# Count of Subarrays in an array containing numbers from 1 to the length of subarray

• Difficulty Level : Medium
• Last Updated : 30 Aug, 2022

Given an array arr[] of length N containing all elements from 1 to N, the task is to find the number of sub-arrays that contain numbers from 1 to M, where M is the length of the sub-array.

Examples:

Input: arr[] = {4, 1, 3, 2, 5, 6}
Output:
Explanation:
Desired Sub-arrays = { {4, 1, 3, 2}, {1}, {1, 3, 2}, {4, 1, 3, 2, 5}, {4, 1, 3, 2, 5, 6} }
Count(Sub-arrays) = 5

Input: arr[] = {3, 2, 4, 1}
Output:
Explanation:
Desired Sub-arrays = { {1}, {3, 2, 4, 1} }
Count(Sub-arrays) = 2

Naive Approach: Generate all subarrays of the array and check for each subarray that it contains each element 1 to the length of the subarray.

Efficient Approach: Create a vector that maps each element of the array with its index in sorted order. Now iterate over this vector and check whether the difference of maximum and minimum index till the ith element is less than the number of elements iterated till now, which is the value of i itself.

Below is the implementation of the above approach

## C++

 `// C++ Implementation to Count the no. of``// Sub-arrays which contains all elements``// from 1 to length of subarray` `#include ``using` `namespace` `std;` `// Function to count the number``// Sub-arrays which contains all elements``// 1 to length of subarray``int` `countOfSubarrays(``int``* arr, ``int` `n)``{``    ``int` `count = 0;``    ``vector<``int``> v(n + 1);` `    ``// Map all elements of array with their index``    ``for` `(``int` `i = 0; i < n; i++)``        ``v[arr[i]] = i;` `    ``// Set the max and min index equal to the``    ``// min and max value of integer respectively.``    ``int` `maximum = INT_MIN;``    ``int` `minimum = INT_MAX;` `    ``for` `(``int` `i = 1; i <= n; i++) {` `        ``// Update the value of maximum index``        ``maximum = max(maximum, v[i]);` `        ``// Update the value of minimum index``        ``minimum = min(minimum, v[i]);` `        ``// Increase the counter if difference of``        ``// max. and min. index is less than the``        ``// elements iterated till now``        ``if` `(maximum - minimum < i)``            ``count = count + 1;``    ``}` `    ``return` `count;``}` `// Driver Function``int` `main()``{``    ``int` `arr[] = { 4, 1, 3, 2, 5, 6 };``    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr[0]);``    ``cout << countOfSubarrays(arr, n) << endl;``    ``return` `0;``}`

## Java

 `// Java Implementation to Count the no. of``// Sub-arrays which contains all elements``// from 1 to length of subarray``class` `GFG``{` `// Function to count the number``// Sub-arrays which contains all elements``// 1 to length of subarray``static` `int` `countOfSubarrays(``int` `[]arr, ``int` `n)``{``    ``int` `count = ``0``;``    ``int` `[]v = ``new` `int``[n + ``1``];` `    ``// Map all elements of array with their index``    ``for` `(``int` `i = ``0``; i < n; i++)``        ``v[arr[i]] = i;` `    ``// Set the max and min index equal to the``    ``// min and max value of integer respectively.``    ``int` `maximum = Integer.MIN_VALUE;``    ``int` `minimum = Integer.MAX_VALUE;` `    ``for` `(``int` `i = ``1``; i <= n; i++)``    ``{` `        ``// Update the value of maximum index``        ``maximum = Math.max(maximum, v[i]);` `        ``// Update the value of minimum index``        ``minimum = Math.min(minimum, v[i]);` `        ``// Increase the counter if difference of``        ``// max. and min. index is less than the``        ``// elements iterated till now``        ``if` `(maximum - minimum < i)``            ``count = count + ``1``;``    ``}` `    ``return` `count;``}` `// Driver code``public` `static` `void` `main(String[] args)``{``    ``int` `arr[] = { ``4``, ``1``, ``3``, ``2``, ``5``, ``6` `};``    ``int` `n = arr.length;``    ``System.out.print(countOfSubarrays(arr, n) +``"\n"``);``}``}` `// This code is contributed by PrinciRaj1992`

## Python3

 `# Python3 Implementation to Count the no. of``# Sub-arrays which contains all elements``# from 1 to length of subarray``import` `sys` `INT_MAX ``=` `sys.maxsize;``INT_MIN ``=` `-``(sys.maxsize ``-` `1``);` `# Function to count the number``# Sub-arrays which contains all elements``# 1 to length of subarray``def` `countOfSubarrays(arr, n) :` `    ``count ``=` `0``;``    ``v ``=` `[``0``]``*``(n ``+` `1``);` `    ``# Map all elements of array with their index``    ``for` `i ``in` `range``(n) :``        ``v[arr[i]] ``=` `i;` `    ``# Set the max and min index equal to the``    ``# min and max value of integer respectively.``    ``maximum ``=` `INT_MIN;``    ``minimum ``=` `INT_MAX;` `    ``for` `i ``in` `range``(``1``, n ``+` `1``) :` `        ``# Update the value of maximum index``        ``maximum ``=` `max``(maximum, v[i]);` `        ``# Update the value of minimum index``        ``minimum ``=` `min``(minimum, v[i]);` `        ``# Increase the counter if difference of``        ``# max. and min. index is less than the``        ``# elements iterated till now``        ``if` `(maximum ``-` `minimum < i) :``            ``count ``=` `count ``+` `1``;` `    ``return` `count;` `# Driver code``if` `__name__ ``=``=` `"__main__"` `:` `    ``arr ``=` `[ ``4``, ``1``, ``3``, ``2``, ``5``, ``6` `];``    ``n ``=` `len``(arr);``    ``print``(countOfSubarrays(arr, n));` `# This code is contributed by AnkitRai01`

## C#

 `// C# Implementation to Count the no. of``// Sub-arrays which contains all elements``// from 1 to length of subarray``using` `System;` `class` `GFG``{` `// Function to count the number``// Sub-arrays which contains all elements``// 1 to length of subarray``static` `int` `countOfSubarrays(``int` `[]arr, ``int` `n)``{``    ``int` `count = 0;``    ``int` `[]v = ``new` `int``[n + 1];` `    ``// Map all elements of array with their index``    ``for` `(``int` `i = 0; i < n; i++)``        ``v[arr[i]] = i;` `    ``// Set the max and min index equal to the``    ``// min and max value of integer respectively.``    ``int` `maximum = ``int``.MinValue;``    ``int` `minimum = ``int``.MaxValue;` `    ``for` `(``int` `i = 1; i <= n; i++)``    ``{` `        ``// Update the value of maximum index``        ``maximum = Math.Max(maximum, v[i]);` `        ``// Update the value of minimum index``        ``minimum = Math.Min(minimum, v[i]);` `        ``// Increase the counter if difference of``        ``// max. and min. index is less than the``        ``// elements iterated till now``        ``if` `(maximum - minimum < i)``            ``count = count + 1;``    ``}` `    ``return` `count;``}` `// Driver code``public` `static` `void` `Main(String[] args)``{``    ``int` `[]arr = { 4, 1, 3, 2, 5, 6 };``    ``int` `n = arr.Length;``    ``Console.Write(countOfSubarrays(arr, n) +``"\n"``);``}``}` `// This code is contributed by PrinciRaj1992`

## Javascript

 ``

Output:

`5`

Time Complexity: O(N), for traversal over the array.
Auxiliary Space: O(N), for creating an extra array of size N + 1.

My Personal Notes arrow_drop_up