Submission #434126

#	Time	Username	Problem	Language	Result	Execution time	Memory
434126		rqi	Chessboard (IZhO18_chessboard)	C++14	70 / 100	396 ms	3396 KiB

chessboard

#include <bits/stdc++.h>
using namespace std;

typedef pair<int, int> pi;
typedef vector<int> vi;
typedef long long ll;
typedef pair<ll, ll> pl;

#define pb push_back
#define mp make_pair
#define f first
#define s second

#define sz(x) (int)(x).size()

void ckmin(ll& a, ll b){
	a = min(a, b);
}

void ADD(pl& a, pl b){
	a.f+=b.f;
	a.s+=b.s;
}

void print(pi a){
	cout << a.f << " " << a.s << "\n";
	cout.flush();
}

const ll INF = 1e18;

const int mx = 100005;

int N, K;
int X1[mx];
int Y1[mx];
int X2[mx];
int Y2[mx];

pl shouldBe(int X, int Y, int SZ, bool white_corn){
	assert(X % SZ == 0 && Y % SZ == 0);

	ll squares = ll(X/SZ)*ll(Y/SZ);
	ll white_squares = (squares+1)/2;

	if(!white_corn){
		white_squares = squares-white_squares;
	}

	
	ll should_be_white = white_squares*ll(SZ)*ll(SZ);

	// cout << "squares: " << squares << "\n";
	// cout << "should_be_white: " << should_be_white << "\n";

	return mp(should_be_white, ll(X)*ll(Y)-should_be_white);
}

int SZ;

bool shouldBeWhite(const pi& a){
	return (a.f/SZ+a.s/SZ) % 2;
}

pl doSingle(pi corner11, pi corner22){
	ll area = ll(corner22.s+1-corner11.s)*ll(corner22.f+1-corner11.f);
	if(shouldBeWhite(corner11)){
		return mp(area, 0);
	}
	return mp(0, area);
}

pl doEdge(pi corner11, pi corner22){
	// cout << corner11.f << " " << corner11.s << " " << corner22.f << " " << corner22.s << "\n";
	// cout.flush();
	if(corner11.f/SZ != corner22.f/SZ){
		swap(corner11.f, corner11.s);
		swap(corner22.f, corner22.s);
	}

	assert((corner22.s+1) % SZ == 0);
	assert(corner11.f/SZ == corner22.f/SZ);

	int rect_num = (corner22.s+1-corner11.s)/SZ;
	ll rect_area = ll(corner22.f-corner11.f+1)*SZ;

	int white_num = (rect_num+1)/2;
	int black_num = rect_num-white_num;

	// if(corner11 == mp(3, 2) && corner22 == mp(3, 1)){
	// 	cout << "HI" << " " << rect_num << " " << rect_area << " " << white_num << " " << black_num << "\n";
	// }
	if(!shouldBeWhite(corner11)){
		swap(white_num, black_num);
	}

	return mp(rect_area*white_num, rect_area*black_num);
}

pl doBig(pi corner11, pi corner22){
	assert(corner11.f % SZ == 0 && corner11.s % SZ == 0);
	assert((corner22.f+1) % SZ == 0 && (corner22.s+1) % SZ == 0);

	ll rect_num = ll(corner22.f+1-corner11.f)*ll(corner22.s+1-corner11.s);
	ll white_num = (rect_num+1)/2;
	ll black_num = rect_num-white_num;
	if(shouldBeWhite(corner11)){
		swap(white_num, black_num);
	}

	ll square_area = ll(SZ)*ll(SZ);
	return mp(square_area*white_num, square_area*black_num);
}

ll getAns(){ //bottom left should be white, count # of flips
	// cout << "SZ = " << SZ << "\n";
	// cout.flush();
	ll flip_to_white = 0;
	ll flip_to_black = 0;

	for(int i = 1; i <= K; i++){
		pi corner11 = mp(X1[i], Y1[i]);
		pi corner22 = mp(X2[i], Y2[i]);

		
		
		pl res = mp(0, 0);
		if(corner11.f/SZ < corner22.f/SZ && corner11.s/SZ < corner22.s/SZ){
			pi CORNER11 = mp(corner11.f/SZ*SZ+SZ-1, corner11.s/SZ*SZ+SZ-1);
			pi CORNER22 = mp(corner22.f/SZ*SZ, corner22.s/SZ*SZ);

			// print(corner11);
			// print(CORNER11);
			// print(CORNER22);
			// print(corner22);

			ADD(res, doSingle(corner11, CORNER11));
			ADD(res, doSingle(CORNER22, corner22));
			
			ADD(res, doSingle(mp(corner11.f, CORNER22.s), mp(CORNER11.f, corner22.s)));
			ADD(res, doSingle(mp(CORNER22.f, corner11.s), mp(corner22.f, CORNER11.s)));

			ADD(res, doEdge(mp(corner11.f, CORNER11.s+1), mp(CORNER11.f, CORNER22.s-1)));
			ADD(res, doEdge(mp(CORNER11.f+1, corner11.s), mp(CORNER22.f-1, CORNER11.s)));
			ADD(res, doEdge(mp(CORNER22.f, CORNER11.s+1), mp(corner22.f, CORNER22.s-1)));
			ADD(res, doEdge(mp(CORNER11.f+1, CORNER22.s), mp(CORNER22.f-1, corner22.s)));
			
			ADD(res, doBig(mp(CORNER11.f+1, CORNER22.f+1), mp(CORNER22.f-1, CORNER22.s-1)));
		}
		else if(corner11.f/SZ == corner22.f/SZ && corner11.s/SZ == corner22.s/SZ){
			ADD(res, doSingle(corner11, corner22));

		}
		else{
			pi CORNER11 = mp(-1, -1);
			pi CORNER22 = mp(-1, -1);
			if(corner11.f/SZ == corner22.f/SZ){
				CORNER11 = mp(corner22.f, corner11.s/SZ*SZ+SZ-1);
				CORNER22 = mp(corner11.f, corner22.s/SZ*SZ);
			}
			else{
				CORNER11 = mp(corner11.f/SZ*SZ+SZ-1, corner22.s);
				CORNER22 = mp(corner22.f/SZ*SZ, corner11.s);
			}
			ADD(res, doSingle(corner11, CORNER11));
			// cout << "EDGE" << " " << res.f << " " << res.s << "\n";
			ADD(res, doSingle(CORNER22, corner22));

			// cout << "EDGE" << " " << res.f << " " << res.s << "\n";
			// print(corner11);
			// print(CORNER11);
			// print(CORNER22);
			// print(corner22);

			if(corner11.f/SZ == corner22.f/SZ){
				ADD(res, doEdge(mp(corner11.f, CORNER11.s+1), mp(corner22.f, CORNER22.s-1)));
				// cout << "CASE 1 " << "\n";
			}
			else{
				ADD(res, doEdge(mp(CORNER11.f+1, corner11.s), mp(CORNER22.f-1, corner22.s)));
			}
			// cout << "EDGE" << " " << res.f << " " << res.s << "\n";
		}

		//cout << i << " (" << res.f << ", " << res.s << ") \n";

		flip_to_white+=res.f;
		flip_to_black+=res.s;
	}


	// cout << "flip_to_white, black: " << flip_to_white << ", " << flip_to_black << "\n"; 
	ll should_be_black = shouldBe(N, N, SZ, 0).s;

	return flip_to_white+(should_be_black-flip_to_black);
}

int main(){
	cin.tie(0)->sync_with_stdio(0);
	cin >> N >> K;
	for(int i = 1; i <= K; i++){
		cin >> X1[i] >> Y1[i] >> X2[i] >> Y2[i];
		X1[i]--; Y1[i]--; X2[i]--; Y2[i]--;
	}

	ll ans = INF;

	for(int i = 1; i < N; i++){
		if(N % i == 0){
			SZ = i;
			ll res = getAns();
			// cout << "i, res: " << i << ", " << res << "\n";
			ckmin(ans, res);
			ckmin(ans, ll(N)*ll(N)-res);
		}
	}

	cout << ans << "\n";
}

• Subtask 1: 8 / 8
• Subtask 2: 8 / 8
• Subtask 3: 15 / 15
• Subtask 4: 16 / 16
• Subtask 5: 23 / 23
• Subtask 6: 0 / 30