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답안 #434110

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
434110 2021-06-20T15:07:39 Z rqi Chessboard (IZhO18_chessboard) C++14
70 / 100
 399 ms 5620 KB 
#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";
}

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){
	if(corner11.s % SZ != 0){
		assert(corner11.f % SZ == 0);
		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";
	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);
			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
8.0 / 8.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 204 KB Output is correct
2 Correct 1 ms 204 KB Output is correct
3 Correct 1 ms 204 KB Output is correct
4 Correct 1 ms 204 KB Output is correct
5 Correct 1 ms 204 KB Output is correct
6 Correct 1 ms 204 KB Output is correct
7 Correct 1 ms 204 KB Output is correct
8 Correct 1 ms 324 KB Output is correct

Subtask #2
8.0 / 8.0

# 결과 실행 시간 메모리 Grader output
1 Correct 34 ms 2792 KB Output is correct
2 Correct 8 ms 844 KB Output is correct
3 Correct 22 ms 1780 KB Output is correct
4 Correct 23 ms 1812 KB Output is correct
5 Correct 32 ms 2380 KB Output is correct
6 Correct 16 ms 1600 KB Output is correct
7 Correct 5 ms 576 KB Output is correct
8 Correct 16 ms 1688 KB Output is correct
9 Correct 50 ms 3700 KB Output is correct
10 Correct 27 ms 2232 KB Output is correct

Subtask #3
15.0 / 15.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 332 KB Output is correct
2 Correct 1 ms 204 KB Output is correct
3 Correct 1 ms 332 KB Output is correct
4 Correct 1 ms 332 KB Output is correct
5 Correct 1 ms 328 KB Output is correct
6 Correct 1 ms 332 KB Output is correct
7 Correct 1 ms 332 KB Output is correct
8 Correct 1 ms 332 KB Output is correct
9 Correct 1 ms 320 KB Output is correct
10 Correct 1 ms 204 KB Output is correct
11 Correct 1 ms 332 KB Output is correct
12 Correct 1 ms 332 KB Output is correct
13 Correct 1 ms 332 KB Output is correct
14 Correct 1 ms 324 KB Output is correct
15 Correct 1 ms 332 KB Output is correct

Subtask #4
16.0 / 16.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 332 KB Output is correct
2 Correct 1 ms 204 KB Output is correct
3 Correct 1 ms 332 KB Output is correct
4 Correct 1 ms 332 KB Output is correct
5 Correct 1 ms 328 KB Output is correct
6 Correct 1 ms 332 KB Output is correct
7 Correct 1 ms 332 KB Output is correct
8 Correct 1 ms 332 KB Output is correct
9 Correct 1 ms 320 KB Output is correct
10 Correct 1 ms 204 KB Output is correct
11 Correct 1 ms 332 KB Output is correct
12 Correct 1 ms 332 KB Output is correct
13 Correct 1 ms 332 KB Output is correct
14 Correct 1 ms 324 KB Output is correct
15 Correct 1 ms 332 KB Output is correct
16 Correct 14 ms 1192 KB Output is correct
17 Correct 34 ms 2872 KB Output is correct
18 Correct 48 ms 3384 KB Output is correct
19 Correct 112 ms 3124 KB Output is correct
20 Correct 113 ms 3400 KB Output is correct
21 Correct 31 ms 2808 KB Output is correct
22 Correct 2 ms 332 KB Output is correct
23 Correct 24 ms 1612 KB Output is correct
24 Correct 39 ms 3148 KB Output is correct
25 Correct 5 ms 588 KB Output is correct
26 Correct 25 ms 2124 KB Output is correct
27 Correct 35 ms 2372 KB Output is correct
28 Correct 42 ms 3312 KB Output is correct
29 Correct 13 ms 1392 KB Output is correct
30 Correct 2 ms 440 KB Output is correct

Subtask #5
23.0 / 23.0

# 결과 실행 시간 메모리 Grader output
1 Correct 34 ms 2792 KB Output is correct
2 Correct 8 ms 844 KB Output is correct
3 Correct 22 ms 1780 KB Output is correct
4 Correct 23 ms 1812 KB Output is correct
5 Correct 32 ms 2380 KB Output is correct
6 Correct 16 ms 1600 KB Output is correct
7 Correct 5 ms 576 KB Output is correct
8 Correct 16 ms 1688 KB Output is correct
9 Correct 50 ms 3700 KB Output is correct
10 Correct 27 ms 2232 KB Output is correct
11 Correct 1 ms 332 KB Output is correct
12 Correct 1 ms 204 KB Output is correct
13 Correct 1 ms 332 KB Output is correct
14 Correct 1 ms 332 KB Output is correct
15 Correct 1 ms 328 KB Output is correct
16 Correct 1 ms 332 KB Output is correct
17 Correct 1 ms 332 KB Output is correct
18 Correct 1 ms 332 KB Output is correct
19 Correct 1 ms 320 KB Output is correct
20 Correct 1 ms 204 KB Output is correct
21 Correct 1 ms 332 KB Output is correct
22 Correct 1 ms 332 KB Output is correct
23 Correct 1 ms 332 KB Output is correct
24 Correct 1 ms 324 KB Output is correct
25 Correct 1 ms 332 KB Output is correct
26 Correct 14 ms 1192 KB Output is correct
27 Correct 34 ms 2872 KB Output is correct
28 Correct 48 ms 3384 KB Output is correct
29 Correct 112 ms 3124 KB Output is correct
30 Correct 113 ms 3400 KB Output is correct
31 Correct 31 ms 2808 KB Output is correct
32 Correct 2 ms 332 KB Output is correct
33 Correct 24 ms 1612 KB Output is correct
34 Correct 39 ms 3148 KB Output is correct
35 Correct 5 ms 588 KB Output is correct
36 Correct 25 ms 2124 KB Output is correct
37 Correct 35 ms 2372 KB Output is correct
38 Correct 42 ms 3312 KB Output is correct
39 Correct 13 ms 1392 KB Output is correct
40 Correct 2 ms 440 KB Output is correct
41 Correct 88 ms 3544 KB Output is correct
42 Correct 49 ms 4040 KB Output is correct
43 Correct 63 ms 3604 KB Output is correct
44 Correct 46 ms 3840 KB Output is correct
45 Correct 43 ms 4112 KB Output is correct
46 Correct 102 ms 3988 KB Output is correct
47 Correct 38 ms 3588 KB Output is correct
48 Correct 62 ms 3720 KB Output is correct
49 Correct 44 ms 3624 KB Output is correct
50 Correct 374 ms 3892 KB Output is correct
51 Correct 392 ms 4140 KB Output is correct
52 Correct 360 ms 3868 KB Output is correct
53 Correct 387 ms 4112 KB Output is correct
54 Correct 356 ms 3824 KB Output is correct
55 Correct 399 ms 4248 KB Output is correct
56 Correct 349 ms 3656 KB Output is correct

Subtask #6
0 / 30.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 204 KB Output is correct
2 Correct 1 ms 204 KB Output is correct
3 Correct 1 ms 204 KB Output is correct
4 Correct 1 ms 204 KB Output is correct
5 Correct 1 ms 204 KB Output is correct
6 Correct 1 ms 204 KB Output is correct
7 Correct 1 ms 204 KB Output is correct
8 Correct 1 ms 324 KB Output is correct
9 Correct 34 ms 2792 KB Output is correct
10 Correct 8 ms 844 KB Output is correct
11 Correct 22 ms 1780 KB Output is correct
12 Correct 23 ms 1812 KB Output is correct
13 Correct 32 ms 2380 KB Output is correct
14 Correct 16 ms 1600 KB Output is correct
15 Correct 5 ms 576 KB Output is correct
16 Correct 16 ms 1688 KB Output is correct
17 Correct 50 ms 3700 KB Output is correct
18 Correct 27 ms 2232 KB Output is correct
19 Correct 1 ms 332 KB Output is correct
20 Correct 1 ms 204 KB Output is correct
21 Correct 1 ms 332 KB Output is correct
22 Correct 1 ms 332 KB Output is correct
23 Correct 1 ms 328 KB Output is correct
24 Correct 1 ms 332 KB Output is correct
25 Correct 1 ms 332 KB Output is correct
26 Correct 1 ms 332 KB Output is correct
27 Correct 1 ms 320 KB Output is correct
28 Correct 1 ms 204 KB Output is correct
29 Correct 1 ms 332 KB Output is correct
30 Correct 1 ms 332 KB Output is correct
31 Correct 1 ms 332 KB Output is correct
32 Correct 1 ms 324 KB Output is correct
33 Correct 1 ms 332 KB Output is correct
34 Correct 14 ms 1192 KB Output is correct
35 Correct 34 ms 2872 KB Output is correct
36 Correct 48 ms 3384 KB Output is correct
37 Correct 112 ms 3124 KB Output is correct
38 Correct 113 ms 3400 KB Output is correct
39 Correct 31 ms 2808 KB Output is correct
40 Correct 2 ms 332 KB Output is correct
41 Correct 24 ms 1612 KB Output is correct
42 Correct 39 ms 3148 KB Output is correct
43 Correct 5 ms 588 KB Output is correct
44 Correct 25 ms 2124 KB Output is correct
45 Correct 35 ms 2372 KB Output is correct
46 Correct 42 ms 3312 KB Output is correct
47 Correct 13 ms 1392 KB Output is correct
48 Correct 2 ms 440 KB Output is correct
49 Correct 88 ms 3544 KB Output is correct
50 Correct 49 ms 4040 KB Output is correct
51 Correct 63 ms 3604 KB Output is correct
52 Correct 46 ms 3840 KB Output is correct
53 Correct 43 ms 4112 KB Output is correct
54 Correct 102 ms 3988 KB Output is correct
55 Correct 38 ms 3588 KB Output is correct
56 Correct 62 ms 3720 KB Output is correct
57 Correct 44 ms 3624 KB Output is correct
58 Correct 374 ms 3892 KB Output is correct
59 Correct 392 ms 4140 KB Output is correct
60 Correct 360 ms 3868 KB Output is correct
61 Correct 387 ms 4112 KB Output is correct
62 Correct 356 ms 3824 KB Output is correct
63 Correct 399 ms 4248 KB Output is correct
64 Correct 349 ms 3656 KB Output is correct
65 Correct 1 ms 332 KB Output is correct
66 Correct 1 ms 204 KB Output is correct
67 Runtime error 46 ms 5620 KB Execution killed with signal 6
68 Halted 0 ms 0 KB -