LightOj1285 - Drawing Simple Polygon（连接多边形各点）

#include <stdio.h>
#include <algorithm>
#include <cstring>
#include <cmath>
using namespace std;
const int N = 2010;
const double eps = 1e-6;
const double PI = acos(-1);
struct point
{
double x, y;
int Id;
point(){}
point(double x, double y) : x(x), y(y) {}
point friend operator - (const point &p1, const point &p2)///矢量p2p1;
{
return point(p1.x-p2.x, p1.y-p2.y);
}
double friend operator ^ (const point &p1, const point &p2)///p1×p2;
{
return p1.x*p2.y - p1.y*p2.x;
}
};

point p
;

double Dist(point p1, point p2)
{
double dx = p1.x - p2.x, dy = p1.y - p2.y;
return sqrt(dx*dx + dy*dy);
}
int cmp1(point p1, point p2)///位置排序，找到最下方的；
{
if(p1.y != p2.y)
return p1.y < p2.y;
return p1.x < p2.x;///若有多个下方的找左边的；
}
int cmp2(point p1, point p2)///极角排序；若极角相同，距离近的在前面；
{
double k = (p1-p[0])^(p2-p[0]);
if( k>eps || (fabs(k)<eps && Dist(p1, p[0]) < Dist(p2, p[0]) ))
return 1;
return 0;
}

int main()
{
int n, T, t=1;
scanf("%d", &T);
while(T--)
{
scanf("%d", &n);
for(int i=0; i<n; i++)
{
scanf("%lf %lf", &p[i].x, &p[i].y);
p[i].Id = i;
}

sort(p, p+n, cmp1);///p[0]为最下方靠左的点；
sort(p+1, p+n, cmp2);///以p[0]为基点，按叉积进行排序；

int flag = 0;
for(int i=n-2; i>0; i--)
{
if(((p[n-1]-p[0])^(p[i]-p[0]))!=0)
{
flag = i;
break;
}
}
printf("Case %d:\n", t++);
if(flag==0)
{
printf("Impossible\n");
continue;
}
reverse(p+flag+1, p+n);
for(int i=0; i<n; i++)
printf("%d%c", p[i].Id, i==n-1?'\n':' ');
}
return 0;
}