# Count of subarrays whose maximum element is greater than k

Given an array of n elements and an integer k. The task is to find the count of subarray which has maximum element greater than K.

Examples :

```Input : arr[] = {1, 2, 3} and k = 2.
Output : 3
All the possible subarrays of arr[] are
{ 1 }, { 2 }, { 3 }, { 1, 2 }, { 2, 3 },
{ 1, 2, 3 }.
Their maximum elements are 1, 2, 3, 2, 3, 3.
There are only 3 maximum elements > 2.
```

## Recommended: Please solve it on “PRACTICE ” first, before moving on to the solution.

The idea is to approach problem by counting subarrays whose maximum element is less than or equal to k as counting such subarrays is easier. To find the number of subarray whose maximum element is less than or equal to k, remove all the element which is greater than K and find the number of subarray with the left elements.
Once we find above count, we can subtract it from n*(n+1)/2 to get our required result. Observe, there can be n*(n+1)/2 possible number of subarray of any array of size n. So, finding the number of subarray whose maximum element is less than or equal to K and substracting it from n*(n+1)/2 gets us the answer.

Below is the implementation of this approach:

## C++

 `// C++ program to count number of subarrays ` `// whose maximum element is greater than K. ` `#include ` `using` `namespace` `std; ` ` `  `// Return number of subarrays whose maximum ` `// element is less than or equal to K. ` `int` `countSubarray(``int` `arr[], ``int` `n, ``int` `k) ` `{ ` `    ``// To store count of subarrays with all ` `    ``// elements less than or equal to k. ` `    ``int` `s = 0; ` ` `  `    ``// Traversing the array. ` `    ``int` `i = 0; ` `    ``while` `(i < n) { ` `        ``// If element is greater than k, ignore. ` `        ``if` `(arr[i] > k) { ` `            ``i++; ` `            ``continue``; ` `        ``} ` ` `  `        ``// Counting the subarray length whose ` `        ``// each element is less than equal to k. ` `        ``int` `count = 0; ` `        ``while` `(i < n && arr[i] <= k) { ` `            ``i++; ` `            ``count++; ` `        ``} ` ` `  `        ``// Suming number of subarray whose ` `        ``// maximum element is less than equal to k. ` `        ``s += ((count * (count + 1)) / 2); ` `    ``} ` ` `  `    ``return` `(n * (n + 1) / 2 - s); ` `} ` ` `  `// Driven Program ` `int` `main() ` `{ ` `    ``int` `arr[] = { 1, 2, 3 }; ` `    ``int` `k = 2; ` `    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr[0]); ` `    ``cout << countSubarray(arr, n, k); ` `    ``return` `0; ` `} `

## Java

 `// Java program to count number of subarrays ` `// whose maximum element is greater than K. ` `import` `java.util.*; ` ` `  `class` `GFG { ` ` `  `    ``// Return number of subarrays whose maximum ` `    ``// element is less than or equal to K. ` `    ``static` `int` `countSubarray(``int` `arr[], ``int` `n, ``int` `k) ` `    ``{ ` ` `  `        ``// To store count of subarrays with all ` `        ``// elements less than or equal to k. ` `        ``int` `s = ``0``; ` ` `  `        ``// Traversing the array. ` `        ``int` `i = ``0``; ` `        ``while` `(i < n) { ` ` `  `            ``// If element is greater than k, ignore. ` `            ``if` `(arr[i] > k) { ` `                ``i++; ` `                ``continue``; ` `            ``} ` ` `  `            ``// Counting the subarray length whose ` `            ``// each element is less than equal to k. ` `            ``int` `count = ``0``; ` `            ``while` `(i < n && arr[i] <= k) { ` `                ``i++; ` `                ``count++; ` `            ``} ` ` `  `            ``// Suming number of subarray whose ` `            ``// maximum element is less than equal to k. ` `            ``s += ((count * (count + ``1``)) / ``2``); ` `        ``} ` ` `  `        ``return` `(n * (n + ``1``) / ``2` `- s); ` `    ``} ` ` `  `    ``// Driver code ` `    ``public` `static` `void` `main(String[] args) ` `    ``{ ` ` `  `        ``int` `arr[] = { ``1``, ``2``, ``3` `}; ` `        ``int` `k = ``2``; ` `        ``int` `n = arr.length; ` `        ``System.out.print(countSubarray(arr, n, k)); ` `    ``} ` `} ` ` `  `// This code is contributed by Anant Agarwal. `

## Python3

 `# Python program to count ` `# number of subarrays ` `# whose maximum element ` `# is greater than K. ` ` `  `# Return number of ` `# subarrays whose maximum ` `# element is less than or equal to K. ` `def` `countSubarray(arr, n, k): ` ` `  `    ``# To store count of ` `    ``# subarrays with all ` `    ``# elements less than ` `    ``# or equal to k. ` `    ``s ``=` `0` `  `  `    ``# Traversing the array. ` `    ``i ``=` `0` `    ``while` `(i < n): ` `     `  `        ``# If element is greater ` `        ``# than k, ignore. ` `        ``if` `(arr[i] > k): ` `         `  `            ``i ``=` `i ``+` `1` `            ``continue` `         `  `        ``# Counting the subarray ` `        ``# length whose ` `        ``# each element is less ` `        ``# than equal to k. ` `        ``count ``=` `0` `        ``while` `(i < n ``and` `arr[i] <``=` `k): ` `         `  `            ``i ``=` `i ``+` `1` `            ``count ``=` `count ``+` `1` `         `  `  `  `        ``# Suming number of subarray whose ` `        ``# maximum element is less ` `        ``# than equal to k. ` `        ``s ``=` `s ``+` `((count``*``(count ``+` `1``))``/``/``2``) ` `     `  `  `  `    ``return` `(n``*``(n ``+` `1``)``/``/``2` `-` `s) ` `     `  `# Driver code ` ` `  `arr ``=` `[``1``, ``2``, ``3``] ` `k ``=` `2` `n ``=` `len``(arr) ` ` `  `print``(countSubarray(arr, n, k)) ` ` `  `# This code is contributed ` `# by Anant Agarwal. `

## C#

 `// C# program to count number of subarrays ` `// whose maximum element is greater than K. ` `using` `System; ` ` `  `class` `GFG { ` ` `  `    ``// Return number of subarrays whose maximum ` `    ``// element is less than or equal to K. ` `    ``static` `int` `countSubarray(``int``[] arr, ``int` `n, ``int` `k) ` `    ``{ ` `        ``// To store count of subarrays with all ` `        ``// elements less than or equal to k. ` `        ``int` `s = 0; ` ` `  `        ``// Traversing the array. ` `        ``int` `i = 0; ` `        ``while` `(i < n) { ` ` `  `            ``// If element is greater than k, ignore. ` `            ``if` `(arr[i] > k) { ` `                ``i++; ` `                ``continue``; ` `            ``} ` ` `  `            ``// Counting the subarray length whose ` `            ``// each element is less than equal to k. ` `            ``int` `count = 0; ` `            ``while` `(i < n && arr[i] <= k) { ` `                ``i++; ` `                ``count++; ` `            ``} ` ` `  `            ``// Suming number of subarray whose ` `            ``// maximum element is less than equal to k. ` `            ``s += ((count * (count + 1)) / 2); ` `        ``} ` ` `  `        ``return` `(n * (n + 1) / 2 - s); ` `    ``} ` ` `  `    ``// Driver code ` `    ``public` `static` `void` `Main() ` `    ``{ ` `        ``int``[] arr = {1, 2, 3}; ` `        ``int` `k = 2; ` `        ``int` `n = arr.Length; ` `        ``Console.WriteLine(countSubarray(arr, n, k)); ` `    ``} ` `} ` ` `  `// This code is contributed by vt_m. `

## PHP

 ` ``\$k``) { ` `            ``\$i``++; ` `            ``continue``; ` `        ``} ` ` `  `        ``// Counting the subarray length  ` `        ``// whose each element is less ` `        ``// than equal to k. ` `        ``\$count` `= 0; ` `        ``while` `(``\$i` `< ``\$n` `and` `\$arr``[``\$i``] <= ``\$k``) { ` `            ``\$i``++; ` `            ``\$count``++; ` `        ``} ` ` `  `        ``// Suming number of subarray whose ` `        ``// maximum element is less than ` `        ``// equal to k. ` `        ``\$s` `+= ((``\$count` `* (``\$count` `+ 1)) / 2); ` `    ``} ` ` `  `    ``return` `(``\$n` `* (``\$n` `+ 1) / 2 - ``\$s``); ` `} ` ` `  `// Driven Program ` `    ``\$arr` `= ``array``( 1, 2, 3 ); ` `    ``\$k` `= 2; ` `    ``\$n` `= ``count``(``\$arr``); ` `    ``echo` `countSubarray(``\$arr``, ``\$n``, ``\$k``); ` ` `  `// This code is contributed by anuj_67. ` `?> `

Output:

```3
```

Time Complexity: O(n).

This article is contributed by Anuj Chauhan. 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.

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Improved By : vt_m