Is Maximal Score After Applying K Operations easy or hard?

The problem is rated Medium on LeetCode with an acceptance rate around 63%. The greedy idea is straightforward, but recognizing that a max heap is needed to efficiently repeat the operation k times is the key insight.

Maximal Score After Applying K Operations Python/Java solution

Most implementations use a priority queue. Python typically uses heapq with negated values to simulate a max heap, while Java uses PriorityQueue with a custom comparator. JavaScript and C++ also provide efficient heap structures for the same O(k log n) approach.

How to solve Maximal Score After Applying K Operations in O(k log n)?

Use a max heap to always access the largest value in the array. Push all elements into the heap, repeat k times: pop the maximum, add it to the score, compute ceil(value / 3), and push the result back. Each iteration takes O(log n).

What is the best approach for Maximal Score After Applying K Operations?

The optimal approach uses a max heap (priority queue). Insert all numbers into the heap, repeatedly extract the largest value, add it to the score, then push back ceil(value / 3). Each operation costs O(log n), so the overall complexity is O((n + k) log n).

Is Maximal Score After Applying K Operations asked at Google/Amazon/Meta?

Greedy + heap problems similar to this appear frequently in interviews at companies like Amazon, Google, and Meta. The pattern of repeatedly selecting the maximum element with a priority queue is a common interview theme.

What data structure is used in Maximal Score After Applying K Operations?

A max heap (priority queue) is the primary data structure. It allows efficient extraction of the largest value and reinsertion after updating the element, keeping operations at O(log n).

What is the time complexity of Maximal Score After Applying K Operations?

The heap-based solution runs in O((n + k) log n) time because building the heap takes O(n) and each of the k operations performs a pop and push, both O(log n). Space complexity is O(n) for storing elements in the heap.

Description Hints 2 Solution Video 7:44

2530. Maximal Score After Applying K Operations

Medium63.7% acceptance6 companies

You are given a 0-indexed integer array nums and an integer k. You have a starting score of 0.

In one operation:

choose an index i such that 0 <= i < nums.length,
increase your score by nums[i], and
replace nums[i] with ceil(nums[i] / 3).

Return the maximum possible score you can attain after applying exactly k operations.

The ceiling function ceil(val) is the least integer greater than or equal to val.

Example 1:

Input: nums = [10,10,10,10,10], k = 5
Output: 50
Explanation: Apply the operation to each array element exactly once. The final score is 10 + 10 + 10 + 10 + 10 = 50.

Example 2:

Input: nums = [1,10,3,3,3], k = 3
Output: 17
Explanation: You can do the following operations:
Operation 1: Select i = 1, so nums becomes [1,4,3,3,3]. Your score increases by 10.
Operation 2: Select i = 1, so nums becomes [1,2,3,3,3]. Your score increases by 4.
Operation 3: Select i = 2, so nums becomes [1,2,1,3,3]. Your score increases by 3.
The final score is 10 + 4 + 3 = 17.

Constraints: