Cut Rectangles

When a rectangle is cut by a straight line, we can easily obtain two polygons as the result. But the reversed problem is harder: given two polygons, your task is to check whether or not they could be obtained by cutting a rectangle.

To give you more trouble, the input polygons are possibly moved, rotated (90 degrees, 180 degrees, or 270 degrees counter-clockwise), or even flipped (mirrored).

It is assumed that the original rectangle's edges are parallel to the axis.

Input Specification:

Each input file contains one test case. For each case, the first line gives a positive integer N (≤), and then N pairs of polygons are given. Each polygon is described in the format:

k x​1​​ y​1​​ ⋯ x​k​​ y​k​​

where k (2) is the number of vertices on the polygon, and (x​i​​, y​i​​) (0) are the coordinates of the vertices, given in either clockwise or counter-clockwise order.

Note: there is no redundant vertex. That is, it is guaranteed that all the vertices are distinct for each polygon, and that no three consecutive vertices are on the same line.

Output Specification:

For each pair of polygons, print in a line either YES or NO as the answer.

Sample Input:

8
3 0 0 1 0 1 1
3 0 0 1 1 0 1
3 0 0 1 0 1 1
3 0 0 1 1 0 2
4 0 4 1 4 1 0 0 0
4 4 0 4 1 0 1 0 0
3 0 0 1 1 0 1
4 2 3 1 4 1 7 2 7
5 10 10 10 12 12 12 14 11 14 10
3 28 35 29 35 29 37
3 7 9 8 11 8 9
5 87 26 92 26 92 23 90 22 87 22
5 0 0 2 0 1 1 1 2 0 2
4 0 0 1 1 2 1 2 0
4 0 0 0 1 1 1 2 0
4 0 0 0 1 1 1 2 0

 

Sample Output:

YES
NO
YES
YES
YES
YES
NO
YES

#include<bits/stdc++.h>
using namespace std;
int main()
{
//  ios::sync_with_stdio(false);
 //   freopen("data.txt","r",stdin);
    int n,k,x;
    int c1,c2;
    scanf("%d",&n);
    for(;n--;)
    {
        int p411=-1,p412=-1,p421=-1,p422=-1;
        vector<pair<int,int> > v1,v2; 
        bool flag=false;
        pair<int,int> p1(0,0);
        pair<int,int> p2(0,0);
        scanf("%d",&k);
        for(int i=0;i<k;i++)
        {
            scanf("%d %d",&c1,&c2);
            if((!v1.empty())&&(c1-v1.back().first)&&(c2-v1.back().second))
            {
                if(!p1.first||!p1.second)
                {
                    p1.first=abs(c1-v1.back().first);
                    p1.second=abs(c2-v1.back().second);
                    if(k>3)
                    {
                        p411=i-1;
                        p412=i;
                    }
                }
                else
                {
                    p1.first=-1;
                    p1.second=-1;                    
                }
            }
            v1.push_back(pair<int,int>(c1,c2));
        }
        if(!p1.first||!p1.second)
        {
            p1.first=abs(v1.front().first-v1.back().first);
            p1.second=abs(v1.front().second-v1.back().second);
            if(k>3)
            {
                p411=k-1;
                p412=0;
            }
        }
        else if((v1.front().first-c1)&&(v1.front().second-c2))
        {
            p1.first=-1;
            p1.second=-1;
        }
        scanf("%d",&k);
        for(int i=0;i<k;i++)
        {
            scanf("%d %d",&c1,&c2);
            if((!v2.empty())&&(c1-v2.back().first)&&(c2-v2.back().second))
            {        
                if(!p2.first||!p2.second)
                {
                    p2.first=abs(c1-v2.back().first);
                    p2.second=abs(c2-v2.back().second);
                    if(k>3)
                    {
                        p421=i-1;
                        p422=i;
                    }
                }
                else
                {
                    p2.first=-2;
                    p2.second=-2;
                }
            }
            v2.push_back(pair<int,int>(c1,c2));
        }
        if(!p2.first||!p2.second)
        {
            p2.first=abs(v2.front().first-v2.back().first);
            p2.second=abs(v2.front().second-v2.back().second);
            if(k>3)
            {
                p421=k-1;
                p422=0;
            }            
        }
        else if((v2.front().first-c1)&&(v2.front().second-c2))
        {
            p2.first=-2;
            p2.second=-2;
        }
        if(p1.first>p1.second)
        swap(p1.first,p1.second);
        if(p2.first>p2.second)
        swap(p2.first,p2.second);
        if(p1==p2)
        {
            if(v1.size()==3)
            flag=true;
            else if(v1.size()==4)
            {
                flag=true;
                if(v2.size()==4)
                {
                    if(!p1.first)
                    flag=true;
                    else if(p1.first!=p1.second)
                    {
                        int m1=max(abs(v1[(p411+2)%4].first-v1[(p411+3)%4].first),abs(v1[(p411+2)%4].second-v1[(p411+3)%4].second));
                        int m2=max(abs(v2[(p421+2)%4].first-v2[(p421+3)%4].first),abs(v2[(p421+2)%4].second-v2[(p421+3)%4].second));
                        if(m1!=m2)
                        flag=false;
                    }
                }
                else if(v2.size()>4)
                flag=false;
            }
            else if(v1.size()==5)
            {
                if(v2.size()==3)
                flag=true;
            }
        }
        if(flag)
        printf("YES
");
        else
        printf("NO
");
    }
      return 0;
}