swust OJ 249 求凸包面积模板

用Graham_scan 求出凸点，再用叉积求面积，一个三角形的面积等于叉积的一半。

#define IOS ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);
#include<bits/stdc++.h>
#define int long long
using namespace std;
typedef pair<int,int> pii;
typedef long long ll;

const int INF = 0x3f3f3f3f;
const double eps = 1e-5;
const int mod = 2013;
const int N = 1e5+10;

int n;
struct Point{
	int x,y;
}point[N];
// 叉积 求 ab x ac -> >0 c在 b 左 
int cross(Point a,Point b,Point c){
	int x1 = b.x - a.x,y1 = b.y - a.y;
	int x2 = c.x - a.x,y2 = c.y - a.y;
	return x1*y2 - x2*y1;
}

#define C(x) ((x)*(x))
int dis(Point a,Point b){
	return C(a.x - b.x) + C(a.y - b.y);
}

bool cmp(Point a,Point b){
	int t = cross(point[0],a,b);
	return t?t>0:dis(point[0],a) > dis(point[0],b);
}

//进行处理，用栈来存元素，当有有拐趋势，则出栈。 
int stk[N],top = -1;
void Graham_scan(){
	stk[++top] = 0;
	stk[++top] = 1;
	stk[++top] = 2;
	for(int i=3;i<n;i++){
		while(cross(point[stk[top-1]],point[stk[top]],point[i]) <= 0)
			--top;
		stk[++top] = i;
	}
}

signed main(){
	IOS
    #ifdef ddgo
		freopen("C:\\Users\\asus\\Desktop\\ddgoin.txt","r",stdin);
    #endif
	
	int tt; cin>>tt;
	while(tt --){
		cin>>n;
		top = -1;
		for(int i=0;i<n;i++){
			cin>>point[i].x>>point[i].y;
			if(i){
				if(point[i].y == point[0].y && point[i].x < point[0].x)
					swap(point[0],point[i]);
				else if(point[i].y < point[0].y) swap(point[0],point[i]);
			}
		}
		if(n < 3){
			cout<<"0.0"<<endl;
			continue;
		}
		sort(point+1,point+n,cmp);
		int cnt = 2;
		for (int i=2;i<n;i++)
			if(cross(point[0],point[i-1],point[i]) != 0) point[cnt++] = point[i];
		n = cnt;
		Graham_scan();
		double res = 0;
		for(int i=2;i<=top;i++)
			res += cross(point[0],point[stk[i-1]],point[stk[i]]);
		cout<<fixed<<setprecision(1)<<(res/2)<<endl;
	}
    return 0;
    
}

本文地址：https://blog.csdn.net/qq_45604735/article/details/109616280