Number of ways in which N can be represented as the sum of two positive integers

Given a number N, the task is to find the number of unique ways in which N can be represented as a sum of two positive integers.

Examples:

Input: N = 7
Output: 3
(1 + 6), (2 + 5) and (3 + 4).



Input: N = 200
Output: 100

Approach: The number of ways in which the number can be expressed as the sum of two positive integers are 1 + (N – 1), 2 + (N – 2), …, (N – 1) + 1 and (N – 2) + 2. There are N – 1 terms in the series and they appear in identical pairs i.e. (X + Y, Y + X). So the required count will be N / 2.

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 number of
// distinct ways to represent n
// as the sum of two integers
int ways(int n)
{
    return n / 2;
}
  
// Driver code
int main()
{
    int n = 2;
  
    cout << ways(n);
  
    return 0;
}

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Java

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// Java implementation of the approach 
  
class GFG 
      
    // Function to return the number of 
    // distinct ways to represent n 
    // as the sum of two integers 
    static int ways(int n) 
    
        return n / 2
    
      
    // Driver code 
    public static void main(String args[]) 
    
        int n = 2
      
        System.out.println(ways(n)); 
    
}
  
// This code is contributed by AnkitRai01 

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Python3

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# Python3 implementation of the approach
  
# Function to return the number of
# distinct ways to represent n
# as the sum of two integers
def ways(n):
    return n // 2
  
# Driver code
n = 2
  
print(ways(n))
  
# This code is contributed by Mohit Kumar

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C#

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// C# implementation of the approach
using System;
  
class GFG
{
      
// Function to return the number of
// distinct ways to represent n
// as the sum of two integers
static int ways(int n)
{
    return n / 2;
}
  
// Driver code
public static void Main()
{
    int n = 2;
  
    Console.WriteLine(ways(n));
}
}
  
// This code is contributed by Nidhi_Biet

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Output:

1


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