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Friday 22 April 2022

Antipodal Points Solution | CodeChef Problem Solution 2022 | April Long Two

You are given a set of N distinct points P1,P2,P3,,PN on a 2-D plane.

A triplet (i,j,k) is called a holy triplet if

  • 1i<j<kN
  • PiPj and Pk are non-collinear and
  • Any two of the points PiPj and Pk are antipodal points of the circle that passes through all three of them.

Two points on a circle are said to be antipodal points of the circle if they are diametrically opposite to each other.

Find the total number of holy triplets.

Solution Click Below:- 

Input Format

  • The first line contains a single integer T - the number of test cases. Then the test cases follow.
  • The first line of each test case contains an integer N - the number of points.
  • Each of the next N lines contains two space separated integers xi and yi, denoting the co-ordinates of i-th point Pi.

Output Format

For each test case output a single line denoting the number of holy triplets.

Constraints

  • 1T10
  • 3N2000
  • Sum of N over all test cases does not exceed 2000
  • 109xi,yi109
  • All points P1,P2,,PN in each test case are distinct.

Sample Input 1 

1
4
0 1
0 -1
1 0
-1 0

Sample Output 1 

4

Explanation

Test case 1: The holy triplets in this case are :

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