B. Rectangle and Square

题目连接：

http://codeforces.com/contest/135/problem/B

Description

Little Petya very much likes rectangles and especially squares. Recently he has received 8 points on the plane as a gift from his mother. The points are pairwise distinct. Petya decided to split them into two sets each containing 4 points so that the points from the first set lay at the vertexes of some square and the points from the second set lay at the vertexes of a rectangle. Each point of initial 8 should belong to exactly one set. It is acceptable for a rectangle from the second set was also a square. If there are several partitions, Petya will be satisfied by any of them. Help him find such partition. Note that the rectangle and the square from the partition should have non-zero areas. The sides of the figures do not have to be parallel to the coordinate axes, though it might be the case.

Input

You are given 8 pairs of integers, a pair per line — the coordinates of the points Petya has. The absolute value of all coordinates does not exceed 104. It is guaranteed that no two points coincide.

Output

Print in the first output line “YES” (without the quotes), if the desired partition exists. In the second line output 4 space-separated numbers — point indexes from the input, which lie at the vertexes of the square. The points are numbered starting from 1. The numbers can be printed in any order. In the third line print the indexes of points lying at the vertexes of a rectangle in the similar format. All printed numbers should be pairwise distinct.

If the required partition does not exist, the first line should contain the word “NO” (without the quotes), after which no output is needed.

Sample Input

xudyhduxyz
0 0
10 11
10 0
0 11
1 1
2 2
2 1
1 2

Sample Output

YES
5 6 7 8
1 2 3 4

题意

给你8个点，你需要分成2个set，使得左边那个set里面的点构成正方形，右边那个set里面的点构成长方形

问你可不可以，如果可以输出方案

题解：

只有8个点，直接暴力就好了……

判断直角，就直接点积就好了

代码

#include<bits/stdc++.h>
using namespace std;
const double eps = 1e-6;
double a[10],b[10];
vector<int>tmp,ans1,ans2;
double dis(int x,int y)
{
    return (a[x]-a[y])*(a[x]-a[y])+(b[x]-b[y])*(b[x]-b[y]);
}
double pointx(int x,int y,int z)
{
    double x1=a[y]-a[x],y1=b[y]-b[x];
    double x2=a[z]-a[x],y2=b[z]-b[x];
    return x1*x2+y1*y2;
}
bool check()
{
    double len[4];
    for(int i=0;i<4;i++)len[i]=dis(tmp[i],tmp[(i+1)%4]);
    for(int i=0;i<4;i++)for(int j=0;j<4;j++)if(fabs(len[i]-len[j])>eps)return false;
    if(fabs(pointx(tmp[0],tmp[1],tmp[3]))>eps)return false;
    if(fabs(pointx(tmp[1],tmp[0],tmp[2]))>eps)return false;
    if(fabs(pointx(tmp[2],tmp[1],tmp[3]))>eps)return false;
    if(fabs(pointx(tmp[3],tmp[2],tmp[0]))>eps)return false;

    for(int i=0;i<4;i++)len[i]=dis(tmp[i+4],tmp[(i+1)%4+4]);
    if(fabs(len[0]-len[2])>eps)return false;
    if(fabs(len[1]-len[3])>eps)return false;

    if(fabs(pointx(tmp[4],tmp[5],tmp[7]))>eps)return false;
    if(fabs(pointx(tmp[5],tmp[4],tmp[6]))>eps)return false;
    if(fabs(pointx(tmp[6],tmp[5],tmp[7]))>eps)return false;
    if(fabs(pointx(tmp[7],tmp[6],tmp[4]))>eps)return false;

    return true;
}
int main()
{
    for(int i=0;i<8;i++)
    {
        scanf("%lf%lf",&a[i],&b[i]);
        tmp.push_back(i);
    }
    do{
        if(check())
        {
            printf("YES\n");
            for(int i=0;i<4;i++)cout<<tmp[i]+1<<" ";
            printf("\n");
            for(int i=4;i<8;i++)cout<<tmp[i]+1<<" ";
            return 0;
        }
    }while(next_permutation(tmp.begin(),tmp.end()));
    printf("NO\n");
}