Count triplet pairs (A, B, C) of points in 2-D space that satisfy the given condition

Given N points in 2 dimensional space. The task is to count the number of triplets pairs (A, B, C) such that point B is the midpoint of line segment formed by joining points A and C.

Examples:

Input: points = {{1, 1}, {2, 2}, {3, 3}}
Output: 1
The point (2, 2) is the midpoint of the line segment joining points (1, 1) and (3, 3).

Input: points = {{1, 1}, {1, 2}, {1, 5}}
Output: 0

Approach: Consider a pair of points A and C. The midpoint of the line segment joining these points will be ((A * X + C * X) / 2, (A * Y + C * Y) / 2)). If the point is present in the given list of points, we have found a triplet. To quickly check if a point is in our list of points we can use a set. Doing this for all pairs of points will give us the required count.

Below is the implementation of the above approach:

C++

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// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
  
// Function to return the count of possible triplets
int countTriplets(int n, vector<pair<int, int> > points)
{
    set<pair<int, int> > pts;
    int ct = 0;
  
    // Insert all the points in a set
    for (int i = 0; i < n; i++)
        pts.insert(points[i]);
  
    for (int i = 0; i < n; i++)
        for (int j = i + 1; j < n; j++) {
            int x = points[i].first + points[j].first;
            int y = points[i].second + points[j].second;
  
            // If the mid point exists in the set
            if (x % 2 == 0 && y % 2 == 0)
                if (pts.find(make_pair(x / 2, y / 2))
                    != pts.end())
                    ct++;
        }
  
    // Return the count of valid triplets
    return ct;
}
  
// Driver code
int main()
{
    vector<pair<int, int> > points
        = { { 1, 1 }, { 2, 2 }, { 3, 3 } };
    int n = points.size();
    cout << countTriplets(n, points);
}

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Java

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// Java implementation of the approach
import java.util.*;
  
class GFG
{
      
static class pair
{
    int first,second;
  
    public pair(int first, int second) 
    {
        this.first = first;
        this.second = second;
    }
      
}
  
// Function to return the count of possible triplets
static int countTriplets(int n, Vector<pair> points)
{
    Set<pair> pts = new HashSet<pair>();
    int ct = 0;
  
    // Insert all the points in a set
    for (int i = 0; i < n; i++)
        pts.add(points.get(i));
  
    for (int i = 0; i < n; i++)
        for (int j = i + 1; j < n; j++) 
        {
            int x = points.get(i).first + points.get(j).first;
            int y = points.get(i).second + points.get(j).second;
  
            // If the mid point exists in the set
            if (x % 2 == 0 && y % 2 == 0)
                if (!pts.contains(new pair(x / 2, y / 2)))
                    ct++;
        }
  
    // Return the count of valid triplets
    return ct;
}
  
// Driver code
public static void main(String args[]) 
{
    Vector<pair> points = new Vector<>();
    points.add(new pair(1,1));
    points.add(new pair(2,2));
    points.add(new pair(3,3));
    int n = points.size();
    System.out.println(countTriplets(n, points));
}
}
  
// This code is contributed by Princi Singh

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Python3

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# Python3 implementation of the approach 
  
# Function to return the count 
# of possible triplets 
def countTriplets(n, points) :
      
    pts = [] 
    ct = 0
  
    # Insert all the points in a set 
    for i in range(n) :
        pts.append(points[i]); 
  
    for i in range(n) :
        for j in range(i + 1, n) : 
            x = points[i][0] + points[j][0]; 
            y = points[i][1] + points[j][1]; 
  
            # If the mid point exists in the set 
            if (x % 2 == 0 and y % 2 == 0) :
                if [x // 2, y // 2] in pts :
                    ct += 1
                      
    # Return the count of valid triplets 
    return ct 
  
# Driver code 
if __name__ == "__main__" :
      
    points = [[ 1, 1 ], [ 2, 2 ], [ 3, 3 ]]
    n = len(points) 
    print(countTriplets(n, points))
  
# This code is contributed by Ryuga

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C#

// C# implementation of the approach
using System;
using System.Collections.Generic;

class GFG
{

public class pair
{
public int first,second;

public pair(int first, int second)
{
this.first = first;
this.second = second;
}

}

// Function to return the count of possible triplets
static int countTriplets(int n, List points)
{
HashSet pts = new HashSet();
int ct = 0;

// Insert all the points in a set
for (int i = 0; i < n; i++) pts.Add(points[i]); for (int i = 0; i < n; i++) for (int j = i + 1; j < n; j++) { int x = points[i].first + points[j].first; int y = points[i].second + points[j].second; // If the mid point exists in the set if (x % 2 == 0 && y % 2 == 0) if (!pts.Contains(new pair(x / 2, y / 2))) ct++; } // Return the count of valid triplets return ct; } // Driver code public static void Main(String []args) { List points = new List();
points.Add(new pair(1, 1));
points.Add(new pair(2, 2));
points.Add(new pair(3, 3));
int n = points.Count;
Console.WriteLine(countTriplets(n, points));
}
}

// This code is contributed by 29AjayKumar

PHP

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<?php
// PHP implementation of the approach 
  
// Function to return the count 
// of possible triplets 
function countTriplets($n, $points)
{
    $pts = array();
    $ct = 0; 
  
    // Insert all the points in a set 
    for ($i = 0; $i < count($points); $i++) 
    {
        for ($j = 0; 
             $j < count($points[$i]); $j++)
        {
            $pts[] = $points[$i][$j];
        }
    }
  
    for ($i = 0; $i < $n; $i++)
        for ($j = $i + 1; $j < $n; $j++)
        {
            $x = $points[$i][0] + $points[$j][0]; 
            $y = $points[$i][1] + $points[$j][1]; 
  
            // If the mid point exists in the set 
            if ($x % 2 == 0 and $y % 2 == 0) 
                if (in_array((int)($x / 2), $pts) and 
                    in_array((int)($y / 2), $pts))
                    $ct += 1;
        }
          
    // Return the count of valid triplets 
    return $ct
}
  
// Driver code 
$points = array(array( 1, 1 ), 
                array( 2, 2 ), 
                array( 3, 3 ));
$n = count($points);
print(countTriplets($n, $points));
  
// This code is contributed by chandan_jnu
?>

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Output:

1


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