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# Sum of Array maximums after K operations by reducing max element to its half

Given an array arr[] of N integers and an integer K, the task is to find the sum of maximum of the array possible wherein each operation the current maximum of the array is replaced with its half.

Example:

Input: arr[] = {2, 4, 6, 8, 10}, K = 5
Output: 33
Explanation: In 1st operation, the maximum of the given array is 10. Hence, the value becomes 10 and the array after 1st operation becomes arr[] = {2, 4, 6, 8, 5}.
The value after 2nd operation = 18 and arr[] = {2, 4, 6, 4, 5}.
Similarly, proceeding forward, value after 5th operation will be 33.

Input: arr[] = {6, 5}, K = 3
Output: 14

Approach: The given problem can be solved with the help of a greedy approach. The idea is to use a max heap data structure. Therefore, traverse the given array and insert all the elements in the array arr[] into a max priority queue. At each operation, remove the maximum from the heap using pop operation, add it to the value and reinsert the value after dividing it by two into the heap. The value after repeating the above operation K times is the required answer.

Below is the implementation of the above approach:

## C++

 // C++ program of the above approach#include using namespace std; // Function to find maximum possible// value after K given operationsint maxValue(vector arr, int K){    // Stores required value    int val = 0;     // Initializing priority queue    // with all elements of array    priority_queue pq(arr.begin(),                           arr.end());     // Loop to iterate through    // each operation    while (K--) {         // Current Maximum        int max = pq.top();        pq.pop();         // Update value        val += max;         // Reinsert maximum        pq.push(max / 2);    }     // Return Answer    return val;} // Driver Callint main(){    vector arr = { 2, 4, 6, 8, 10 };    int K = 5;    cout << maxValue(arr, K);}

## Java

 // Java code for the above approachimport java.util.Comparator;import java.util.PriorityQueue;class CustomComparator implements Comparator {   @Override  public int compare(Integer number1, Integer number2)  {    int value =  number1.compareTo(number2);     // elements are sorted in reverse order    if (value > 0) {      return -1;    }    else if (value < 0) {      return 1;    }    else {      return 0;    }  }}class GFG {   // Function to find maximum possible  // value after K given operations  static int maxValue(int[] arr, int K)  {     // Stores required value    int val = 0;     // Initializing priority queue    // with all elements of array    PriorityQueue pq      = new PriorityQueue(new CustomComparator());     for (int i = 0; i < arr.length; i++) {      pq.add(arr[i]);    }     // Loop to iterate through    // each operation    while (K != 0) {       // Current Maximum      int max = pq.poll();       // Update value      val += max;       // Reinsert maximum      pq.add((int)Math.floor(max / 2));      K = K - 1;    }     // Return Answer    return val;  }   // Driver Call  public static void main(String[] args)  {    int[] arr = { 2, 4, 6, 8, 10 };    int K = 5;    System.out.println(maxValue(arr, K));  }} // This code is conbtributed by Potta Lokesh

## Python3

 # python3 program of the above approachfrom queue import PriorityQueue # Function to find maximum possible# value after K given operationsdef maxValue(arr, K):     # Stores required value    val = 0     # Initializing priority queue    # with all elements of array    pq = PriorityQueue()     for dt in arr:        pq.put(-1*dt)     # Loop to iterate through    # each operation    while (True):         # Current Maximum        max = -1 * pq.get()         # Update value        val += max         # Reinsert maximum        pq.put(-1 * (max // 2))         K -= 1         if K == 0:            break     # Return Answer    return val # Driver Callif __name__ == "__main__":     arr = [2, 4, 6, 8, 10]    K = 5    print(maxValue(arr, K))     # This code is contributed by rakeshsahni

## C#

 // C# code for the above approachusing System;using System.Collections.Generic; class CustomComparator : IComparer {  public int Compare(int number1, int number2)  {    int value = number1.CompareTo(number2);     // elements are sorted in reverse order    if (value > 0) {      return -1;    }    else if (value < 0) {      return 1;    }    else {      return 0;    }  }} public class GFG {   // Function to find maximum possible  // value after K given operations  static int maxValue(int[] arr, int K)  {     // Stores required value    int val = 0;     // Initializing priority queue    // with all elements of array    SortedSet pq      = new SortedSet(new CustomComparator());    for (int i = 0; i < arr.Length; i++) {      pq.Add(arr[i]);    }     // Loop to iterate through each operation    while (K != 0) {      // Current Maximum      int max = pq.Min;       // Update value      val += max;       // Reinsert maximum      pq.Add((int)Math.Floor((double)max / 2));      pq.Remove(max);      K = K - 1;    }     // Return Answer    return val;  }   static public void Main()  {     // Code    int[] arr = { 2, 4, 6, 8, 10 };    int K = 5;    Console.WriteLine(maxValue(arr, K));  }} // This code is conbtributed by lokesh.

## Javascript

 class PriorityQueue {  constructor(comparator) {    this.heap = [];    this.comparator = comparator;  }   add(element) {    this.heap.push(element);    this.bubbleUp(this.heap.length - 1);  }   peek() {    return this.heap[0];  }   poll() {    const poppedValue = this.heap[0];    const bottom = this.heap.length - 1;    if (bottom > 0) {      this.swap(0, bottom);    }    this.heap.pop();    this.bubbleDown(0);    return poppedValue;  }   size() {    return this.heap.length;  }   bubbleUp(index) {    while (index > 0) {      const parentIndex = Math.floor((index + 1) / 2) - 1;      if (this.comparator(this.heap[index], this.heap[parentIndex]) < 0) {        this.swap(index, parentIndex);        index = parentIndex;      } else {        break;      }    }  }   bubbleDown(index) {    let swapping = true;    while (swapping) {      const leftChildIndex = 2 * (index + 1) - 1;      const rightChildIndex = 2 * (index + 1);      let minIndex = index;      if (        leftChildIndex < this.heap.length &&        this.comparator(this.heap[leftChildIndex], this.heap[minIndex]) < 0      ) {        minIndex = leftChildIndex;      }      if (        rightChildIndex < this.heap.length &&        this.comparator(this.heap[rightChildIndex], this.heap[minIndex]) < 0      ) {        minIndex = rightChildIndex;      }      if (minIndex !== index) {        this.swap(index, minIndex);        index = minIndex;      } else {        swapping = false;      }    }  }   swap(index1, index2) {    const temp = this.heap[index1];    this.heap[index1] = this.heap[index2];    this.heap[index2] = temp;  }} // Function to find maximum possible// value after K given operationsfunction maxValue(arr, K) {  // Stores required value  let val = 0;   // Initializing priority queue  // with all elements of array  const pq = new PriorityQueue((a, b) => b - a);  arr.forEach((element) => pq.add(element));   // Loop to iterate through  // each operation  while (K--) {    // Current Maximum    const max = pq.peek();    pq.poll();     // Update value    val += max;     // Reinsert maximum    pq.add(Math.floor(max / 2));  }   // Return Answer  return val;} // Driver Callconst arr = [2, 4, 6, 8, 10];const K = 5;document.write(maxValue(arr, K));

Output

33

Time Complexity: O(K*log N)
Auxiliary Space: O(N)