-
愤怒的小鸟
Emmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmm
-
黄川山
LV 7
@
2026-7-22 21:14:54
#include <bits/stdc++.h>
using namespace std;
const int MAXN = 18;
const double EPS = 1e-8;
int T, n, m;
double x[MAXN], y[MAXN];
int line[MAXN][MAXN]; // line[i][j]表示经过i和j的抛物线能覆盖的猪的集合
int dp[1 << MAXN];
// 解方程:y1 = a*x1^2 + b*x1, y2 = a*x2^2 + b*x2
// 返回a和b是否合法(a < 0)
bool solve(double x1, double y1, double x2, double y2, double &a, double &b) {
if (fabs(x1 - x2) < EPS) return false;
// 克莱姆法则
double det = x1 * x1 * x2 - x1 * x2 * x2;
if (fabs(det) < EPS) return false;
a = (y1 * x2 - y2 * x1) / det;
b = (y1 * x2 * x2 - y2 * x1 * x1) / (x1 * x2 * x2 - x1 * x1 * x2);
return a < -EPS; // a必须小于0
}
int main() {
cin >> T;
while (T--) {
cin >> n >> m;
for (int i = 0; i < n; i++) {
cin >> x[i] >> y[i];
}
// 初始化
memset(line, 0, sizeof(line));
for (int i = 0; i < n; i++) {
line[i][i] = 1 << i; // 单独一个点可以用任意抛物线(只要a<0)
}
// 预处理所有抛物线
for (int i = 0; i < n; i++) {
for (int j = i + 1; j < n; j++) {
double a, b;
if (!solve(x[i], y[i], x[j], y[j], a, b)) {
line[i][j] = 0;
continue;
}
int mask = 0;
for (int k = 0; k < n; k++) {
// 检查点k是否在这条抛物线上
double val = a * x[k] * x[k] + b * x[k];
if (fabs(val - y[k]) < EPS) {
mask |= (1 << k);
}
}
line[i][j] = mask;
line[j][i] = mask;
}
}
// DP
for (int i = 0; i < (1 << n); i++) {
dp[i] = 1e9;
}
dp[0] = 0;
for (int mask = 0; mask < (1 << n); mask++) {
if (dp[mask] >= 1e9) continue;
// 找到第一个还没被覆盖的猪
int first = -1;
for (int i = 0; i < n; i++) {
if (!(mask & (1 << i))) {
first = i;
break;
}
}
if (first == -1) continue;
// 选择一只单独的小鸟
dp[mask | (1 << first)] = min(dp[mask | (1 << first)], dp[mask] + 1);
// 选择经过first和另外一只猪的抛物线
for (int j = 0; j < n; j++) {
if (j == first) continue;
if (line[first][j] == 0) continue;
int newMask = mask | line[first][j];
dp[newMask] = min(dp[newMask], dp[mask] + 1);
}
}
cout << dp[(1 << n) - 1] << endl;
}
return 0;
}