LeetCode #2386 — HARD

Find the K-Sum of an Array

Break down a hard problem into reliable checkpoints, edge-case handling, and complexity trade-offs.

Solve on LeetCode
The Problem

Problem Statement

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 kth 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)

Roadmap

  1. Brute Force Baseline
  2. Core Insight
  3. Algorithm Walkthrough
  4. Edge Cases
  5. Full Annotated Code
  6. Interactive Study Demo
  7. Complexity Analysis
Step 01

Brute Force Baseline

Problem summary: 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 kth 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.

Baseline thinking

Start with the most direct exhaustive search. That gives a correctness anchor before optimizing.

Pattern signal: Array

Example 1

[2,4,-2]
5

Example 2

[1,-2,3,4,-10,12]
16
Step 02

Core Insight

What unlocks the optimal approach

  • Start from the largest sum possible, and keep finding the next largest sum until you reach the kth sum.
  • Starting from a sum, what are the two next largest sums that you can obtain from it?
Interview move: turn each hint into an invariant you can check after every iteration/recursion step.
Step 03

Algorithm Walkthrough

Iteration Checklist

  1. Define state (indices, window, stack, map, DP cell, or recursion frame).
  2. Apply one transition step and update the invariant.
  3. Record answer candidate when condition is met.
  4. Continue until all input is consumed.
Use the first example testcase as your mental trace to verify each transition.
Step 04

Edge Cases

Minimum Input
Single element / shortest valid input
Validate boundary behavior before entering the main loop or recursion.
Duplicates & Repeats
Repeated values / repeated states
Decide whether duplicates should be merged, skipped, or counted explicitly.
Extreme Constraints
Largest constraint values
Re-check complexity target against constraints to avoid time-limit issues.
Invalid / Corner Shape
Empty collections, zeros, or disconnected structures
Handle special-case structure before the core algorithm path.
Step 05

Full Annotated Code

Source-backed implementations are provided below for direct study and interview prep.

// Accepted solution for LeetCode #2386: Find the K-Sum of an Array
class Solution {
    public long kSum(int[] nums, int k) {
        long mx = 0;
        int n = nums.length;
        for (int i = 0; i < n; ++i) {
            if (nums[i] > 0) {
                mx += nums[i];
            } else {
                nums[i] *= -1;
            }
        }
        Arrays.sort(nums);
        PriorityQueue<Pair<Long, Integer>> pq
            = new PriorityQueue<>(Comparator.comparing(Pair::getKey));
        pq.offer(new Pair<>(0L, 0));
        while (--k > 0) {
            var p = pq.poll();
            long s = p.getKey();
            int i = p.getValue();
            if (i < n) {
                pq.offer(new Pair<>(s + nums[i], i + 1));
                if (i > 0) {
                    pq.offer(new Pair<>(s + nums[i] - nums[i - 1], i + 1));
                }
            }
        }
        return mx - pq.peek().getKey();
    }
}
Step 06

Interactive Study Demo

Use this to step through a reusable interview workflow for this problem.

Press Step or Run All to begin.
Step 07

Complexity Analysis

Time
O(n)
Space
O(1)

Approach Breakdown

BRUTE FORCE
O(n²) time
O(1) space

Two nested loops check every pair or subarray. The outer loop fixes a starting point, the inner loop extends or searches. For n elements this gives up to n²/2 operations. No extra space, but the quadratic time is prohibitive for large inputs.

OPTIMIZED
O(n) time
O(1) space

Most array problems have an O(n²) brute force (nested loops) and an O(n) optimal (single pass with clever state tracking). The key is identifying what information to maintain as you scan: a running max, a prefix sum, a hash map of seen values, or two pointers.

Shortcut: If you are using nested loops on an array, there is almost always an O(n) solution. Look for the right auxiliary state.
Coach Notes

Common Mistakes

Review these before coding to avoid predictable interview regressions.

Off-by-one on range boundaries

Wrong move: Loop endpoints miss first/last candidate.

Usually fails on: Fails on minimal arrays and exact-boundary answers.

Fix: Re-derive loops from inclusive/exclusive ranges before coding.