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uva1432
2022-08-08 17:50:00 【小刀刺大熊】
#include <iostream>
#include <istream>
#include <sstream>
#include <vector>
#include <stack>
#include <list>
#include <map>
#include <set>
#include <deque>
#include <queue>
#include <cstring>
#include <unordered_map>
#include <unordered_set>
#include <algorithm>
#include <numeric>
#include <chrono>
#include <ctime>
#include <cmath>
#include <cctype>
#include <string>
#include <cstdio>
#include <iomanip>
#include <thread>
#include <mutex>
#include <condition_variable>
#include <functional>
#include <iterator>
using namespace std;
const int maxn = 5007, INF = 0x3f3f3f3f;
const double PI = acos(-1.0);
int n, k, arr[maxn];
struct Node {
int x, y, tot;
double r, at;
bool operator<(const Node& input) {
return r < input.r;
}
void Get() {
cin >> x >> y;
r = sqrt(x * x * 1.0 + y * y * 1.0);
at = atan2(y, x);
tot = 1;
}
}node[maxn];
bool cmp(const Node& a, const Node& b) {
return a.at < b.at;
}
bool LessEqual(int i, int j) {
if (node[i].r < node[j].r || fabs(node[i].r - node[j].r) < 1e-9) {
return true;
}
return false;
}
double GetResult() {
if (k == 0) return 0;
double ans = INF;
sort(node, node + n, cmp);
set<double> mset;
for (int i = 0; i < n; i++) {
if (node[i].tot < k)continue;
double angle = 2 * PI, r = node[i].r;
if (mset.count(r))continue;
mset.insert(r);
int cnt = 0;
for (int j = 0; j < n; j++) {
if (LessEqual(j,i)) {
arr[cnt++] = j;
if (cnt >= k) {
angle = min(angle, node[arr[cnt - 1]].at - node[arr[cnt - k]].at);
}
}
}
if (cnt < k) continue;
for (int j = 0; j < k; j++) {
angle = min(angle, node[arr[j]].at - node[arr[cnt + j - k + 1]].at + 2 * PI);
}
ans = min(ans, r * r * angle / 2);
}
return ans;
}
int main()
{
int kCase = 1;
while (cin >> n >> k && n + k) {
for (int i = 0; i < n; i++) {
node[i].Get();
}
sort(node, node + n);
for (int i = 1; i < n; i++) {
node[i].tot += node[i - 1].tot;
}
cout << "Case #" << kCase++ << ": " << fixed << setprecision(2) << GetResult() << endl;
}
return 0;
}
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