poj 1696 Space Ant （极角排序）

版权声明：转载注明下出处就行了。 https://blog.csdn.net/LJD201724114126/article/details/83743549

题目链接：poj 1696

题意：是给你n个点，一只蚂蚁要从y坐标最小的那个点开始，逆时针依次走过所有的点，要求不能走之前走过的点，蚂蚁只能逆时针（向左转）前进。

题解：极角排序一下，每次出发都取左偏量最小的跑。

///极角排序，每次出发都取左偏量最小的点

#include<cstring>
#include<cstdio>
#include<algorithm>
#include<cmath>

using namespace std;

struct point
{
    double x,y;
    int index;
    point(){}
    point(double _x,double _y){
        x=_x;y=_y;
    }
}node[100];

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);}
point operator / (point a,double p){ return point(a.x/p,a.y/p);}

bool operator < (const point &a,const point &b){
    return a.x<b.x||(a.x==b.x&&a.y<b.y);
}
const double esp=1e-8;
int dcmp(double x){
    if(fabs(x)<esp) return 0;
    else return x<0?-1:1;
}
bool operator ==(const point &a,const point &b){
    return dcmp(a.x-b.x)==0&&dcmp(a.y-b.y)==0;
}

double Dot(point A,point B) { return A.x*B.x+A.y*B.y;}///2，点积，即是|a||b|*cos<a,b>，可用来判断角度的范围
double Length(point A) {return sqrt(Dot(A,A));} ///两点之间的距离
double Cross(point a,point b) { return a.x*b.y-a.y*b.x;}


int pos; ///极角排序时的根据
bool cmp(point a,point b){

    double item=Cross(a-node[pos],b-node[pos]);

    if(dcmp(item)==0) return Length(a-node[pos])<Length(b-node[pos]);
    else if(dcmp(item)>0) return true;///如果叉积大于0，说明pos到a点的极角大于b
    else return false;
}

int main()
{
    int ncase;
    scanf("%d",&ncase);

    while(ncase--)
    {
        int n;
        scanf("%d",&n);

        for(int i=0;i<n;i++)
        {
            scanf("%d%lf%lf",&node[i].index,&node[i].x,&node[i].y);
            if(node[i].y<node[0].y||(node[i].y==node[0].y&&node[i].x<node[0].x))
                swap(node[0],node[i]);
        }

        pos=0;
        for(int i=1;i<n;i++)
        {
            sort(node+i,node+n,cmp);
            pos++;
        }

        printf("%d ",n);
        for(int i=0;i<n;i++)
            printf("%d ",node[i].index);
        puts("");
    }
    return 0;
}