Maximum points of intersection n circles

Given a number n, we need to find the maximum number of times n circles intersect.

Examples:

Input :  n = 2
Output : 2

Input :  n = 3
Output : 6

Description and Derivation

As we can see in above diagram, for each pair of circles, there can be maximum two intersectuib points. Therefore if we have n circles then there can be ⁿC₂ pairs of circles in which each pair will have two intersections. So by this we can conclude that by looking at all possible pairs of circles the mathematical formula can be made for the maximum number of intersection by n circles is given by 2 * ⁿC₂.

2 * ⁿC₂ = 2 * n * (n – 1)/2 = n * (n-1)

C++

// CPP program to find maximum umber of  
// intersections of n circles 
#include <bits/stdc++.h> 
using namespace std; 
  
// Returns maximum number of intersections 
int intersection(int n) 
{ 
   return n * (n - 1); 
} 
  
int main() 
{ 
    cout << intersection(3) << endl; 
    return 0; 
} 
// This code is contributed by  
// Manish Kumar Rai. 

Java

// Java program to find maximum umber of  
// intersections of n circles 
import java.io.*; 
  
public class GFG { 
  
    // for the calculation of 2*(nC2) 
    static int intersection(int n) 
    { 
       return n * (n - 1); 
    } 
  
    public static void main(String[] args) throws IOException 
    { 
        System.out.println(intersection(3)); 
    } 
} 
// This code is contributed by  
// Manish Kumar Rai 

Python3

# python program to find maximum umber of  
# intersections of n circles 
# Returns maximum number of intersections 
def intersection(n): 
      
   return n * (n - 1); 
  
# Drive code 
print(intersection(3)) 
  
# This code is contributed by Sam007 

/div>

C#

// C# program to find maximum umber of  
// intersections of n circles 
using System; 
class GFG { 
  
    // for the calculation of 2*(nC2) 
    static int intersection(int n) 
    { 
        return n * (n - 1); 
    } 
  
// Driver Code 
public static void Main() 
{ 
    Console.WriteLine(intersection(3)); 
} 
  
} 
  
// This code is contributed by Sam007 

php

<?php 
// php program to find maximum umber of  
// intersections of n circles 
  
// Returns maximum number of intersections 
function intersection($n) 
{ 
   return $n * ($n - 1); 
} 
   
// Drive code 
  
echo intersection(3); 
  
  
// This code is contributed by Sam007 
?> 

Output:

Maximum points of intersection n circles

Description and Derivation

C++

Java

Python3

C#

php

tags:

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