Minimal Area(向量叉乘计算三角形面积)

题目链接：Minimal Area

题意：按逆时针给你凸多边形的所有点，让你选三个点使得得到的三角形面积最小。

思路：不难证明相邻的三个点是面积最小的，然后叉乘直接计算取最小值就可以。

#include<iostream>
#include<cstdio>
#include<cstring>
#include<cstdlib>
#include<cmath>
#include<algorithm>
#include<queue>
#include<stack>
#include<vector>
#include<map>
#include<set>
#define inf 0x3f3f3f3f3f3f3f3f
using namespace std;

typedef long long ll;

const int N = 200010;

struct node
{
    ll x, y;
} s[N];

int main()
{
    ll n;
    scanf("%lld", &n);
    for(int i = 0; i < n; i++)
    {
        scanf("%lld %lld", &s[i].x, &s[i].y);
    }
    ll ans = inf;
    for(int i = 0; i < n; i++)
    {
        ll x1 = s[(i-1+n)%n].x-s[(i-2+n)%n].x;
        ll y1 = s[(i-1+n)%n].y-s[(i-2+n)%n].y;
        ll x2 = s[i].x-s[(i-1+n)%n].x;
        ll y2 = s[i].y-s[(i-1+n)%n].y;
        ll now = abs(x1*y2-x2*y1);
        ans = min(ans, now);
    }
    printf("%lld\n", ans);
    return 0;
}