How do you solve Maximum Sum With Exactly K Elements on LeetCode?

Maximum Sum With Exactly K Elements (LeetCode #2656) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n + k log n) time complexity and O(n) space complexity. Key insight: Choosing the maximum element at each step maximizes the score.

What is the brute force solution for Maximum Sum With Exactly K Elements ?

The brute force approach for Maximum Sum With Exactly K Elements is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach involves trying all possible combinations of selecting elements from the array, simulating the process of removing and adding elements to maximize the score. This method is straightforward but inefficient for larger inputs. The optimal Optimal Solution approach improves this to O(n + k log n).

What algorithm or data structure is used to solve Maximum Sum With Exactly K Elements ?

Maximum Sum With Exactly K Elements uses the following concepts: Array, Greedy. The recommended patterns to study are: Greedy, Heap, Priority Queue.

What are the interview tips for Maximum Sum With Exactly K Elements ?

Explain your thought process clearly when discussing the brute force approach. Highlight the importance of efficiency and how you can improve the solution. Practice implementing heaps, as they are commonly used in optimization problems.

What are common mistakes when solving Maximum Sum With Exactly K Elements ?

Not using a max-heap and relying on linear searches. Failing to account for the updated values correctly after each operation.

#2656

Maximum Sum With Exactly K Elements

Easy

ArrayGreedyGreedyHeapPriority Queue

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n + k log n)
Space	O(1)	O(n)

💡

Intuition

Time O(n + k log n)Space O(n)

The optimal approach uses a max-heap (or priority queue) to efficiently retrieve the maximum element in each iteration. This allows us to perform the operation in logarithmic time, leading to a significant reduction in overall complexity.

⚙️

Algorithm

3 steps

1Step 1: Create a max-heap from the `nums` array.
2Step 2: Initialize a variable `score` to 0.
3Step 3: For `k` iterations, extract the maximum element from the heap, add it to `score`, and insert `max + 1` back into the heap.

solution.py12 lines

1# Full working Python code
2import heapq
3
4def maxSumOptimal(nums, k):
5    max_heap = [-num for num in nums]  # Negate for max-heap
6    heapq.heapify(max_heap)
7    score = 0
8    for _ in range(k):
9        max_num = -heapq.heappop(max_heap)
10        score += max_num
11        heapq.heappush(max_heap, -(max_num + 1))
12    return score

ℹ

Complexity note: The complexity is O(n + k log n) because we first build the max-heap in O(n) time, and then each of the k operations (extract and insert) takes O(log n) time, leading to a total of O(k log n).

1Choosing the maximum element at each step maximizes the score.
2Using a max-heap allows efficient retrieval and updating of the maximum element.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.