QOJ.ac

QOJ

IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#561247#8946. 一眼丁真5sb100 ✓4654ms4408kbC++233.6kb2024-09-12 21:26:202024-09-12 21:26:21

Judging History

你现在查看的是最新测评结果

  • [2024-09-12 21:26:21]
  • 评测
  • 测评结果:100
  • 用时:4654ms
  • 内存:4408kb
  • [2024-09-12 21:26:20]
  • 提交

answer

#include <bits/stdc++.h>

using std::numbers::pi;

struct point {
	double x, y;

	friend point operator+(point p, point q) {
		return point{p.x + q.x, p.y + q.y};
	}
	friend point operator-(point p, point q) {
		return point{p.x - q.x, p.y - q.y};
	}
	friend point operator*(point p, double q) {
		return point{p.x * q, p.y * q};
	}
	friend point operator/(point p, double q) {
		return point{p.x / q, p.y / q};
	}

	friend double cross(point p, point q) {
		return p.x * q.y - p.y * q.x;
	}
	friend double dot(point p, point q) {
		return p.x * q.x + p.y * q.y;
	}
	friend double ang(point p, point q) {
		return std::atan2(p.y - q.y, p.x - q.x);
	}
	friend double dis(point p, point q) {
		return std::hypot(p.x - q.x, p.y - q.y);
	}
	friend double dis_sq(point p, point q) {
		return std::pow(p.x - q.x, 2) + std::pow(p.y - q.y, 2);
	}

	friend std::istream &operator>>(std::istream &is, point &p) {
		return is >> p.x >> p.y;
	}
	friend std::ostream &operator<<(std::ostream &os, point p) {
		return os << p.x << ' ' << p.y;
	}
};
struct line {
	point x, y;
	friend double dis_sq(point p, line l) {
		return std::pow(cross(p - l.x, l.y - l.x), 2) / dis_sq(l.x, l.y);
	}
};

void solve() {
	int n, m;
	std::cin >> n >> m;
	std::vector<std::pair<point, double>> a(n);
	for (auto &[p, _] : a) std::cin >> p;

	point cen{0, 0};
	for (auto [p, _] : a) cen = cen + p;
	cen = cen / n;

	auto calc = [&a](point q) {
		double s = 0;
		for (auto [p, _] : a) s += std::pow(dis(p, q) - 1, 2);
		return s;
	};
	double mn = calc(cen);

	for (double delta = .1; delta > 1e-8; delta *= .95) {
		point old = cen;
		for (int dx = -1; dx <= 1; dx++) {
			for (int dy = -1; dy <= 1; dy++) {
				point cur{old.x + delta * dx, old.y + delta * dy};
				double val = calc(cur);
				if (val < mn) {
					mn = val;
					cen = cur;
				}
			}
		}
	}

	// std::cerr << std::fixed << std::setprecision(10) << dis(cen, point{0, 0}) << '\n';
	
	for (auto &[p, g] : a) g = ang(p, cen);
	std::sort(a.begin(), a.end(), [](auto p, auto q) {
		return p.second < q.second;
	});

	auto b = a;
	std::sort(b.begin(), b.end(), [cen](auto p, auto q) {
		return dis(p.first, cen) > dis(q.first, cen);
	});
	int lim = std::min(n, 20), delta = std::min(n - 1, 1);
	std::vector<double> can;
	can.reserve(lim * (delta + 1 + delta));
	for (int i = 0; i < lim; i++) {
		double g = b[i].second;
		for (int d = -delta; d <= delta; d++) {
			can.push_back(g + (1. * d / n) * (2 * pi));
		}
	}

	double best = 1e18;
	int ans = -1;

	for (int num = std::max(3, m - 5); num <= m; num++) {
		for (double g : can) {
			double sum = 0;

			std::vector<std::pair<point, double>> ver(num);
			for (int i = 0; i < num; i++) {
				double cur = g + (1. * i / num) * (2 * pi);
				ver[i].first = point{cen.x + std::cos(cur), cen.y + std::sin(cur)};
				ver[i].second = ang(ver[i].first, cen);
			}
			std::sort(ver.begin(), ver.end(), [](auto p, auto q) {
				return p.second < q.second;
			});

			std::vector<line> edge(num);
			for (int i = 0; i < num; i++) {
				int j = i == 0 ? num - 1 : i - 1;
				edge[i] = {ver[j].first, ver[i].first};
			}

			int pos = 0;
			for (auto [p, x] : a) {
				while (pos != num && ver[pos].second < x) pos++;
				int i = pos == num ? 0 : pos;
				sum += dis_sq(p, edge[i]);
				if (sum >= best) break;
			}

			if (sum < best) {
				best = sum;
				ans = num;
			}
		}
	}

	std::cout << ans << '\n';
}

int main() {
	// freopen("gen.in", "r", stdin);
	// freopen("gen.out", "w", stdout);
	std::cin.tie(nullptr)->sync_with_stdio(false);
	int t;
	std::cin >> t;
	while (t--) solve();
}

Details

Tip: Click on the bar to expand more detailed information

Pretests


Final Tests

Test #1:

score: 10
Accepted
time: 4437ms
memory: 4360kb

input:

200
1000 4
-1.65882 -0.468078
-0.559879 0.302541
-1.67025 -0.452322
-0.54312 -1.40252
0.116365 -0.958391
-1.57137 -0.386501
-1.20353 -0.13415
0.123479 -0.934878
-0.597084 -1.41011
-1.69629 -0.489381
-0.0114821 -1.03665
-0.546439 -1.39593
-0.573469 -1.41618
-1.06124 -1.4763
-1.52521 -0.371347
-1.4609...

output:

4
4
3
4
4
3
3
4
4
3
4
4
4
3
4
4
3
4
4
4
4
3
4
3
4
3
3
3
4
3
3
3
3
3
3
3
3
3
4
3
3
4
3
4
3
3
3
3
4
3
3
3
3
4
3
4
3
3
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4
3
4
3
4
3
4
4
3
3
3
4
3
3
3
4
4
3
3
3
3
4
4
3
3
3
4
3
3
3
3
4
3
4
3
3
3
4
3
3
4
3
3
4
3
4
4
3
3
4
4
3
4
3
4
4
4
3
4
3
4
3
3
3
3
4
3
4
3
3
3
3
3
3
3
4
4
4
3
4
4
3
4
4
4
4
3
3
3
3
3
...

result:

ok #(wrong) = 0, #(correct) = 200

Test #2:

score: 10
Accepted
time: 4422ms
memory: 4408kb

input:

200
1000 4
0.22827 0.536959
-0.743134 0.215561
-0.0821736 -0.804273
0.470104 -0.194576
0.819679 0.553173
0.212657 0.515942
-0.379762 -0.349824
0.140334 -0.864474
-0.033494 0.513621
0.673108 0.243877
0.716308 0.318053
-0.108843 -0.719375
0.102132 -0.924612
0.0141018 -0.921927
0.710421 0.53719
-0.4572...

output:

3
4
3
4
3
3
3
3
4
3
4
4
4
4
4
4
4
3
4
4
3
3
3
4
4
4
4
4
3
3
3
4
4
4
4
4
3
3
3
4
4
4
3
3
4
4
3
4
3
4
3
4
3
3
4
4
3
3
3
4
4
3
4
4
4
4
3
3
3
3
3
3
4
4
3
4
4
4
4
4
3
3
3
4
3
4
3
3
3
3
3
3
3
3
4
4
4
4
4
3
3
3
3
4
3
4
4
3
3
3
4
4
3
4
3
3
4
3
4
3
4
3
4
4
3
4
4
4
3
3
3
3
3
4
4
3
4
4
3
4
4
4
4
4
3
4
3
3
4
3
...

result:

ok #(wrong) = 0, #(correct) = 200

Test #3:

score: 10
Accepted
time: 4479ms
memory: 4200kb

input:

200
1000 10
0.171063 0.768938
0.339764 0.873943
1.15161 0.672578
0.805594 0.765797
1.15695 0.666805
1.26595 -0.695135
1.20927 0.578729
-0.356686 -0.292753
0.940372 -0.919379
-0.269337 -0.62435
-0.0757841 0.550908
1.52432 0.00176461
-0.366525 0.00974288
0.524328 0.851771
1.37215 0.224858
0.655827 -0....

output:

7
10
7
5
6
8
10
6
8
10
9
5
9
6
10
7
7
5
10
6
10
7
7
10
7
8
8
7
7
7
10
8
6
8
5
7
9
7
5
10
10
7
5
8
6
8
10
8
8
5
7
10
5
8
8
7
5
6
8
10
7
7
6
6
10
8
10
8
5
9
6
6
9
10
6
9
6
5
5
9
7
8
8
7
7
5
5
7
7
8
6
8
10
6
6
6
7
7
8
7
8
8
8
8
8
6
6
9
5
6
10
5
5
5
10
10
10
10
6
10
8
6
9
9
9
6
6
7
9
10
8
8
7
7
6
10
10
...

result:

ok #(wrong) = 0, #(correct) = 200

Test #4:

score: 10
Accepted
time: 4478ms
memory: 4160kb

input:

200
1000 10
-0.83557 -0.43386
-0.900052 0.302486
0.843787 0.446154
-0.0854311 -0.918758
0.501433 0.844022
-0.955344 -0.173521
0.516729 0.8388
-0.917289 0.0698801
-0.925852 0.0681056
-0.848415 0.471305
0.098655 0.922883
0.958545 0.273256
0.67931 0.611085
-0.951816 -0.0694206
-0.245102 0.947475
0.9397...

output:

8
10
10
6
7
9
7
9
10
8
6
5
10
7
9
8
6
10
8
7
8
5
6
8
6
7
5
7
9
6
5
9
7
5
7
5
10
6
6
6
8
8
10
9
8
5
8
6
9
10
7
7
10
9
9
8
9
7
8
5
5
7
6
6
6
8
5
6
9
6
6
8
9
10
5
6
7
8
8
6
10
8
8
10
10
6
10
9
5
7
5
9
6
7
7
6
5
5
10
7
8
9
6
7
5
5
9
8
7
10
6
9
5
9
10
10
6
9
5
9
10
6
8
9
8
10
6
9
5
10
9
8
5
6
7
7
10
9
5
...

result:

ok #(wrong) = 0, #(correct) = 200

Test #5:

score: 10
Accepted
time: 4560ms
memory: 4264kb

input:

200
1000 20
1.10645 1.72762
0.00828014 0.0575131
-0.300448 0.537454
0.138879 1.67906
0.73884 1.83804
-0.331532 1.01263
1.57294 1.17098
1.61097 0.722726
0.267742 1.7481
0.805786 -0.115483
1.63489 0.918378
0.358705 -0.0984941
-0.303133 1.14962
1.59952 1.0805
-0.22276 1.35792
1.06748 1.74928
1.48122 1....

output:

19
18
20
19
19
16
20
18
16
15
16
18
16
16
19
20
20
16
19
19
15
19
20
18
16
15
16
19
15
17
19
17
20
18
20
16
20
17
17
16
17
20
20
15
18
18
19
15
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18
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18
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17
20
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16
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18
20
18
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16
17
18
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19
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19
15
15
16
19
20
17
19
16
16
18
16
15
15
16
15
18
17
17
15
18
17
15
17
20
16
...

result:

ok #(wrong) = 0, #(correct) = 200

Test #6:

score: 10
Accepted
time: 4571ms
memory: 4348kb

input:

200
1000 20
0.306231 0.947555
-0.470695 -0.867584
0.0798229 -0.979712
0.972425 -0.18076
0.205552 0.977367
0.503871 -0.843521
0.931879 -0.34759
-0.528287 -0.821234
0.384399 0.889843
0.0427201 -0.995252
0.911209 0.407903
-0.925169 0.281163
1.01054 0.00777535
0.829844 0.506267
0.145597 -0.98502
-0.2980...

output:

19
20
18
15
20
16
15
16
19
16
17
20
19
15
20
19
20
20
19
15
20
17
18
16
20
15
17
16
16
17
17
19
18
15
20
20
16
16
20
17
20
16
15
17
19
15
15
19
16
19
16
18
20
19
18
16
19
19
15
18
15
18
17
15
16
19
20
20
16
18
19
20
17
16
15
15
20
18
16
20
19
20
20
19
15
20
16
19
17
17
20
18
19
20
20
20
20
15
20
20
...

result:

ok #(wrong) = 0, #(correct) = 200

Test #7:

score: 10
Accepted
time: 4621ms
memory: 4348kb

input:

200
1000 25
-0.150207 0.698438
0.0893216 1.09445
1.69859 -0.01418
0.00876932 1.00054
-0.0563829 0.902229
0.736602 1.41841
-0.147213 0.274848
-0.182403 0.345741
1.63542 -0.149404
1.80616 0.580086
1.56376 -0.247799
0.32449 1.26092
0.627195 1.41568
-0.0382449 -0.105866
0.129226 1.13973
0.0847462 -0.261...

output:

23
22
25
25
21
23
20
22
24
20
23
25
21
23
22
24
24
21
25
25
22
20
24
23
23
21
20
21
25
24
22
24
21
23
22
22
21
24
21
21
21
25
25
20
21
21
24
24
24
22
22
22
21
24
22
22
23
25
20
24
25
22
24
25
23
22
24
21
22
23
22
21
25
21
22
21
20
25
25
22
20
20
20
22
23
24
20
23
24
25
24
25
25
21
24
21
25
20
20
24
...

result:

ok #(wrong) = 0, #(correct) = 200

Test #8:

score: 10
Accepted
time: 4620ms
memory: 4360kb

input:

200
1000 25
0.964683 -0.212993
0.98252 -0.136339
-0.168828 -0.971035
0.865174 -0.484339
0.571258 -0.82591
-0.797776 -0.589278
-0.307998 -0.948622
-0.80831 0.593024
-0.659663 0.745975
0.923635 -0.380449
0.996853 -0.0380425
0.679349 0.732259
-0.0225609 1.00911
0.717309 -0.710159
-0.425272 -0.901905
0....

output:

21
25
25
25
25
24
24
24
22
22
22
25
25
22
20
24
21
24
21
23
22
21
23
22
21
25
23
25
22
23
22
24
21
25
21
22
20
22
20
23
21
22
23
24
24
22
24
21
22
21
23
23
20
24
25
21
24
25
23
22
24
23
21
20
20
24
23
22
20
24
25
20
20
20
24
23
22
23
22
24
23
25
22
23
25
23
25
20
24
24
25
20
21
24
25
24
21
24
25
21
...

result:

ok #(wrong) = 0, #(correct) = 200

Test #9:

score: 10
Accepted
time: 4654ms
memory: 4208kb

input:

200
1000 30
-0.823086 -1.0434
0.105428 -0.15483
-0.502513 -0.953264
0.0771079 -0.121858
-1.23449 0.876862
-0.0812511 -0.664993
-0.241982 0.678029
-0.622296 0.896641
-1.20049 0.882673
-1.88268 -0.190726
0.0489134 -0.354098
0.0159866 -0.415372
-0.167045 -0.751293
-0.0637444 -0.612609
0.0696068 -0.3288...

output:

29
28
29
26
26
28
27
30
27
26
28
28
29
28
26
29
28
30
26
28
26
28
28
29
28
28
30
27
27
28
29
26
30
30
27
30
28
30
28
27
27
28
30
25
27
27
28
30
25
30
27
26
25
29
27
26
25
30
27
30
29
28
28
27
27
25
25
25
28
29
25
25
28
29
29
27
27
29
27
29
28
30
25
30
25
28
26
29
27
29
28
29
29
25
25
30
30
27
30
29
...

result:

ok #(wrong) = 0, #(correct) = 200

Test #10:

score: 10
Accepted
time: 4631ms
memory: 4352kb

input:

200
1000 30
-0.922656 0.353773
0.603763 -0.788179
-0.461439 0.857645
-0.991954 -0.0838754
-0.144937 0.982998
0.605566 -0.771346
0.0629471 0.988433
0.995332 -0.0164629
-0.878948 0.473977
-0.852896 0.501311
0.840425 0.516425
0.440577 0.898323
-0.515795 0.861164
0.116181 -1.00427
-0.477573 -0.879226
0....

output:

25
29
28
29
25
25
25
26
29
27
26
27
30
26
27
28
28
27
25
29
28
25
30
28
27
27
28
29
25
28
26
28
26
30
26
30
30
25
30
25
29
30
26
27
30
28
25
28
28
29
25
27
26
28
25
27
29
26
29
30
28
26
26
29
30
25
28
27
29
29
30
28
29
27
29
30
25
25
26
28
26
25
26
30
25
25
26
29
28
25
25
25
30
27
25
29
25
29
30
27
...

result:

ok #(wrong) = 0, #(correct) = 200