
1 ms |
364 KB |
Output is correct |
| 6 |
Correct |
1 ms |
364 KB |
Output is correct |
| 7 |
Correct |
1 ms |
364 KB |
Output is correct |
| 8 |
Correct |
1 ms |
364 KB |
Output is correct |
| 9 |
Incorrect |
24 ms |
2796 KB |
Output isn't correct |
| 10 |
Halted |
0 ms |
0 KB |
- |
