# Count of possible subarrays and subsequences using given length of Array

Given an integer **N** which denotes the length of an array, the task is to count the number of subarray and subsequence possible with the given length of the array.

**Examples:**

Input:N = 5

Output:

Count of subarray = 15

Count of subsequence = 32

Input:N = 3

Output:

Count of subarray = 6

Count of subsequence = 8

**Approach:** The key observation fact for the count of the subarray is the number of ends position possible for each index elements of the array can be (N – i), Therefore the count of the subarray for an array of size **N** can be:

Count of Sub-arrays = (N) * (N + 1) --------------- 2

The key observation fact for the count of the subsequence possible is each element of the array can be included in a subsequence or not. Therefore, the choice for each element is 2.

Count of subsequences = 2^{N}

Below is the implementation of the above approach:

## C++

`// C++ implementation to count ` `// the subarray and subsequence of ` `// given length of the array ` `#include <bits/stdc++.h> ` `using` `namespace` `std; ` ` ` `// Function to count the subarray ` `// for the given array ` `int` `countSubarray(` `int` `n){ ` ` ` `return` `((n)*(n + 1))/2; ` `} ` ` ` `// Function to count the subsequence ` `// for the given array length ` `int` `countSubsequence(` `int` `n){ ` ` ` `return` `pow` `(2, n); ` `} ` ` ` `// Driver Code ` `int` `main() ` `{ ` ` ` `int` `n = 5; ` ` ` `cout << (countSubarray(n)) << endl; ` ` ` `cout << (countSubsequence(n)) << endl; ` ` ` `return` `0; ` `} ` ` ` `// This code is contributed by mohit kumar 29 ` |

*chevron_right*

*filter_none*

## Java

`// Java implementation to count ` `// the subarray and subsequence of ` `// given length of the array ` `class` `GFG{ ` ` ` `// Function to count the subarray ` `// for the given array ` `static` `int` `countSubarray(` `int` `n){ ` ` ` `return` `((n)*(n + ` `1` `))/` `2` `; ` `} ` ` ` `// Function to count the subsequence ` `// for the given array length ` `static` `int` `countSubsequence(` `int` `n){ ` ` ` `return` `(` `int` `) Math.pow(` `2` `, n); ` `} ` ` ` `// Driver Code ` `public` `static` `void` `main(String[] args) ` `{ ` ` ` `int` `n = ` `5` `; ` ` ` `System.out.print((countSubarray(n)) +` `"\n"` `); ` ` ` `System.out.print((countSubsequence(n)) +` `"\n"` `); ` `} ` `} ` ` ` `// This code is contributed by Princi Singh ` |

*chevron_right*

*filter_none*

## Python

`# Python implementation to count ` `# the subarray and subsequence of ` `# given length of the array ` ` ` `# Function to count the subarray ` `# for the given array ` `def` `countSubarray(n): ` ` ` `return` `((n)` `*` `(n ` `+` `1` `))` `/` `/` `2` ` ` `# Function to count the subsequence ` `# for the given array length ` `def` `countSubsequence(n): ` ` ` `return` `(` `2` `*` `*` `n) ` ` ` `# Driver Code ` `if` `__name__ ` `=` `=` `"__main__"` `: ` ` ` `n ` `=` `5` ` ` `print` `(countSubarray(n)) ` ` ` `print` `(countSubsequence(n)) ` |

*chevron_right*

*filter_none*

## C#

`// C# implementation to count ` `// the subarray and subsequence of ` `// given length of the array ` `using` `System; ` ` ` `class` `GFG{ ` ` ` `// Function to count the subarray ` `// for the given array ` `static` `int` `countSubarray(` `int` `n){ ` ` ` `return` `((n)*(n + 1))/2; ` `} ` ` ` `// Function to count the subsequence ` `// for the given array length ` `static` `int` `countSubsequence(` `int` `n){ ` ` ` `return` `(` `int` `) Math.Pow(2, n); ` `} ` ` ` `// Driver Code ` `public` `static` `void` `Main(String[] args) ` `{ ` ` ` `int` `n = 5; ` ` ` `Console.Write((countSubarray(n)) +` `"\n"` `); ` ` ` `Console.Write((countSubsequence(n)) +` `"\n"` `); ` `} ` `} ` ` ` `// This code is contributed by Rajput-Ji ` |

*chevron_right*

*filter_none*

**Output:**

15 32

## Recommended Posts:

- Count of Subarrays in an array containing numbers from 1 to the length of subarray
- Count unique subsequences of length K
- Count of subsequences of length 4 in form (x, x, x+1, x+1) | Set 2
- Count the number of subsequences of length k having equal LCM and HCF
- Count of subsequences of length atmost K containing distinct prime elements
- Create an array such that XOR of subarrays of length K is X
- Generate a unique Array of length N with sum of all subarrays divisible by N
- Count of subsequences in an array with sum less than or equal to X
- Count subarrays with non-zero sum in the given Array
- Count subarrays consisting of only 0's and only 1's in a binary array
- Count of subarrays of an Array having all unique digits
- Count subarrays having total distinct elements same as original array
- Minimum count of increment of K size subarrays required to form a given Array
- Sum of all subsequences of length K
- Maximum length L such that the sum of all subarrays of length L is less than K
- Unique subsequences of length K with given sum
- Number of palindromic subsequences of length k where k <= 3
- Number of K length subsequences with minimum sum
- Count number of even and odd length elements in an Array
- Count of integers in an Array whose length is a multiple of K

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.