LeetCode #3478 — MEDIUM

Choose K Elements With Maximum Sum

Move from brute-force thinking to an efficient approach using array strategy.

Solve on LeetCode
The Problem

Problem Statement

You are given two integer arrays, nums1 and nums2, both of length n, along with a positive integer k.

For each index i from 0 to n - 1, perform the following:

  • Find all indices j where nums1[j] is less than nums1[i].
  • Choose at most k values of nums2[j] at these indices to maximize the total sum.

Return an array answer of size n, where answer[i] represents the result for the corresponding index i.

Example 1:

Input: nums1 = [4,2,1,5,3], nums2 = [10,20,30,40,50], k = 2

Output: [80,30,0,80,50]

Explanation:

  • For i = 0: Select the 2 largest values from nums2 at indices [1, 2, 4] where nums1[j] < nums1[0], resulting in 50 + 30 = 80.
  • For i = 1: Select the 2 largest values from nums2 at index [2] where nums1[j] < nums1[1], resulting in 30.
  • For i = 2: No indices satisfy nums1[j] < nums1[2], resulting in 0.
  • For i = 3: Select the 2 largest values from nums2 at indices [0, 1, 2, 4] where nums1[j] < nums1[3], resulting in 50 + 30 = 80.
  • For i = 4: Select the 2 largest values from nums2 at indices [1, 2] where nums1[j] < nums1[4], resulting in 30 + 20 = 50.

Example 2:

Input: nums1 = [2,2,2,2], nums2 = [3,1,2,3], k = 1

Output: [0,0,0,0]

Explanation:

Since all elements in nums1 are equal, no indices satisfy the condition nums1[j] < nums1[i] for any i, resulting in 0 for all positions.

Constraints:

  • n == nums1.length == nums2.length
  • 1 <= n <= 105
  • 1 <= nums1[i], nums2[i] <= 106
  • 1 <= k <= n

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 two integer arrays, nums1 and nums2, both of length n, along with a positive integer k. For each index i from 0 to n - 1, perform the following: Find all indices j where nums1[j] is less than nums1[i]. Choose at most k values of nums2[j] at these indices to maximize the total sum. Return an array answer of size n, where answer[i] represents the result for the corresponding index i.

Baseline thinking

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

Pattern signal: Array

Example 1

[4,2,1,5,3]
[10,20,30,40,50]
2

Example 2

[2,2,2,2]
[3,1,2,3]
1
Step 02

Core Insight

What unlocks the optimal approach

  • Sort <code>nums1</code> and its corresponding <code>nums2</code> values together based on <code>nums1</code>.
  • Use a max heap to track the top <code>k</code> values of <code>nums2</code> as you process each element in the sorted order.
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
Upper-end input sizes
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 #3478: Choose K Elements With Maximum Sum
class Solution {
    public long[] findMaxSum(int[] nums1, int[] nums2, int k) {
        int n = nums1.length;
        int[][] arr = new int[n][0];
        for (int i = 0; i < n; ++i) {
            arr[i] = new int[] {nums1[i], i};
        }
        Arrays.sort(arr, (a, b) -> a[0] - b[0]);
        PriorityQueue<Integer> pq = new PriorityQueue<>();
        long s = 0;
        long[] ans = new long[n];
        int j = 0;
        for (int h = 0; h < n; ++h) {
            int x = arr[h][0], i = arr[h][1];
            while (j < h && arr[j][0] < x) {
                int y = nums2[arr[j][1]];
                pq.offer(y);
                s += y;
                if (pq.size() > k) {
                    s -= pq.poll();
                }
                ++j;
            }
            ans[i] = s;
        }
        return ans;
    }
}
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 log n)
Space
O(n)

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.