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

Last Updated : 19 Mar, 2022

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 ` `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

 ``

Output:

`1`

Time Complexity: O(1)

Auxiliary Space: O(1)

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