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Submission #434126

# Submission time Handle Problem Language Result Execution time Memory
434126 2021-06-20T15:21:45 Z rqi Chessboard (IZhO18_chessboard) C++14
70 / 100
 396 ms 3396 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";
	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
8.0 / 8.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 204 KB Output is correct
2 Correct 1 ms 204 KB Output is correct
3 Correct 0 ms 204 KB Output is correct
4 Correct 0 ms 204 KB Output is correct
5 Correct 0 ms 204 KB Output is correct
6 Correct 0 ms 204 KB Output is correct
7 Correct 0 ms 204 KB Output is correct
8 Correct 1 ms 204 KB Output is correct

Subtask #2
8.0 / 8.0

# Verdict Execution time Memory Grader output
1 Correct 31 ms 1228 KB Output is correct
2 Correct 8 ms 588 KB Output is correct
3 Correct 18 ms 940 KB Output is correct
4 Correct 22 ms 1100 KB Output is correct
5 Correct 25 ms 1112 KB Output is correct
6 Correct 16 ms 848 KB Output is correct
7 Correct 4 ms 332 KB Output is correct
8 Correct 16 ms 844 KB Output is correct
9 Correct 41 ms 1604 KB Output is correct
10 Correct 23 ms 1080 KB Output is correct

Subtask #3
15.0 / 15.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 332 KB Output is correct
2 Correct 1 ms 332 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 332 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 332 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 332 KB Output is correct
15 Correct 1 ms 332 KB Output is correct

Subtask #4
16.0 / 16.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 332 KB Output is correct
2 Correct 1 ms 332 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 332 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 332 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 332 KB Output is correct
15 Correct 1 ms 332 KB Output is correct
16 Correct 12 ms 716 KB Output is correct
17 Correct 34 ms 1596 KB Output is correct
18 Correct 43 ms 1724 KB Output is correct
19 Correct 96 ms 1612 KB Output is correct
20 Correct 105 ms 1788 KB Output is correct
21 Correct 31 ms 1488 KB Output is correct
22 Correct 1 ms 332 KB Output is correct
23 Correct 23 ms 976 KB Output is correct
24 Correct 45 ms 1604 KB Output is correct
25 Correct 5 ms 460 KB Output is correct
26 Correct 26 ms 1100 KB Output is correct
27 Correct 33 ms 1256 KB Output is correct
28 Correct 41 ms 1764 KB Output is correct
29 Correct 14 ms 844 KB Output is correct
30 Correct 2 ms 332 KB Output is correct

Subtask #5
23.0 / 23.0

# Verdict Execution time Memory Grader output
1 Correct 31 ms 1228 KB Output is correct
2 Correct 8 ms 588 KB Output is correct
3 Correct 18 ms 940 KB Output is correct
4 Correct 22 ms 1100 KB Output is correct
5 Correct 25 ms 1112 KB Output is correct
6 Correct 16 ms 848 KB Output is correct
7 Correct 4 ms 332 KB Output is correct
8 Correct 16 ms 844 KB Output is correct
9 Correct 41 ms 1604 KB Output is correct
10 Correct 23 ms 1080 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 332 KB Output is correct
15 Correct 1 ms 332 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 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 332 KB Output is correct
24 Correct 1 ms 332 KB Output is correct
25 Correct 1 ms 332 KB Output is correct
26 Correct 12 ms 716 KB Output is correct
27 Correct 34 ms 1596 KB Output is correct
28 Correct 43 ms 1724 KB Output is correct
29 Correct 96 ms 1612 KB Output is correct
30 Correct 105 ms 1788 KB Output is correct
31 Correct 31 ms 1488 KB Output is correct
32 Correct 1 ms 332 KB Output is correct
33 Correct 23 ms 976 KB Output is correct
34 Correct 45 ms 1604 KB Output is correct
35 Correct 5 ms 460 KB Output is correct
36 Correct 26 ms 1100 KB Output is correct
37 Correct 33 ms 1256 KB Output is correct
38 Correct 41 ms 1764 KB Output is correct
39 Correct 14 ms 844 KB Output is correct
40 Correct 2 ms 332 KB Output is correct
41 Correct 90 ms 1604 KB Output is correct
42 Correct 47 ms 1696 KB Output is correct
43 Correct 60 ms 1524 KB Output is correct
44 Correct 45 ms 1728 KB Output is correct
45 Correct 43 ms 1824 KB Output is correct
46 Correct 99 ms 1668 KB Output is correct
47 Correct 38 ms 1596 KB Output is correct
48 Correct 53 ms 1600 KB Output is correct
49 Correct 43 ms 1628 KB Output is correct
50 Correct 356 ms 1728 KB Output is correct
51 Correct 381 ms 1728 KB Output is correct
52 Correct 357 ms 1716 KB Output is correct
53 Correct 376 ms 1860 KB Output is correct
54 Correct 348 ms 1644 KB Output is correct
55 Correct 396 ms 1988 KB Output is correct
56 Correct 338 ms 1656 KB Output is correct

Subtask #6
0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 204 KB Output is correct
2 Correct 1 ms 204 KB Output is correct
3 Correct 0 ms 204 KB Output is correct
4 Correct 0 ms 204 KB Output is correct
5 Correct 0 ms 204 KB Output is correct
6 Correct 0 ms 204 KB Output is correct
7 Correct 0 ms 204 KB Output is correct
8 Correct 1 ms 204 KB Output is correct
9 Correct 31 ms 1228 KB Output is correct
10 Correct 8 ms 588 KB Output is correct
11 Correct 18 ms 940 KB Output is correct
12 Correct 22 ms 1100 KB Output is correct
13 Correct 25 ms 1112 KB Output is correct
14 Correct 16 ms 848 KB Output is correct
15 Correct 4 ms 332 KB Output is correct
16 Correct 16 ms 844 KB Output is correct
17 Correct 41 ms 1604 KB Output is correct
18 Correct 23 ms 1080 KB Output is correct
19 Correct 1 ms 332 KB Output is correct
20 Correct 1 ms 332 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 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 332 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 332 KB Output is correct
33 Correct 1 ms 332 KB Output is correct
34 Correct 12 ms 716 KB Output is correct
35 Correct 34 ms 1596 KB Output is correct
36 Correct 43 ms 1724 KB Output is correct
37 Correct 96 ms 1612 KB Output is correct
38 Correct 105 ms 1788 KB Output is correct
39 Correct 31 ms 1488 KB Output is correct
40 Correct 1 ms 332 KB Output is correct
41 Correct 23 ms 976 KB Output is correct
42 Correct 45 ms 1604 KB Output is correct
43 Correct 5 ms 460 KB Output is correct
44 Correct 26 ms 1100 KB Output is correct
45 Correct 33 ms 1256 KB Output is correct
46 Correct 41 ms 1764 KB Output is correct
47 Correct 14 ms 844 KB Output is correct
48 Correct 2 ms 332 KB Output is correct
49 Correct 90 ms 1604 KB Output is correct
50 Correct 47 ms 1696 KB Output is correct
51 Correct 60 ms 1524 KB Output is correct
52 Correct 45 ms 1728 KB Output is correct
53 Correct 43 ms 1824 KB Output is correct
54 Correct 99 ms 1668 KB Output is correct
55 Correct 38 ms 1596 KB Output is correct
56 Correct 53 ms 1600 KB Output is correct
57 Correct 43 ms 1628 KB Output is correct
58 Correct 356 ms 1728 KB Output is correct
59 Correct 381 ms 1728 KB Output is correct
60 Correct 357 ms 1716 KB Output is correct
61 Correct 376 ms 1860 KB Output is correct
62 Correct 348 ms 1644 KB Output is correct
63 Correct 396 ms 1988 KB Output is correct
64 Correct 338 ms 1656 KB Output is correct
65 Correct 0 ms 204 KB Output is correct
66 Correct 0 ms 204 KB Output is correct
67 Runtime error 54 ms 3396 KB Execution killed with signal 6
68 Halted 0 ms 0 KB -