poj2187 凸包问题

Pseudo-Code: Graham Scan Algorithm

   Input: a set of pointsS = {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;}