Reference blog https://blog.csdn.net/yangkunpengD/article/details/51329115
It has been modified in the same way.

Judgment method: three conditions are met at the same time (1: four sides are equal, 2: the side is not 0, 3: there is a right angle)

Train of thought:
(1) Set point.
Sort the points and fix the serial number of four points
Note: when sorting, you can arrange and combine them in ascending or descending order of abscissa or ordinate. There is no problem.
Such as:

bool cmp(point a, point b)
{
    if (a.x != b.x)
        return a.x < b.x; //If the abscissa is not equal, all points are arranged in ascending order of abscissa
    return a.y < b.y;//If the abscissa is equal, all points are arranged in ascending order of ordinate
}

perhaps

bool cmp(point a, point b)
{
    if (a.y != b.y)
        return a.y > b.y; //If the ordinates are not equal, all points are arranged in descending order of ordinates
    return a.x < b.x;//If the ordinates are equal, all points are arranged in ascending order of abscissa
}

(2) Determine the edge.
Calculate the side length.
(3) Judge whether it is a square
Judgment method: three conditions are met at the same time (1: four sides are equal, 2: the side is not 0, 3: there is a right angle)

The code is as follows:

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

struct point
{
    double x, y;
} a[4];

bool cmp(point a, point b)
{
    if (a.x != b.x)
        return a.x < b.x; //If the abscissa is not equal, all points are arranged in ascending order of abscissa
    return a.y < b.y;//If the abscissa is equal, all points are arranged in ascending order of ordinate
}

double TwoPointDiatance(point a, point b)//Calculate the distance between two points
{
    return sqrt(pow((a.x - b.x), 2) + pow((a.y - b.y), 2));
}

bool IsRightAngle(point a, point b, point c)//Judge whether it is a right angle
{
    double x;
    x = (a.x - b.x)* (a.x - c.x) + (a.y - b.y)*(a.y - c.y);
    if (x < 0.00001)
        return 1;
    else
        return 0;
}

int main()
{
    int t, k;
    double s1, s2, s3, s4;
    cout << "Please enter the number of times you want to play: ";
    cin >> t;
    cout << "Enter the coordinates of the 4 points:" << endl;
    while (t--)
    {
        for (int i = 0; i < 4; i++)
            cin >> a[i].x >> a[i].y;

        //Fix point, sort, label point
        sort(a, a + 4, cmp);

        //Fixed edge
        s1 = TwoPointDiatance(a[0], a[2]);
        s2 = TwoPointDiatance(a[0], a[1]);
        s3 = TwoPointDiatance(a[3], a[1]);
        s4 = TwoPointDiatance(a[2], a[3]);

        //Whether the analysis is square
        if (s1 == s2&&s3 == s4&&s1 == s2&&s1 != 0 && IsRightAngle(a[0], a[1], a[2]))//Three conditions are satisfied at the same time (1: four sides are equal, 2: the side is not 0, 3: there is a right angle)
            cout << "Yes" << endl;
        else
            cout << "No" << endl;
        cout << "Left " << t << " Second time." << endl;
        cout << "Enter the coordinates of the 4 points:" << endl;
    }

    return 0;
}
/*
Several sets of square test coordinates:
0 1 1 1 1 0 0 0

0 2 3 -2 -1 -5 -4 -1

0 4 4 7 7 3 3 0

0 1 1 6 5 0 6 5
*/