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Submission #434159

# Submission time Handle Problem Language Result Execution time Memory
434159 2021-06-20T16:10:48 Z rqi Chessboard (IZhO18_chessboard) C++14
100 / 100
 614 ms 4256 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)/SZ*ll(corner22.s+1-corner11.s)/SZ;
	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;

	ll area_sum = 0;
	for(int i = 1; i <= K; i++){
		pi corner11 = mp(X1[i], Y1[i]);
		pi corner22 = mp(X2[i], Y2[i]);

		area_sum+=ll(corner22.s-corner11.s+1)*ll(corner22.f-corner11.f+1);
		
		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)));
			// print(res);
		}
		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;
	}

	// assert(area_sum == flip_to_white+flip_to_black);
	// 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 0 ms 204 KB Output is correct
2 Correct 0 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 0 ms 204 KB Output is correct

Subtask #2
8.0 / 8.0

# Verdict Execution time Memory Grader output
1 Correct 33 ms 1284 KB Output is correct
2 Correct 7 ms 588 KB Output is correct
3 Correct 17 ms 844 KB Output is correct
4 Correct 20 ms 1044 KB Output is correct
5 Correct 24 ms 1176 KB Output is correct
6 Correct 16 ms 764 KB Output is correct
7 Correct 4 ms 332 KB Output is correct
8 Correct 17 ms 844 KB Output is correct
9 Correct 40 ms 1688 KB Output is correct
10 Correct 27 ms 1032 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 0 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 0 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 37 ms 1568 KB Output is correct
18 Correct 42 ms 1804 KB Output is correct
19 Correct 91 ms 1604 KB Output is correct
20 Correct 104 ms 1852 KB Output is correct
21 Correct 36 ms 1668 KB Output is correct
22 Correct 1 ms 336 KB Output is correct
23 Correct 23 ms 888 KB Output is correct
24 Correct 39 ms 1636 KB Output is correct
25 Correct 5 ms 332 KB Output is correct
26 Correct 26 ms 1220 KB Output is correct
27 Correct 32 ms 1276 KB Output is correct
28 Correct 42 ms 1804 KB Output is correct
29 Correct 13 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 33 ms 1284 KB Output is correct
2 Correct 7 ms 588 KB Output is correct
3 Correct 17 ms 844 KB Output is correct
4 Correct 20 ms 1044 KB Output is correct
5 Correct 24 ms 1176 KB Output is correct
6 Correct 16 ms 764 KB Output is correct
7 Correct 4 ms 332 KB Output is correct
8 Correct 17 ms 844 KB Output is correct
9 Correct 40 ms 1688 KB Output is correct
10 Correct 27 ms 1032 KB Output is correct
11 Correct 1 ms 332 KB Output is correct
12 Correct 0 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 37 ms 1568 KB Output is correct
28 Correct 42 ms 1804 KB Output is correct
29 Correct 91 ms 1604 KB Output is correct
30 Correct 104 ms 1852 KB Output is correct
31 Correct 36 ms 1668 KB Output is correct
32 Correct 1 ms 336 KB Output is correct
33 Correct 23 ms 888 KB Output is correct
34 Correct 39 ms 1636 KB Output is correct
35 Correct 5 ms 332 KB Output is correct
36 Correct 26 ms 1220 KB Output is correct
37 Correct 32 ms 1276 KB Output is correct
38 Correct 42 ms 1804 KB Output is correct
39 Correct 13 ms 844 KB Output is correct
40 Correct 2 ms 332 KB Output is correct
41 Correct 87 ms 1564 KB Output is correct
42 Correct 57 ms 1748 KB Output is correct
43 Correct 60 ms 1496 KB Output is correct
44 Correct 45 ms 1732 KB Output is correct
45 Correct 45 ms 1732 KB Output is correct
46 Correct 97 ms 1732 KB Output is correct
47 Correct 38 ms 1640 KB Output is correct
48 Correct 52 ms 1612 KB Output is correct
49 Correct 41 ms 1608 KB Output is correct
50 Correct 357 ms 1600 KB Output is correct
51 Correct 383 ms 1860 KB Output is correct
52 Correct 364 ms 1728 KB Output is correct
53 Correct 382 ms 1808 KB Output is correct
54 Correct 346 ms 1696 KB Output is correct
55 Correct 389 ms 1936 KB Output is correct
56 Correct 340 ms 1656 KB Output is correct

Subtask #6
30.0 / 30.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 204 KB Output is correct
2 Correct 0 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 0 ms 204 KB Output is correct
9 Correct 33 ms 1284 KB Output is correct
10 Correct 7 ms 588 KB Output is correct
11 Correct 17 ms 844 KB Output is correct
12 Correct 20 ms 1044 KB Output is correct
13 Correct 24 ms 1176 KB Output is correct
14 Correct 16 ms 764 KB Output is correct
15 Correct 4 ms 332 KB Output is correct
16 Correct 17 ms 844 KB Output is correct
17 Correct 40 ms 1688 KB Output is correct
18 Correct 27 ms 1032 KB Output is correct
19 Correct 1 ms 332 KB Output is correct
20 Correct 0 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 37 ms 1568 KB Output is correct
36 Correct 42 ms 1804 KB Output is correct
37 Correct 91 ms 1604 KB Output is correct
38 Correct 104 ms 1852 KB Output is correct
39 Correct 36 ms 1668 KB Output is correct
40 Correct 1 ms 336 KB Output is correct
41 Correct 23 ms 888 KB Output is correct
42 Correct 39 ms 1636 KB Output is correct
43 Correct 5 ms 332 KB Output is correct
44 Correct 26 ms 1220 KB Output is correct
45 Correct 32 ms 1276 KB Output is correct
46 Correct 42 ms 1804 KB Output is correct
47 Correct 13 ms 844 KB Output is correct
48 Correct 2 ms 332 KB Output is correct
49 Correct 87 ms 1564 KB Output is correct
50 Correct 57 ms 1748 KB Output is correct
51 Correct 60 ms 1496 KB Output is correct
52 Correct 45 ms 1732 KB Output is correct
53 Correct 45 ms 1732 KB Output is correct
54 Correct 97 ms 1732 KB Output is correct
55 Correct 38 ms 1640 KB Output is correct
56 Correct 52 ms 1612 KB Output is correct
57 Correct 41 ms 1608 KB Output is correct
58 Correct 357 ms 1600 KB Output is correct
59 Correct 383 ms 1860 KB Output is correct
60 Correct 364 ms 1728 KB Output is correct
61 Correct 382 ms 1808 KB Output is correct
62 Correct 346 ms 1696 KB Output is correct
63 Correct 389 ms 1936 KB Output is correct
64 Correct 340 ms 1656 KB Output is correct
65 Correct 1 ms 204 KB Output is correct
66 Correct 0 ms 332 KB Output is correct
67 Correct 607 ms 1828 KB Output is correct
68 Correct 595 ms 1764 KB Output is correct
69 Correct 499 ms 1604 KB Output is correct
70 Correct 504 ms 1708 KB Output is correct
71 Correct 546 ms 1688 KB Output is correct
72 Correct 524 ms 1664 KB Output is correct
73 Correct 568 ms 1604 KB Output is correct
74 Correct 585 ms 1816 KB Output is correct
75 Correct 539 ms 1672 KB Output is correct
76 Correct 583 ms 4032 KB Output is correct
77 Correct 136 ms 4224 KB Output is correct
78 Correct 58 ms 3728 KB Output is correct
79 Correct 93 ms 3552 KB Output is correct
80 Correct 98 ms 3780 KB Output is correct
81 Correct 95 ms 3488 KB Output is correct
82 Correct 83 ms 4004 KB Output is correct
83 Correct 75 ms 3648 KB Output is correct
84 Correct 371 ms 4124 KB Output is correct
85 Correct 614 ms 4164 KB Output is correct
86 Correct 3 ms 332 KB Output is correct
87 Correct 2 ms 204 KB Output is correct
88 Correct 614 ms 4256 KB Output is correct
89 Correct 143 ms 1056 KB Output is correct
90 Correct 1 ms 332 KB Output is correct