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Submission #434151

# Submission time Handle Problem Language Result Execution time Memory
434151 2021-06-20T15:53:16 Z rqi Chessboard (IZhO18_chessboard) C++17
70 / 100
 616 ms 1908 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();
}

void print(pl a){
	cout << "pl: " << 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 + 1) % 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.s/SZ == corner22.s/SZ && corner11.f % SZ == 0 && (corner22.f+1) % 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(!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)));

			// print(res);

			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)));

			// print(res);
			ADD(res, doBig(mp(CORNER11.f+1, CORNER11.s+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, 1).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 1 ms 204 KB Output is correct
4 Correct 0 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 204 KB Output is correct

Subtask #2
8.0 / 8.0

# Verdict Execution time Memory Grader output
1 Correct 33 ms 1228 KB Output is correct
2 Correct 8 ms 588 KB Output is correct
3 Correct 24 ms 828 KB Output is correct
4 Correct 20 ms 1052 KB Output is correct
5 Correct 25 ms 1072 KB Output is correct
6 Correct 19 ms 864 KB Output is correct
7 Correct 4 ms 332 KB Output is correct
8 Correct 16 ms 836 KB Output is correct
9 Correct 40 ms 1608 KB Output is correct
10 Correct 23 ms 1100 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 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 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 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 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 15 ms 700 KB Output is correct
17 Correct 40 ms 1500 KB Output is correct
18 Correct 50 ms 1780 KB Output is correct
19 Correct 94 ms 1784 KB Output is correct
20 Correct 110 ms 1860 KB Output is correct
21 Correct 30 ms 1520 KB Output is correct
22 Correct 1 ms 204 KB Output is correct
23 Correct 23 ms 956 KB Output is correct
24 Correct 40 ms 1616 KB Output is correct
25 Correct 5 ms 456 KB Output is correct
26 Correct 25 ms 1100 KB Output is correct
27 Correct 36 ms 1388 KB Output is correct
28 Correct 41 ms 1732 KB Output is correct
29 Correct 13 ms 756 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 33 ms 1228 KB Output is correct
2 Correct 8 ms 588 KB Output is correct
3 Correct 24 ms 828 KB Output is correct
4 Correct 20 ms 1052 KB Output is correct
5 Correct 25 ms 1072 KB Output is correct
6 Correct 19 ms 864 KB Output is correct
7 Correct 4 ms 332 KB Output is correct
8 Correct 16 ms 836 KB Output is correct
9 Correct 40 ms 1608 KB Output is correct
10 Correct 23 ms 1100 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 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 15 ms 700 KB Output is correct
27 Correct 40 ms 1500 KB Output is correct
28 Correct 50 ms 1780 KB Output is correct
29 Correct 94 ms 1784 KB Output is correct
30 Correct 110 ms 1860 KB Output is correct
31 Correct 30 ms 1520 KB Output is correct
32 Correct 1 ms 204 KB Output is correct
33 Correct 23 ms 956 KB Output is correct
34 Correct 40 ms 1616 KB Output is correct
35 Correct 5 ms 456 KB Output is correct
36 Correct 25 ms 1100 KB Output is correct
37 Correct 36 ms 1388 KB Output is correct
38 Correct 41 ms 1732 KB Output is correct
39 Correct 13 ms 756 KB Output is correct
40 Correct 2 ms 332 KB Output is correct
41 Correct 87 ms 1584 KB Output is correct
42 Correct 48 ms 1780 KB Output is correct
43 Correct 59 ms 1520 KB Output is correct
44 Correct 50 ms 1732 KB Output is correct
45 Correct 43 ms 1736 KB Output is correct
46 Correct 99 ms 1732 KB Output is correct
47 Correct 38 ms 1600 KB Output is correct
48 Correct 56 ms 1664 KB Output is correct
49 Correct 42 ms 1532 KB Output is correct
50 Correct 363 ms 1728 KB Output is correct
51 Correct 387 ms 1704 KB Output is correct
52 Correct 363 ms 1788 KB Output is correct
53 Correct 382 ms 1812 KB Output is correct
54 Correct 350 ms 1636 KB Output is correct
55 Correct 397 ms 1908 KB Output is correct
56 Correct 343 ms 1732 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 1 ms 204 KB Output is correct
4 Correct 0 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 204 KB Output is correct
9 Correct 33 ms 1228 KB Output is correct
10 Correct 8 ms 588 KB Output is correct
11 Correct 24 ms 828 KB Output is correct
12 Correct 20 ms 1052 KB Output is correct
13 Correct 25 ms 1072 KB Output is correct
14 Correct 19 ms 864 KB Output is correct
15 Correct 4 ms 332 KB Output is correct
16 Correct 16 ms 836 KB Output is correct
17 Correct 40 ms 1608 KB Output is correct
18 Correct 23 ms 1100 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 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 15 ms 700 KB Output is correct
35 Correct 40 ms 1500 KB Output is correct
36 Correct 50 ms 1780 KB Output is correct
37 Correct 94 ms 1784 KB Output is correct
38 Correct 110 ms 1860 KB Output is correct
39 Correct 30 ms 1520 KB Output is correct
40 Correct 1 ms 204 KB Output is correct
41 Correct 23 ms 956 KB Output is correct
42 Correct 40 ms 1616 KB Output is correct
43 Correct 5 ms 456 KB Output is correct
44 Correct 25 ms 1100 KB Output is correct
45 Correct 36 ms 1388 KB Output is correct
46 Correct 41 ms 1732 KB Output is correct
47 Correct 13 ms 756 KB Output is correct
48 Correct 2 ms 332 KB Output is correct
49 Correct 87 ms 1584 KB Output is correct
50 Correct 48 ms 1780 KB Output is correct
51 Correct 59 ms 1520 KB Output is correct
52 Correct 50 ms 1732 KB Output is correct
53 Correct 43 ms 1736 KB Output is correct
54 Correct 99 ms 1732 KB Output is correct
55 Correct 38 ms 1600 KB Output is correct
56 Correct 56 ms 1664 KB Output is correct
57 Correct 42 ms 1532 KB Output is correct
58 Correct 363 ms 1728 KB Output is correct
59 Correct 387 ms 1704 KB Output is correct
60 Correct 363 ms 1788 KB Output is correct
61 Correct 382 ms 1812 KB Output is correct
62 Correct 350 ms 1636 KB Output is correct
63 Correct 397 ms 1908 KB Output is correct
64 Correct 343 ms 1732 KB Output is correct
65 Correct 1 ms 204 KB Output is correct
66 Correct 1 ms 204 KB Output is correct
67 Correct 579 ms 1768 KB Output is correct
68 Correct 604 ms 1764 KB Output is correct
69 Correct 505 ms 1568 KB Output is correct
70 Correct 518 ms 1700 KB Output is correct
71 Correct 552 ms 1700 KB Output is correct
72 Correct 520 ms 1664 KB Output is correct
73 Correct 540 ms 1632 KB Output is correct
74 Correct 616 ms 1756 KB Output is correct
75 Incorrect 545 ms 1772 KB Output isn't correct
76 Halted 0 ms 0 KB -