二维凸包模板 【Graham扫描算法】

推荐链接：讲的很好

模板：

时间复杂度O(nlogn)

#include 
#include 
#include 
#include 
#define eps 1e-8
#define MAXN 110
using namespace std;
struct Point
{
    double x, y;
    Point(){}
    Point(double X, double Y){
        x = X; y = Y;
    }
};
Point P[MAXN];
int dcmp(double x)
{
    if(fabs(x) < eps)
        return 0;
    else
        return x < 0 ? -1 : 1;
}
Point operator - (Point A, Point B){
    return Point(A.x-B.x, A.y-B.y);
}
Point operator + (Point A, Point B){
    return Point(A.x+B.x, A.y+B.y);
}
Point operator * (Point A, double p){
    return Point(A.x*p, A.y*p);;
}
double Cross(Point A, Point B){
    return A.x*B.y - A.y*B.x;
}
double Dot(Point A, Point B){
    return A.x*B.x + A.y*B.y;
}
double Dis(Point A, Point B){
    return sqrt((A.x-B.x)*(A.x-B.x) + (A.y-B.y)*(A.y-B.y));
}
bool operator == (Point A, Point B){
    return dcmp(A.x-B.x) == 0 && dcmp(A.y-B.y) == 0;
}
bool cmp(Point A, Point B)//按极角升序排序，若角度相等距离小的在前面
{
    double temp = Cross(A-P[0], B-P[0]);
    if(dcmp(temp) > 0) return true;
    if(dcmp(temp) == 0 && dcmp(Dis(P[0], A) - Dis(P[0], B)) < 0) return true;
    return false;
}
int Stack[MAXN], top;//下标从0开始计数到top
void input(int n)
{
    scanf("%lf%lf", &P[0].x, &P[0].y);
    double xx = P[0].x, yy = P[0].y;
    int id = 0;//找到y坐标最小的点，若有多个选择x坐标最小的记录下标
    for(int i = 1; i < n; i++)
    {
        scanf("%lf%lf", &P[i].x, &P[i].y);
        if(P[i].y < yy || (P[i].y == yy && P[i].x < xx))
        {
            xx = P[i].x;
            yy = P[i].y;
            id = i;
        }
    }
    Point T;
    T = P[0]; P[0] = P[id]; P[id] = T;
    sort(P+1, P+n, cmp);//极角排序
}
void Graham(int n)
{
    if(n == 1){ top = 0; Stack[0] = 0;}
    else if(n == 2)
    {
        top = 1;
        Stack[0] = 0;
        Stack[1] = 1;
    }
    else
    {
        for(int i = 0; i <= 1; i++)
            Stack[i] = i;
        top = 1;
        for(int i = 2; i < n; i++)
        {   //如果和上一条边成左旋关系，压栈继续；反之一直弹栈直到和栈顶两点的边成左转关系，压栈继续。
            while(top > 0 && dcmp(Cross(P[Stack[top]]-P[Stack[top-1]], P[i]-P[Stack[top-1]])) <= 0) top--;
            top++;
            Stack[top] = i;
        }
    }
}
int main()
{
    int n;
    input(n);
    Graham(n);
    return 0;
}