Skip to content

Latest commit

 

History

History
79 lines (56 loc) · 3.55 KB

explanation.md

File metadata and controls

79 lines (56 loc) · 3.55 KB
Raw

Maximal Score After Applying K Operations - Step-by-Step Explanation

Problem Overview

We need to maximize the score by choosing elements from the array and updating them by applying the ceil(num[i] / 3) operation exactly k times.

General Approach

  1. Use a Priority Queue or Max-Heap: To always select the largest element available, use a max-heap to keep track of the maximum elements efficiently.
  2. Maximize the Score: Each time, extract the largest element, add it to the score, and then reduce the element using ceil(num[i] / 3) before pushing it back into the heap.
  3. Repeat the Process: Repeat this operation exactly k times and return the total score.

C++ Code Explanation

  1. Step 1: Start by importing necessary headers for the priority queue.
  2. Step 2: Convert the input array into a max-heap using a priority queue.
  3. Step 3: Set up a loop to perform exactly k operations. During each iteration:
    • Extract the maximum value.
    • Add it to the score.
    • Update the value by dividing it by 3 and pushing it back into the heap.
  4. Step 4: Once the loop finishes, return the accumulated score as the result.

Java Code Explanation

  1. Step 1: Import relevant libraries such as PriorityQueue for handling the heap.
  2. Step 2: Initialize a max-heap using the PriorityQueue by inserting all the elements in a reverse order (to simulate a max-heap).
  3. Step 3: For each of the k operations:
    • Poll the maximum element from the queue.
    • Add the polled element to the score.
    • Compute the new value by dividing it by 3 and push it back into the queue.
  4. Step 4: After performing k operations, return the total score as the answer.

JavaScript Code Explanation

  1. Step 1: Start by initializing a max-heap using an array and a custom comparator function to handle the maximum extraction.
  2. Step 2: Push all elements of the array into the heap.
  3. Step 3: For k iterations, perform the following steps:
    • Pop the largest element from the heap.
    • Add this element to the score.
    • Calculate its new value (after dividing by 3) and push it back to the heap.
  4. Step 4: After completing the iterations, return the accumulated score.

Python Code Explanation

  1. Step 1: Use Python’s heapq library to implement a max-heap by pushing negative values.
  2. Step 2: Insert all elements of the array into the max-heap (negating them to simulate max behavior).
  3. Step 3: For each of the k steps:
    • Pop the largest (most negative) element.
    • Add its absolute value to the score.
    • Compute the new value by dividing the element by 3 and push it back into the heap (still negative).
  4. Step 4: After k iterations, return the total score.

Go Code Explanation

  1. Step 1: Import necessary packages including container/heap to simulate the priority queue (max-heap).
  2. Step 2: Push all elements of the array into a custom max-heap.
  3. Step 3: For each operation (up to k times):
    • Pop the largest element from the heap.
    • Add this element to the score.
    • Recalculate the element’s value (divide by 3) and push it back into the heap.
  4. Step 4: After processing the k operations, return the total score.

Conclusion

In all implementations, the core logic revolves around efficiently selecting the largest element using a heap, modifying it, and repeating this process k times to maximize the score. Each language uses its own syntax and heap handling mechanisms, but the overall approach remains consistent.