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QOJ
ID | 题目 | 提交者 | 结果 | 用时 | 内存 | 语言 | 文件大小 | 提交时间 | 测评时间 |
---|---|---|---|---|---|---|---|---|---|
#561247 | #8946. 一眼丁真 | 5sb | 100 ✓ | 4654ms | 4408kb | C++23 | 3.6kb | 2024-09-12 21:26:20 | 2024-09-12 21:26:21 |
Judging History
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();
}
詳細信息
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 4 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 16 17 17 18 18 20 16 16 17 18 18 17 20 17 16 18 18 20 18 16 16 17 18 16 19 15 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