# 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

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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 `

Output:

```1
```

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