poj2187 凸包问题

Pseudo-Code: Graham Scan Algorithm

Input: a set of points S = {P = (P.x,P.y)}

Select the rightmost lowest point P₀ in S.
Sort S angularly about P₀ as a center.
For ties, discard the closer points.
Let P[N] be the sorted array of points.

Push P[0]=P₀ and P[1] onto a stack W.

while i < N
{
Let P_T1 = the top point on W
Let P_T2 = the second top point on W
if (P[i] is strictly left of the line P_T2 to P_T1) {
Push P[i] onto W
i++ // increment i
}
else
Pop the top point P_T1 off the stack

}

Output: W = the convex hull ofS.

转自：凸包问题的几种算法，包括Graham scan 算法

这个算法其实也很好想通的。

第一步：找到y坐标最小的点p0;

第二步：以p0为原点，对所有的点按逆时针顺序排序；

第三步：逐步迭代，加入边界点。（画出一条边，如果一个新的边更靠左，则加入，否则不加入）。

#include<iostream>
#include<fstream>
#include<algorithm>
using namespace std;
const int num=50005;
int N;
struct Point
{
	int x;
	int y;
}points[num],output[num];
inline int ccw(Point p1,Point p2,Point p3)      //交叉乘积
{
	return (p2.x-p1.x)*(p3.y-p1.y)-(p2.y-p1.y)*(p3.x-p1.x);
}
inline int dis(Point p1,Point p2)             //距离
{
	return (p1.x-p2.x)*(p1.x-p2.x)+(p1.y-p2.y)*(p1.y-p2.y);
}
int cmp(const void *po1,const void *po2)      //排序用的比较函数
{
	Point *p1=(Point *)po1;
	Point *p2=(Point *)po2;
	int temp=ccw(points[0],*p1,*p2);        //先判断方向
	if(temp>0)
	{
		return -1;
	}
	else if(temp<0)
	{
		return 1;
	}
	else
	{
		return dis(*p1,points[0])-dis(*p2,points[0]);  //共线时按距离从大到校排序
	}
}

int maxDist( )
{
	int min_index=0;
	for(int i=1;i<N;i++)
	{
		if(points[i].x<points[min_index].x)
			min_index=i;
		else if(points[i].x<points[min_index].x&&points[i].y<points[min_index].y)
			min_index=i;
	}
	swap(points[0],points[min_index]);        //找到y坐标最小的点，并交换到第一个位置
	qsort(points+1,N-1,sizeof(Point),cmp);     //排序
/*	for(int i=0;i<N;i++)
	{
		printf("%d %d\n",points[i].x,points[i].y);

	}*/
	output[0]=points[0];
	output[1]=points[1];
	int top=1;
	int i=2;
	while(i<N)
	{
	//	printf("%d %d\n",points[i].x,points[i].y);

		int temp=ccw(output[top-1],output[top],points[i]);
		if(temp>=0)
		{
			output[++top]=points[i];
			i++;
		}
		/*else if(temp==0)
		{
			output[top]=points[i];
			i++;
		}*/
		else
		{
			top--;
		}
	}
	int maxD=0;
	for(int i=0;i<=top;i++)               //计算边界点之间的距离
	{
	//	printf("%d %d\n",output[i].x,output[i].y);
		for(int j=i+1;j<=top;j++)
		{
			int temp=dis(output[i],output[j]);
			if(temp>maxD)
				maxD=temp;
		}
	}
	printf("%d\n",maxD);
	return maxD;

}

int main()
{
	freopen("input.txt","r",stdin);
	while(	scanf("%d",&N)!=EOF)      //输入
	{
		for(int i=0;i<N;i++)
		{
			scanf("%d %d",&points[i].x,&points[i].y);
			//printf("%d %d\n",points[i].x,points[i].y);
		}
		maxDist();
	}
	return 0;
}