Count ways to express a number as sum of exactly two numbers

Given a positive integer **N**. The task is to find the number of ways in which you can express N as a sum of exactly two numbers **A** and **B** (N = A + B) where A > 0, B > 0 and B > A.

**Examples:**

Input:N = 8Output:3Explanation:N = 8 can be expressed as (1, 7), (2, 6), (3, 5)Input:N = 14Output:6

**Approach:**

- An observation here is that for every number N if we take a number A which is less than N/2 then, there must be a number B which is greater than N/2 and A + B = N.
- This leads to a simple solution of finding the count of numbers for either B or A. Hence the floor value of (N-1)/2 will lead to the solution.

## C++

`// C++ program to Count ways to ` `// express a number as sum of ` `// two numbers. ` `#include <bits/stdc++.h> ` `using` `namespace` `std; ` ` ` `// Function returns the count ` `// of ways express a number ` `// as sum of two numbers. ` `int` `CountWays(` `int` `n) ` `{ ` ` ` `int` `ans = (n - 1) / 2; ` ` ` ` ` `return` `ans; ` `} ` ` ` `// Driver code ` `int` `main() ` `{ ` ` ` `int` `N = 8; ` ` ` ` ` `cout << CountWays(N); ` `} ` |

*chevron_right*

*filter_none*

## Java

`// Java program to count ways to ` `// express a number as sum of ` `// two numbers. ` `class` `GFG{ ` ` ` `// Function returns the count ` `// of ways express a number ` `// as sum of two numbers. ` `static` `int` `CountWays(` `int` `n) ` `{ ` ` ` `int` `ans = (n - ` `1` `) / ` `2` `; ` ` ` ` ` `return` `ans; ` `} ` ` ` `// Driver code ` `public` `static` `void` `main(String[] args) ` `{ ` ` ` `int` `N = ` `8` `; ` ` ` `System.out.print(CountWays(N)); ` `} ` `} ` ` ` `// This code is contributed by Rajput-Ji ` |

*chevron_right*

*filter_none*

## Python3

`# Python3 program to Count ways to ` `# express a number as sum of ` `# two numbers. ` ` ` `# Function returns the count ` `# of ways express a number ` `# as sum of two numbers. ` `def` `CountWays(n) : ` ` ` `ans ` `=` `(n ` `-` `1` `) ` `/` `/` `2` ` ` `return` `ans ` ` ` `# Driver code ` `N ` `=` `8` `print` `(CountWays(N)) ` ` ` `# This code is contributed by Sanjit_Prasad ` |

*chevron_right*

*filter_none*

## C#

`// C# program to count ways to ` `// express a number as sum of ` `// two numbers. ` `using` `System; ` `class` `GFG{ ` ` ` `// Function returns the count ` `// of ways express a number ` `// as sum of two numbers. ` `static` `int` `CountWays(` `int` `n) ` `{ ` ` ` `int` `ans = (n - 1) / 2; ` ` ` ` ` `return` `ans; ` `} ` ` ` `// Driver code ` `public` `static` `void` `Main() ` `{ ` ` ` `int` `N = 8; ` ` ` `Console.Write(CountWays(N)); ` `} ` `} ` ` ` `// This code is contributed by Code_Mech ` |

*chevron_right*

*filter_none*

**Output:**

3

**Time complexity:** O(N)

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the **DSA Self Paced Course** at a student-friendly price and become industry ready.