UVA - 1595 Symmetry

The figure shown on the left is left-right symmetric as it is possible to fold the sheet of paper along a vertical line, drawn as a dashed line, and to cut the figure into two identical halves. The figure on the right is not left-right symmetric as it is impossible to find such a vertical line.

Write a program that determines whether a figure, drawn with dots, is left-right symmetric or not. The dots are all distinct.

Input 

The input consists of T test cases. The number of test cases T is given in the first line of the input file. The first line of each test case contains an integer N , where N ( 1N1, 000) is the number of dots in a figure. Each of the following N lines contains the x-coordinate and y-coordinate of a dot. Both x-coordinates and y-coordinates are integers between -10,000 and 10,000, both inclusive.

Output 

Print exactly one line for each test case. The line should contain `YES' if the figure is left-right symmetric. and `NO', otherwise.

The following shows sample input and output for three test cases.

Sample Input 

3                                            
5                                            
-2 5                                         
0 0 
6 5 
4 0 
2 3 
4 
2 3 
0 4 
4 0 
0 0 
4 
5 14 
6 10
5 10 
6 14

Sample Output 

YES 
NO 
YES

#include <iostream>
#include <algorithm>
#include <vector>
using namespace std;

struct point
{
    int x;
    int y;

    bool operator < (const point &b) const
    {
        int x1 = this->x;
        int y1 = this->y;
        int x2 = b.x;
        int y2 = b.y;
        if(y1 != y2)
            return y1 < y2;
        else
            return x1 < x2;
    }

     bool operator == (const point &b) const
     {
         if(x == b.x  &&  y==b.y)
            return true;
         else
            return false;
     }
};

int main()
{
    int T;
    cin >> T;
    while(T--)
    {
        int N;
        cin >> N;
        vector<point> box;
        for(int i = 0; i<N; i++)
        {
            point temp;
            cin >> temp.x >> temp.y;
            box.push_back(temp);
        }
        sort(box.begin(), box.end());

        double center;
        bool flag;
        for(auto i = box.begin(); i!=box.end() && (*i).y==box[0].y; i++)
        {
            center = ( (*i).x + box[0].x ) / 2.0;
            flag = true;
            for(auto i = box.begin(); i!=box.end(); i++)
            {
                point M;
                M.x = (2.0 * center) - (*i).x;
                M.y = (*i).y;
                if(find(box.begin(), box.end(), M)==box.end())
                {
                    flag = false;
                    break;
                }
            }
            if(flag==true)
            {
                cout << "YES" << endl;
                break;
            }
        }
        if(flag == false)
            cout << "NO" << endl;
    }


    return 0;
}