Is Find the K-Sum of an Array easy or hard?

Find the K-Sum of an Array is classified as Hard because the naive solution involves 2^n subsequences. Efficient solutions require recognizing that subsequence sums can be expressed as reductions from the maximum sum and explored using heaps or binary search techniques.

Find the K-Sum of an Array Python/Java solution

Python implementations typically use the heapq module to maintain the priority queue. Java solutions use PriorityQueue with custom pair states storing the current reduction and index. Both implementations follow the same logic: compute the maximum sum, sort absolute values, and iteratively generate k candidates.

What is the best approach for Find the K-Sum of an Array?

The most practical approach uses a max sum baseline and a min-heap (priority queue) to generate the next smallest reductions. After sorting the absolute values, the heap tracks candidate reductions and expands them iteratively. This method runs in O(n log n + k log n) time and avoids enumerating all 2^n subsequences.

Is Find the K-Sum of an Array asked at Google/Amazon/Meta?

Problems involving k-th largest combinations, heap exploration, and subsequence sums are common at companies like Google, Amazon, and Meta. Variants frequently test priority queues, combinatorial enumeration, and pruning techniques. This problem specifically evaluates your ability to avoid exponential enumeration.

What data structure is used in Find the K-Sum of an Array?

The key data structure is a heap (priority queue). It maintains candidate subsequence reductions in sorted order so the algorithm can extract the next best sum efficiently. Sorting and array traversal are also used to structure the candidate generation process.

What is the time complexity of Find the K-Sum of an Array?

The optimal heap-based solution runs in O(n log n + k log n) time. Sorting the array costs O(n log n), and each of the k heap operations costs O(log n). Space complexity is O(n) due to the priority queue and auxiliary structures.

How to solve Find the K-Sum of an Array in O(n log n + k log n)?

First compute the maximum subsequence sum by adding all positive numbers. Convert values to absolute numbers and sort them. Use a min-heap to track the smallest reductions from the maximum sum. Repeatedly pop the smallest reduction and push new candidate states until the k-th subsequence sum is produced.

Description Hints 2 Solution Video 40:46

2386. Find the K-Sum of an Array

Hard42.0% acceptance3 companies

You are given an integer array nums and a positive integer k. You can choose any subsequence of the array and sum all of its elements together.

We define the K-Sum of the array as the k^th largest subsequence sum that can be obtained (not necessarily distinct).

Return the K-Sum of the array.

A subsequence is an array that can be derived from another array by deleting some or no elements without changing the order of the remaining elements.

Note that the empty subsequence is considered to have a sum of 0.

Example 1:

Input: nums = [2,4,-2], k = 5
Output: 2
Explanation: All the possible subsequence sums that we can obtain are the following sorted in decreasing order:
- 6, 4, 4, 2, 2, 0, 0, -2.
The 5-Sum of the array is 2.

Example 2:

Input: nums = [1,-2,3,4,-10,12], k = 16
Output: 10
Explanation: The 16-Sum of the array is 10.

Constraints:

n == nums.length
1 <= n <= 10⁵
-10⁹ <= nums[i] <= 10⁹
1 <= k <= min(2000, 2ⁿ)

Asked at 3 companies

HubSpot Amazon

Google

Topics

Hints open one at a time

Hint 1

Start from the largest sum possible, and keep finding the next largest sum until you reach the kth sum.

Hint 2

Starting from a sum, what are the two next largest sums that you can obtain from it?

40:46

Still stuck?Read 3 approaches, or watch a walkthrough.

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1class Solution:
2    def kSum(self, nums: List[int], k: int) -> int:
3        

Starter codePython 3Spaces: 4

Examples

Case 1Case 2

Input

[2,4,-2]
5

Input

[1,-2,3,4,-10,12]
16

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