Count of decreasing pairs formed from numbers 1 to N

Given an **integer N**, the task is to count of decreasing pairs from numbers 1 to N.

A pair (x, y) is said to be decreasing if x > y

**Examples:**

Input:N = 8Output:3Explanation:

Decreasing pairs are: (7, 1), (6, 2), (5, 3).

Input:N = 9Output:4Explanation:

Decreasing pairs are: (8, 1), (7, 2), (6, 3), (5, 4).

**Approach:** Consider the below cases:

If N = 1 => Count = 0

If N = 2 => Count = 1 {(2, 1)}

If N = 3 => Count = 1 {(3, 1) or (3, 2)}

If N = 4 => Count = 2 {(4, 3), (2, 1)}

If N = 5 => Count = 2 {(5, 4), (3, 2)}

If N = 6 => Count = 3 {(6, 5), (4, 3), (2, 1)}

.

.

and so on

It can be clearly observed that

Below is the implementation of the above approach:

## C++

`// C++ program to count decreasing` `// pairs formed from numbers 1 to N` ` ` `#include <bits/stdc++.h>` `using` `namespace` `std;` ` ` `// Function to count the` `// possible number of pairs` `int` `divParts(` `int` `N)` `{` ` ` `if` `(N % 2 == 0)` ` ` ` ` `// if the number is even` ` ` `// then the answer in (N/2)-1` ` ` `cout << (N / 2) - 1 << endl;` ` ` ` ` `else` ` ` `// if the number is odd` ` ` `// then the answer in N/2` ` ` `cout << N / 2 << endl;` `}` ` ` `// Driver code` `int` `main()` `{` ` ` `int` `N = 8;` ` ` ` ` `divParts(N);` ` ` ` ` `return` `0;` `}` |

## Java

`// Java program to count decreasing` `// pairs formed from numbers 1 to N` `import` `java.util.*;` `class` `GFG{` ` ` `// Function to count the` `// possible number of pairs` `static` `void` `divParts(` `int` `N)` `{` ` ` `if` `(N % ` `2` `== ` `0` `)` ` ` ` ` `// if the number is even` ` ` `// then the answer in (N/2)-1` ` ` `System.out.println((N / ` `2` `) - ` `1` `);` ` ` ` ` `else` ` ` `// if the number is odd` ` ` `// then the answer in N/2` ` ` `System.out.println((N / ` `2` `));` `}` ` ` `// Driver code` `public` `static` `void` `main(String[] args)` `{` ` ` `int` `N = ` `8` `;` ` ` ` ` `divParts(N);` `}` `}` ` ` `// This code is contributed by offbeat` |

## Python3

`# Python3 program to count decreasing` `# pairs formed from numbers 1 to N` ` ` `# Function to count the` `# possible number of pairs` `def` `divParts(N):` ` ` ` ` `if` `(N ` `%` `2` `=` `=` `0` `):` ` ` ` ` `# if the number is even` ` ` `# then the answer in (N/2)-1` ` ` `print` `((N ` `/` `2` `) ` `-` `1` `);` ` ` ` ` `else` `:` ` ` ` ` `# if the number is odd` ` ` `# then the answer in N/2` ` ` `print` `(N ` `/` `2` `);` ` ` `# Driver code` `N ` `=` `8` `;` `divParts(N);` ` ` `# This code is contributed by Code_Mech` |

## C#

`// C# program to count decreasing` `// pairs formed from numbers 1 to N` `using` `System;` `class` `GFG{` ` ` `// Function to count the` `// possible number of pairs` `static` `void` `divParts(` `int` `N)` `{` ` ` `if` `(N % 2 == 0)` ` ` ` ` `// if the number is even` ` ` `// then the answer in (N/2)-1` ` ` `Console.WriteLine((N / 2) - 1);` ` ` ` ` `else` ` ` `// if the number is odd` ` ` `// then the answer in N/2` ` ` `Console.WriteLine((N / 2));` `}` ` ` `// Driver code` `public` `static` `void` `Main()` `{` ` ` `int` `N = 8;` ` ` ` ` `divParts(N);` `}` `}` ` ` `// This code is contributed by Code_Mech` |

**Output:**

3