Maximum points of intersection n lines

You are given n straight lines. You have to find maximum number of point of intersection with these n lines.

Examples:

Input : n = 4 
Output : 6

Input : n = 2
Output :1

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Approach :

As we have n number of line, and we have to find maximum point of intersection using these n line. So this can be done using combination. This problem can be think as number of ways to select any two line among n line. As every line intersect with other that is selected.
So, total number of points = nC2

Below is the implementation of above approach:

C++

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// CPP program to find maximum intersecting
// points
#include <bits/stdc++.h>
using namespace std;
#define ll long int
  
  
// nC2 = (n)*(n-1)/2;
ll countMaxIntersect(ll n)
{
   return (n) * (n - 1) / 2;
}
  
// Driver code
int main()
{
    // n is number of line
    ll n = 8;
    cout << countMaxIntersect(n) << endl;
    return 0;
}

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Java

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// Java program to find maximum intersecting
// points
  
public class GFG {
      
    // nC2 = (n)*(n-1)/2;
    static long countMaxIntersect(long n)
    {
       return (n) * (n - 1) / 2;
    }
  
      
    // Driver code
    public static void main(String args[])
    {
        // n is number of line
        long n = 8;
        System.out.println(countMaxIntersect(n));
  
  
    }
    // This code is contributed by ANKITRAI1
}

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Python3

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# Python3 program to find maximum 
# intersecting points
  
#nC2 = (n)*(n-1)/2
def countMaxIntersect(n):
    return int(n*(n - 1)/2)
  
#Driver code
if __name__=='__main__':
      
# n is number of line
    n = 8
    print(countMaxIntersect(n))
  
# this code is contributed by 
# Shashank_Sharma

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C#

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// C# program to find maximum intersecting
// points
using System;
  
class GFG 
{
      
    // nC2 = (n)*(n-1)/2;
    public static long countMaxIntersect(long n)
    {
    return (n) * (n - 1) / 2;
    }
  
      
    // Driver code
    public static void Main()
    {
        // n is number of line
        long n = 8;
        Console.WriteLine(countMaxIntersect(n));
    }
}
// This code is contributed by Soumik

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PHP

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<?PHP
// PHP program to find maximum intersecting 
// points
  
// nC2 = (n)*(n-1)/2; 
function countMaxIntersect($n
    return ($n) * ($n - 1) / 2; 
  
// Driver code 
  
// n is number of line 
$n = 8;
echo countMaxIntersect($n) . "\n"
  
// This code is contributed by ChitraNayal
?>

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Output:

28


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