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Submission #434142

# Submission time Handle Problem Language Result Execution time Memory
434142 2021-06-20T15:37:27 Z rqi Chessboard (IZhO18_chessboard) C++14
70 / 100
 608 ms 3992 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.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)));

			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, 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, 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 224 KB Output is correct
2 Correct 1 ms 204 KB Output is correct
3 Correct 1 ms 320 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 204 KB Output is correct

Subtask #2
8.0 / 8.0

# Verdict Execution time Memory Grader output
1 Correct 31 ms 1648 KB Output is correct
2 Correct 8 ms 848 KB Output is correct
3 Correct 20 ms 1236 KB Output is correct
4 Correct 21 ms 1376 KB Output is correct
5 Correct 27 ms 1448 KB Output is correct
6 Correct 16 ms 1152 KB Output is correct
7 Correct 6 ms 588 KB Output is correct
8 Correct 16 ms 1208 KB Output is correct
9 Correct 40 ms 2000 KB Output is correct
10 Correct 23 ms 1428 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 320 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 320 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 14 ms 1100 KB Output is correct
17 Correct 32 ms 1980 KB Output is correct
18 Correct 43 ms 2268 KB Output is correct
19 Correct 101 ms 1988 KB Output is correct
20 Correct 109 ms 2212 KB Output is correct
21 Correct 31 ms 1928 KB Output is correct
22 Correct 1 ms 332 KB Output is correct
23 Correct 23 ms 1252 KB Output is correct
24 Correct 44 ms 1992 KB Output is correct
25 Correct 5 ms 588 KB Output is correct
26 Correct 29 ms 1528 KB Output is correct
27 Correct 33 ms 1668 KB Output is correct
28 Correct 42 ms 2124 KB Output is correct
29 Correct 14 ms 1100 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 1648 KB Output is correct
2 Correct 8 ms 848 KB Output is correct
3 Correct 20 ms 1236 KB Output is correct
4 Correct 21 ms 1376 KB Output is correct
5 Correct 27 ms 1448 KB Output is correct
6 Correct 16 ms 1152 KB Output is correct
7 Correct 6 ms 588 KB Output is correct
8 Correct 16 ms 1208 KB Output is correct
9 Correct 40 ms 2000 KB Output is correct
10 Correct 23 ms 1428 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 320 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 14 ms 1100 KB Output is correct
27 Correct 32 ms 1980 KB Output is correct
28 Correct 43 ms 2268 KB Output is correct
29 Correct 101 ms 1988 KB Output is correct
30 Correct 109 ms 2212 KB Output is correct
31 Correct 31 ms 1928 KB Output is correct
32 Correct 1 ms 332 KB Output is correct
33 Correct 23 ms 1252 KB Output is correct
34 Correct 44 ms 1992 KB Output is correct
35 Correct 5 ms 588 KB Output is correct
36 Correct 29 ms 1528 KB Output is correct
37 Correct 33 ms 1668 KB Output is correct
38 Correct 42 ms 2124 KB Output is correct
39 Correct 14 ms 1100 KB Output is correct
40 Correct 2 ms 332 KB Output is correct
41 Correct 95 ms 1884 KB Output is correct
42 Correct 48 ms 2152 KB Output is correct
43 Correct 60 ms 1896 KB Output is correct
44 Correct 46 ms 2100 KB Output is correct
45 Correct 42 ms 2172 KB Output is correct
46 Correct 100 ms 2116 KB Output is correct
47 Correct 44 ms 2032 KB Output is correct
48 Correct 52 ms 1968 KB Output is correct
49 Correct 41 ms 1860 KB Output is correct
50 Correct 379 ms 2020 KB Output is correct
51 Correct 396 ms 2184 KB Output is correct
52 Correct 360 ms 2080 KB Output is correct
53 Correct 380 ms 2168 KB Output is correct
54 Correct 357 ms 2032 KB Output is correct
55 Correct 409 ms 2220 KB Output is correct
56 Correct 354 ms 2012 KB Output is correct

Subtask #6
0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 224 KB Output is correct
2 Correct 1 ms 204 KB Output is correct
3 Correct 1 ms 320 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 204 KB Output is correct
9 Correct 31 ms 1648 KB Output is correct
10 Correct 8 ms 848 KB Output is correct
11 Correct 20 ms 1236 KB Output is correct
12 Correct 21 ms 1376 KB Output is correct
13 Correct 27 ms 1448 KB Output is correct
14 Correct 16 ms 1152 KB Output is correct
15 Correct 6 ms 588 KB Output is correct
16 Correct 16 ms 1208 KB Output is correct
17 Correct 40 ms 2000 KB Output is correct
18 Correct 23 ms 1428 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 320 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 14 ms 1100 KB Output is correct
35 Correct 32 ms 1980 KB Output is correct
36 Correct 43 ms 2268 KB Output is correct
37 Correct 101 ms 1988 KB Output is correct
38 Correct 109 ms 2212 KB Output is correct
39 Correct 31 ms 1928 KB Output is correct
40 Correct 1 ms 332 KB Output is correct
41 Correct 23 ms 1252 KB Output is correct
42 Correct 44 ms 1992 KB Output is correct
43 Correct 5 ms 588 KB Output is correct
44 Correct 29 ms 1528 KB Output is correct
45 Correct 33 ms 1668 KB Output is correct
46 Correct 42 ms 2124 KB Output is correct
47 Correct 14 ms 1100 KB Output is correct
48 Correct 2 ms 332 KB Output is correct
49 Correct 95 ms 1884 KB Output is correct
50 Correct 48 ms 2152 KB Output is correct
51 Correct 60 ms 1896 KB Output is correct
52 Correct 46 ms 2100 KB Output is correct
53 Correct 42 ms 2172 KB Output is correct
54 Correct 100 ms 2116 KB Output is correct
55 Correct 44 ms 2032 KB Output is correct
56 Correct 52 ms 1968 KB Output is correct
57 Correct 41 ms 1860 KB Output is correct
58 Correct 379 ms 2020 KB Output is correct
59 Correct 396 ms 2184 KB Output is correct
60 Correct 360 ms 2080 KB Output is correct
61 Correct 380 ms 2168 KB Output is correct
62 Correct 357 ms 2032 KB Output is correct
63 Correct 409 ms 2220 KB Output is correct
64 Correct 354 ms 2012 KB Output is correct
65 Correct 1 ms 324 KB Output is correct
66 Correct 1 ms 332 KB Output is correct
67 Correct 591 ms 2128 KB Output is correct
68 Correct 608 ms 3992 KB Output is correct
69 Correct 500 ms 3532 KB Output is correct
70 Correct 514 ms 3880 KB Output is correct
71 Correct 538 ms 3824 KB Output is correct
72 Correct 545 ms 3764 KB Output is correct
73 Correct 555 ms 3672 KB Output is correct
74 Correct 603 ms 3948 KB Output is correct
75 Incorrect 585 ms 3804 KB Output isn't correct
76 Halted 0 ms 0 KB -