# 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.

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 <bits/stdc++.h>` `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

`<?php` `// PHP 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.` `function` `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` `) {` ` ` `$i` `++;` ` ` `continue` `;` ` ` `}` ` ` `// Counting the subarray length` ` ` `// whose each element is less` ` ` `// than equal to k.` ` ` `$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.` `?>` |

## Javascript

`<script>` ` ` `// Javascript 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.` ` ` `function` `countSubarray(arr, n, k)` ` ` `{` ` ` `// To store count of subarrays with all` ` ` `// elements less than or equal to k.` ` ` `let s = 0;` ` ` ` ` `// Traversing the array.` ` ` `let 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.` ` ` `let count = 0;` ` ` `while` `(i < n && arr[i] <= k) {` ` ` `i++;` ` ` `count++;` ` ` `}` ` ` ` ` `// Suming number of subarray whose` ` ` `// maximum element is less than equal to k.` ` ` `s += parseInt((count * (count + 1)) / 2, 10);` ` ` `}` ` ` ` ` `return` `(n * parseInt((n + 1) / 2, 10) - s);` ` ` `}` ` ` ` ` `let arr = [1, 2, 3];` ` ` `let k = 2;` ` ` `let n = arr.length;` ` ` `document.write(countSubarray(arr, n, k));` ` ` `</script>` |

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 write.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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