Is Maximum Total Sum of K Selected Elements easy or hard?

The problem is generally classified as Medium because the optimal solution requires recognizing that selecting the k largest values maximizes the sum and implementing it efficiently using sorting, heaps, or Quickselect.

Maximum Total Sum of K Selected Elements Python/Java solution

Python implementations typically use heapq (with negated values) or built-in sorting to grab the k largest elements. Java solutions often use PriorityQueue configured as a max heap or Arrays.sort followed by summing the top k values.

How to solve Maximum Total Sum of K Selected Elements in O(n)?

Use the Quickselect algorithm to partition the array around the k-th largest element. After partitioning, the first k positions contain the k largest values (order does not matter). Summing those elements gives the maximum total in average O(n) time and O(1) extra space.

What is the best approach for Maximum Total Sum of K Selected Elements?

Quickselect or a max-heap based greedy approach is typically the best. Quickselect finds the k largest elements in average O(n) time without sorting the entire array. If implementation simplicity matters, sorting and summing the top k elements in O(n log n) is also widely accepted in interviews.

Is Maximum Total Sum of K Selected Elements asked at Google/Amazon/Meta?

Variants of this problem appear frequently in interviews at companies like Amazon, Google, and Meta. The core idea—selecting the k largest elements efficiently—tests knowledge of heaps, partial sorting, and selection algorithms such as Quickselect.

What data structure is used in Maximum Total Sum of K Selected Elements?

Common implementations rely on arrays combined with either sorting or a priority queue (max heap). A heap allows repeated extraction of the maximum element in O(log n) time, while Quickselect works directly on the array using partition-based selection.

What is the time complexity of Maximum Total Sum of K Selected Elements?

The complexity depends on the approach used. Sorting the array and summing the largest k elements takes O(n log n) time. Using Quickselect reduces the average complexity to O(n) with O(1) extra space, while a heap-based approach runs in about O(n + k log n).

3974. Maximum Total Sum of K Selected Elements - Practice Online

You are given an integer array nums and two integers k and mul.

Select exactly k elements from nums. Process these elements one by one in any order you choose.

For each selected element, independently choose one of the following:

Add the element's value to the total sum, or
Multiply the element by the current value of mul and add the result to the total sum.

After processing each selected element, mul decreases by 1, regardless of which option was chosen. The current value of mul may become 0 or negative.

Return an integer denoting the maximum possible total sum.

Example 1:

Input: nums = [6,1,2,9], k = 3, mul = 2

Output: 26

Explanation:

One optimal way:

One optimal selection is nums[3] = 9, nums[0] = 6, and nums[2] = 2.
Process nums[3] = 9 first: choose multiplication, so it contributes 9 * 2 = 18. Now, mul becomes 1.
Process nums[0] = 6 next: choose multiplication, so it contributes 6 * 1 = 6. Now, mul becomes 0.
Process nums[2] = 2 last: choose addition, so it contributes 2.
The total sum is 18 + 6 + 2 = 26.

Example 2:

Input: nums = [3,7,5,2], k = 2, mul = 4

Output: 43

Explanation:

One optimal way:

One optimal selection is nums[1] = 7 and nums[2] = 5.
Process nums[1] = 7 first: choose multiplication, so it contributes 7 * 4 = 28. Now, mul becomes 3.
Process nums[2] = 5 next: choose multiplication, so it contributes 5 * 3 = 15.
The total sum is 28 + 15 = 43.

Example 3:

Input: nums = [4,4], k = 1, mul = 1

Output: 4

Explanation:

One optimal way:

One optimal selection is nums[0] = 4.
Process nums[0] = 4: choose multiplication, so it contributes 4 * 1 = 4.
The total sum is 4.

Constraints:

1 <= nums.length <= 10⁵
1 <= nums[i] <= 10⁵
1 <= k <= nums.length
1 <= mul <= 10⁵