# Maximum number of diamonds that can be gained in K minutes

Given an array **arr[]** consisting of **N** positive integers such that **arr[i]** represents that the **i ^{th}** bag contains

**arr[i]**diamonds and a positive integer

**K**, the task is to find the maximum number of diamonds that can be gained in exactly

**K**minutes if dropping a bag takes 1 minute such that if a bag with

**P**diamonds is dropped, then it changes to

**[P/2]**diamonds, and

**P**diamonds are gained.

**Examples:**

Input:arr[] = {2, 1, 7, 4, 2}, K = 3Output:14Explanation:

The initial state of bags is {2, 1, 7, 4, 2}.Operation 1:Take all diamonds from third bag i.e., arr[2](= 7), the state of bags becomes: {2, 1, 3, 4, 2}.Operation 2:Take all diamonds from fourth bag i.e., arr[3](= 4), the state of bags becomes: {2, 1, 3, 2, 2}.Operation 3:Take all diamonds from Third bag i.e., arr[2](= 3), the state of bags becomes{2, 1, 1, 2, 2}.

Therefore, the total diamonds gains is 7 + 4 + 3 = 14.

Input:arr[] = {7, 1, 2}, K = 2Output:10

**Approach:** The given problem can be solved by using the Greedy Approach with the help of max-heap. Follow the steps below to solve the problem:

- Initialize a priority queue, say
**PQ**, and insert all the elements of the given array into**PQ**. - Initialize a variable, say
**ans**as**0**to store the resultant maximum diamond gained. - Iterate a loop until the priority queue
**PQ**is not empty and the value of**K > 0**:- Pop the top element of the priority queue and add the popped element to the variable
**ans**. - Divide the popped element by
**2**and insert it into the priority queue**PQ**. - Decrement the value of
**K**by**1**.

- Pop the top element of the priority queue and add the popped element to the variable
- After completing the above steps, print the value of
**ans**as the result.

Below is the implementation of the above approach:

## C++

`// C++ program for the above approach` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Function to find the maximum number` `// of diamonds that can be gained in` `// exactly K minutes` `void` `maxDiamonds(` `int` `A[], ` `int` `N, ` `int` `K)` `{` ` ` `// Stores all the array elements` ` ` `priority_queue<` `int` `> pq;` ` ` `// Push all the elements to the` ` ` `// priority queue` ` ` `for` `(` `int` `i = 0; i < N; i++) {` ` ` `pq.push(A[i]);` ` ` `}` ` ` `// Stores the required result` ` ` `int` `ans = 0;` ` ` `// Loop while the queue is not` ` ` `// empty and K is positive` ` ` `while` `(!pq.empty() && K--) {` ` ` `// Store the top element` ` ` `// from the pq` ` ` `int` `top = pq.top();` ` ` `// Pop it from the pq` ` ` `pq.pop();` ` ` `// Add it to the answer` ` ` `ans += top;` ` ` `// Divide it by 2 and push it` ` ` `// back to the pq` ` ` `top = top / 2;` ` ` `pq.push(top);` ` ` `}` ` ` `// Print the answer` ` ` `cout << ans;` `}` `// Driver Code` `int` `main()` `{` ` ` `int` `A[] = { 2, 1, 7, 4, 2 };` ` ` `int` `K = 3;` ` ` `int` `N = ` `sizeof` `(A) / ` `sizeof` `(A[0]);` ` ` `maxDiamonds(A, N, K);` ` ` `return` `0;` `}` |

## Java

`// Java program for the above approach` `import` `java.util.*;` `class` `GFG{` `// Function to find the maximum number` `// of diamonds that can be gained in` `// exactly K minutes` `static` `void` `maxDiamonds(` `int` `A[], ` `int` `N, ` `int` `K)` `{` ` ` ` ` `// Stores all the array elements` ` ` `PriorityQueue<Integer> pq = ` `new` `PriorityQueue<>(` ` ` `(a, b) -> b - a);` ` ` `// Push all the elements to the` ` ` `// priority queue` ` ` `for` `(` `int` `i = ` `0` `; i < N; i++)` ` ` `{` ` ` `pq.add(A[i]);` ` ` `}` ` ` `// Stores the required result` ` ` `int` `ans = ` `0` `;` ` ` `// Loop while the queue is not` ` ` `// empty and K is positive` ` ` `while` `(!pq.isEmpty() && K-- > ` `0` `)` ` ` `{` ` ` ` ` `// Store the top element` ` ` `// from the pq` ` ` `int` `top = pq.peek();` ` ` `// Pop it from the pq` ` ` `pq.remove();` ` ` `// Add it to the answer` ` ` `ans += top;` ` ` `// Divide it by 2 and push it` ` ` `// back to the pq` ` ` `top = top / ` `2` `;` ` ` `pq.add(top);` ` ` `}` ` ` `// Print the answer` ` ` `System.out.print(ans);` `}` `// Driver Code` `public` `static` `void` `main(String[] args)` `{` ` ` `int` `A[] = { ` `2` `, ` `1` `, ` `7` `, ` `4` `, ` `2` `};` ` ` `int` `K = ` `3` `;` ` ` `int` `N = A.length;` ` ` ` ` `maxDiamonds(A, N, K);` `}` `}` `// This code is contributed by 29AjayKumar` |

## Python3

`# Python3 program for the above approach` `# Function to find the maximum number` `# of diamonds that can be gained in` `# exactly K minutes` `def` `maxDiamonds(A, N, K):` ` ` ` ` `# Stores all the array elements` ` ` `pq ` `=` `[]` ` ` `# Push all the elements to the` ` ` `# priority queue` ` ` `for` `i ` `in` `range` `(N):` ` ` `pq.append(A[i])` ` ` ` ` `pq.sort()` ` ` `# Stores the required result` ` ` `ans ` `=` `0` ` ` `# Loop while the queue is not` ` ` `# empty and K is positive` ` ` `while` `(` `len` `(pq) > ` `0` `and` `K > ` `0` `):` ` ` `pq.sort()` ` ` ` ` `# Store the top element` ` ` `# from the pq` ` ` `top ` `=` `pq[` `len` `(pq) ` `-` `1` `]` ` ` `# Pop it from the pq` ` ` `pq ` `=` `pq[` `0` `:` `len` `(pq) ` `-` `1` `]` ` ` `# Add it to the answer` ` ` `ans ` `+` `=` `top` ` ` `# Divide it by 2 and push it` ` ` `# back to the pq` ` ` `top ` `=` `top ` `/` `/` `2` `;` ` ` `pq.append(top)` ` ` `K ` `-` `=` `1` ` ` `# Print the answer` ` ` `print` `(ans)` `# Driver Code` `if` `__name__ ` `=` `=` `'__main__'` `:` ` ` ` ` `A ` `=` `[ ` `2` `, ` `1` `, ` `7` `, ` `4` `, ` `2` `]` ` ` `K ` `=` `3` ` ` `N ` `=` `len` `(A)` ` ` ` ` `maxDiamonds(A, N, K)` `# This code is contributed by SURENDRA_GANGWAR` |

## Javascript

`<script>` `// JavaScript program for the above approach` `// Function to find the maximum number` `// of diamonds that can be gained in` `// exactly K minutes` `function` `maxDiamonds(A, N, K) {` ` ` `// Stores all the array elements` ` ` `let pq = [];` ` ` `// Push all the elements to the` ` ` `// priority queue` ` ` `for` `(let i = 0; i < N; i++) {` ` ` `pq.push(A[i]);` ` ` `}` ` ` `// Stores the required result` ` ` `let ans = 0;` ` ` `// Loop while the queue is not` ` ` `// empty and K is positive` ` ` `pq.sort((a, b) => a - b)` ` ` `while` `(pq.length && K--) {` ` ` `pq.sort((a, b) => a - b)` ` ` `// Store the top element` ` ` `// from the pq` ` ` `let top = pq[pq.length - 1];` ` ` `// Pop it from the pq` ` ` `pq.pop();` ` ` `// Add it to the answer` ` ` `ans += top;` ` ` `// Divide it by 2 and push it` ` ` `// back to the pq` ` ` `top = Math.floor(top / 2);` ` ` `pq.push(top);` ` ` `}` ` ` `// Print the answer` ` ` `document.write(ans);` `}` `// Driver Code` `let A = [2, 1, 7, 4, 2];` `let K = 3;` `let N = A.length;` `maxDiamonds(A, N, K);` `</script>` |

**Output:**

14

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

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