Given a list of ‘N’ numbers, and an integer ‘K’. The task is to print the average of max ‘K’ numbers after each query where a query consists of an integer element which needs to be added to the list of elements.**Note:** The queries are defined with an integer array ‘q’

**Examples:**

Input:N = 4, K = 3, arr = {1, 2, 3, 4}, q = {7, 2, 1, 5}Output:4.666666

4.666666

4.666666

5.333333

After query 1, arr = {1, 2, 3, 4, 7} and the average of max K (i.e. {3, 4, 7}) elements is 4.666666.

After query 2, arr = {1, 2, 3, 4, 7, 2} and the average is 4.666666 for {3, 4, 7}.

After query 3, arr = {1, 2, 3, 4, 7, 2, 1} and the average is 4.666666 for {3, 4, 7}.

After query 4, arr = {1, 2, 3, 4, 7, 2, 5} and the average is 5.333333 for {4, 5, 7}.

Input:N = 5, K = 4, arr = {1, 2, 2, 3, 3}, q = {2, 5, 1}Output:2.5

3.25

3.25

**Approach:** Heap (Min Heap) data structure can be used to solve problems like these where insertion and deletions of the elements can be performed in O(log n) time.

- Initially, store the max k elements from the given list of elements in the min heap.
- If the incoming element is less than or equal to the element currently at the root of the min heap then discard the element as it’ll have no effect on the average.
- Else if, the number is greater than the root element then remove the root of the min heap followed by an insertion of the new element and then calculate the average of the elements currently in the heap.
- Print the average and repeat the above two steps for all incoming elements.

Below is the implementation of the above approach:

`// Java implementation of the approach` `import` `java.util.*;` ` ` `class` `GFG {` ` ` ` ` `// Function that returns the` ` ` `// average of max k elements in` ` ` `// the list after each query` ` ` `static` `void` `max_average_k_numbers(` `int` `n,` ` ` `int` `k,` ` ` `int` `m,` ` ` `int` `[] arr,` ` ` `int` `[] query)` ` ` `{` ` ` `double` `max_avg = ` `0.0` `;` ` ` ` ` `// min-heap to maintain` ` ` `// the max k elements at` ` ` `// any point of time;` ` ` `PriorityQueue<Integer> pq = ` `new` `PriorityQueue<Integer>();` ` ` ` ` `// Sort the array` ` ` `// in ascending order` ` ` `Arrays.sort(arr);` ` ` ` ` `// add max k elements` ` ` `// to the heap` ` ` `double` `sum = ` `0` `;` ` ` `for` `(` `int` `i = n - ` `1` `; i >= n - k; i--) {` ` ` `pq.add(arr[i]);` ` ` `sum = sum + arr[i];` ` ` `}` ` ` ` ` `// perform offline queries` ` ` `for` `(` `int` `i = ` `0` `; i < m; i++) {` ` ` ` ` `// if the minimum element in` ` ` `// the heap is less than` ` ` `// the incoming element` ` ` `if` `(query[i] > pq.peek()) {` ` ` `int` `polled = pq.poll();` ` ` `pq.add(query[i]);` ` ` ` ` `// decrement the current` ` ` `// sum by the polled element` ` ` `sum = sum - polled;` ` ` ` ` `// increment sum by the` ` ` `// incoming element` ` ` `sum = sum + query[i];` ` ` `}` ` ` ` ` `// compute the average` ` ` `max_avg = sum / (` `double` `)k;` ` ` `System.out.println(max_avg);` ` ` `}` ` ` `}` ` ` ` ` `// Driver code` ` ` `public` `static` `void` `main(String[] args)` ` ` `{` ` ` `int` `n = ` `4` `;` ` ` `int` `k = ` `3` `;` ` ` `int` `m = ` `4` `;` ` ` `int` `[] arr = ` `new` `int` `[] { ` `1` `, ` `2` `, ` `3` `, ` `4` `};` ` ` `int` `[] query = ` `new` `int` `[] { ` `7` `, ` `2` `, ` `1` `, ` `5` `};` ` ` ` ` `max_average_k_numbers(n, k, m, arr, query);` ` ` `}` `}` |

**Output:**

4.666666666666667 4.666666666666667 4.666666666666667 5.333333333333333

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