凸多边形 HRBUST - 1429 计算几何_凸包_未调完

任选一个点作为起始点，将其他点按与该点连线的极角排序，二分查询点在哪两个射线之间， 并特别判断一下边界即可.

Code:

#include <cstdio>
#include <algorithm>
#include <cstring>
#include <cmath>
#define setIO(s) freopen(s".in","r",stdin)
#define maxn 200000
const double eps = 0.000000000001;
using namespace std;
int n,m;
struct Point {
    double x,y;
    Point (double x = 0,double y = 0) : x(x),y(y){}
}point[maxn],ask[maxn];
int exis(double t) { return (fabs(t) <= eps) ? 0 : (t < 0 ? -1 : 1); }
double det(double x1,double y1,double x2,double y2) { return x1*y2-x2*y1; }
double cross(Point a,Point b,Point c) { return det(b.x-a.x,b.y-a.y,c.x-a.x,c.y-a.y); }
bool solve(){
    memset(point,0,sizeof(point));
    memset(ask,0,sizeof(ask));
    for(int i = 1;i <= n; ++i) scanf("%lf%lf",&point[i].x,&point[i].y);
    scanf("%d",&m);
    for(int i = 1;i <= m; ++i) scanf("%lf%lf",&ask[i].x,&ask[i].y);
    for(int i = 1;i <= m; ++i) {
        int l = 2,r = n,ans = 0;
        if(exis(cross(point[1],ask[i],point[2])) != 1 || exis(cross(point[1],ask[i],point[n])) != -1)
            return false;
        while(l <= r) {
            int mid = (l + r) >> 1;
            if(exis(cross(point[1],point[mid],ask[i])) == -1)
                r = mid - 1;
            else
                ans = mid,l = mid + 1;
        }
        if(!(exis(cross(point[ans-1],point[ans],ask[i])) == -1)) return false;
    }
    return true;
} 

int main(){
    //setIO("input");
    while(scanf("%d",&n)!=EOF)
    {
        if(solve())
            printf("YES\n");
        else
            printf("NO\n");
    }
    return 0;
}