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[神坛]pta

*相邻两条边围成的三角形面积会是最小的

极角排序+叉积计算三角形面积

#include<bits/stdc++.h>
#define int long long
using namespace std;

const int N = 2e5 + 10;
int n, m;
double ans = -1;
struct node{
    int x, y;
    int pos;
}a[N], b[N];

int jd(node s){
    if(s.x > 0 && s.y > 0) return 1;
    if(s.x < 0 && s.y > 0) return 2;
    if(s.x < 0 && s.y < 0) return 3;
    if(s.x > 0 && s.y < 0) return 4;
    return 0;//不加的话，vscode会报错
}

//计算几何：极角排序
bool cmp(node s1, node s2){
    if(s1.pos != s2.pos) return s1.pos < s2.pos;
    return s1.x * s2.y - s1.y * s2.x > 0;
}

signed main(){
    // ios::sync_with_stdio(false);
    // cin.tie(0); cout.tie(0);
    cin >> n;
    for(int i = 1; i <= n; i++) cin >> a[i].x >> a[i].y;
    for(int i = 1; i <= n; i++){
        int cnt = 0;
        for(int j = 1; j <= n; j++){//确定第二个点
            if(i == j) continue;
            b[++cnt].x = a[i].x - a[j].x;
            b[cnt].y = a[i].y - a[j].y;
            b[cnt].pos = jd(b[cnt]);
        }
        sort(b + 1, b + n, cmp);
        for(int j = 1; j < n - 1; j ++){
            if(ans == -1 || abs(b[j].x * b[j + 1].y - b[j].y * b[j + 1].x ) * 0.5 < ans){
                //叉乘计算三角形面积
                ans = abs(b[j].x * b[j + 1].y - b[j].y * b[j + 1].x ) * 0.5;
            }
        }
    }
    printf("%.3lf", ans);
    return 0;
}