hdu 3629 Convex(计数问题)

题目链接：hdu 3269 Convex

题目大意：给出n个点，问任选四个点可以组成多少个凸四边形。

解题思路：和uav11529的做法是一样的，只不过求的东西不一样。

#include <cstdio>
#include <cstring>
#include <cmath>
#include <algorithm>
#include <iostream>

using namespace std;
typedef long long ll;
const int N = 1205;
const double pi = 4 * atan(1.0);
const double eps = 1e-9;

int n;
ll s;
double r[2*N];
struct point {
    double x, y;
}p[N];

ll Count (int d) {
    int c = 0, mv = 0;
    for (int i = 0; i < n; i++) {
        if (i == d)
            continue;

        double a = atan2(p[i].y-p[d].y, p[i].x-p[d].x);
        r[c] = a;
        r[c+n-1] = a + 2*pi;
        c++;
    }

    c = 2 * n - 2;
    sort(r, r + c);

    ll ans = 0;

    for (int i = 0; i < n-1; i++) {
        double tmp = r[i] + pi;

        while (tmp > r[mv])
            mv++;
        ll cnt = mv - i - 1;
        ans = ans + cnt * (cnt-1) / 2;
    }
    return s - ans;
}

ll solve () {
    s = (n-1) * (n-2) * (n-3) / 6;
    ll c = s * n / 4;
    ll ans = 0;

    for (int i = 0; i < n; i++)
        ans += Count(i);

    return c - ans;
}

int main () {
    int cas;
    cin >> cas;
    while (cas--) {
        cin >> n;
        for (int i = 0; i < n; i++)
            cin >> p[i].x >> p[i].y;
        cout << solve() << endl;
    }
    return 0;
}