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

  • Last Updated : 26 Mar, 2021

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:
(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++




// 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;
}

Java




// 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

Python3




# 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

C#




// 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

Javascript




<script>
 
 
// Javascript implementation of the approach
 
// Function to return the number of
// distinct ways to represent n
// as the sum of two integers
function ways(n)
{
    return parseInt(n / 2);
}
 
// Driver code
var n = 2;
document.write(ways(n));
 
// This code is contributed by noob2000.
</script>
Output: 
1

 

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