How do you solve Find the K-Sum of an Array on LeetCode?

Find the K-Sum of an Array (LeetCode #2386) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(k * n log k) time complexity and O(n) space complexity. Key insight: Using a max-heap allows us to efficiently track the largest sums without generating all possible sums.

What is the brute force solution for Find the K-Sum of an Array?

The brute force approach for Find the K-Sum of an Array is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach involves generating all possible subsequence sums, sorting them, and then retrieving the k-th largest sum. This method is straightforward but inefficient for large arrays due to the exponential growth of subsequences. The optimal Optimal Solution approach improves this to O(k * n log k).

What algorithm or data structure is used to solve Find the K-Sum of an Array?

Find the K-Sum of an Array uses the following concepts: Array, Sorting, Heap (Priority Queue). The recommended patterns to study are: Heap (Priority Queue), Dynamic Programming (for subsequence problems).

What are the interview tips for Find the K-Sum of an Array?

Explain your thought process clearly as you work through the problem. Consider edge cases, such as arrays with negative numbers or zeros. Practice writing clean and efficient code, as it reflects your understanding of the problem.

What are common mistakes when solving Find the K-Sum of an Array?

Failing to handle duplicates properly, which can lead to incorrect results. Not considering the empty subsequence sum of 0.

#2386

Find the K-Sum of an Array

Hard

ArraySortingHeap (Priority Queue)Heap (Priority Queue)Dynamic Programming (for subsequence problems)

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

💡

Intuition

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

The optimal approach uses a max-heap to efficiently find the k-th largest subsequence sum without generating all sums. By starting from the largest sum and exploring the next largest sums, we can efficiently track the k largest sums.

⚙️

Algorithm

5 steps

1Step 1: Initialize a max-heap and add the total sum of the array.
2Step 2: While the heap has elements and we haven't found k sums yet, extract the largest sum.
3Step 3: For each extracted sum, generate new sums by adding each element of the array (considering duplicates) and push them back into the heap.
4Step 4: Use a set to avoid duplicate sums in the heap.
5Step 5: Repeat until we extract the k-th largest sum.

solution.py16 lines

1import heapq
2
3def k_sum(nums, k):
4    max_heap = []
5    total_sum = sum(nums)
6    heapq.heappush(max_heap, -total_sum)
7    seen = set([-total_sum])
8    current_sum = 0
9    for _ in range(k):
10        current_sum = -heapq.heappop(max_heap)
11        for num in nums:
12            new_sum = current_sum - num
13            if new_sum not in seen:
14                seen.add(new_sum)
15                heapq.heappush(max_heap, -new_sum)
16    return current_sum

ℹ

Complexity note: The time complexity is O(k * n log k) because we are pushing new sums into the heap, which takes O(log k) time. The space complexity is O(n) due to the storage of unique sums in the set and the heap.

1Using a max-heap allows us to efficiently track the largest sums without generating all possible sums.
2The uniqueness of sums is crucial to avoid unnecessary computations and memory usage.

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