Is Maximum Subarray Sum After at Most K Swaps easy or hard?

Maximum Subarray Sum After at Most K Swaps is classified as Hard because it combines multiple concepts: subarray enumeration, greedy replacement logic, and heap-based candidate tracking. Efficiently managing swap candidates across many possible subarrays is the main challenge.

Maximum Subarray Sum After at Most K Swaps Python/Java solution

Most implementations use heaps or priority queues available in standard libraries. Python typically uses heapq with sign inversion for max-heaps, while Java uses PriorityQueue with custom comparators. The algorithm greedily performs up to k profitable swaps while maintaining heap structures.

How to solve Maximum Subarray Sum After at Most K Swaps in O(n)?

Pure O(n) is difficult because selecting the best swap candidates requires ordered comparisons. Most practical solutions use heaps or balanced structures to track the smallest inside elements and largest outside elements, leading to O(n log n) time. The greedy insight is to always replace the smallest element inside the subarray with the largest available outside value.

What is the best approach for Maximum Subarray Sum After at Most K Swaps?

The most efficient approach combines greedy swapping with priority queues. Maintain the smallest elements inside the chosen subarray and the largest elements outside using heaps, then perform up to k beneficial swaps. This allows selecting the best improvements without sorting repeatedly and typically runs in O(n log n) time.

Is Maximum Subarray Sum After at Most K Swaps asked at Google/Amazon/Meta?

Problems combining maximum subarray logic with greedy swaps and heaps appear in interviews at large tech companies including Google, Amazon, and Meta. Variants test your ability to combine sliding window techniques with priority queues and greedy optimization.

What data structure is used in Maximum Subarray Sum After at Most K Swaps?

Priority queues (min-heap and max-heap) are the key data structures. A min-heap tracks the smallest elements inside the current subarray while a max-heap tracks the largest elements outside. These structures allow efficient selection of the best swap candidates.

What is the time complexity of Maximum Subarray Sum After at Most K Swaps?

The optimized heap-based approach runs in O(n log n) time with O(n) space. A brute force method that checks every subarray and sorts candidates requires O(n^2 log n) time. The heap optimization avoids repeated sorting and tracks swap candidates efficiently.

Description Hints 4 Solution Video 1:32:39

3962. Maximum Subarray Sum After at Most K Swaps

Hard14.2% acceptance1 company

You are given an integer array nums and an integer k.

You are allowed to perform at most k swap operations on the array.

In one swap operation, you may choose any two indices i and j and swap nums[i] and nums[j].

Return an integer denoting the maximum possible subarray sum after performing the swaps.

Example 1:

Input: nums = [1,-1,0,2], k = 1

Output: 3

Explanation:

We can swap on indices 1 and 3, resulting in the array [1, 2, 0, -1].
The subarray [1, 2] has a sum of 3, which is the maximum possible subarray sum after at most k = 1 swap.

Example 2:

Input: nums = [4,3,2,4], k = 2

Output: 13

Explanation:

The maximum possible subarray sum after at most k = 2 swaps is the sum of the entire array, which is 13.

Example 3:

Input: nums = [-1,-2], k = 0

Output: -1

Explanation:

k = 0 swaps are allowed.
The possible subarrays are [-1], [-2], and [-1, -2], with sums -1, -2, and -3 respectively.
Among these sums, the maximum is -1.

Constraints:

1 <= nums.length <= 1500
-10⁵ <= nums[i] <= 10⁵
0 <= k <= nums.length

Asked at 1 company

Google

Topics

Hints open one at a time

Hint 1

Fix a subarray. An optimal swap exchanges one of its smallest elements with one of the largest elements outside it, provided this increases the sum.

Hint 2

If the elements inside are ordered increasingly and those outside decreasingly, the gain from using t swaps is the sum of the t largest outside elements minus the sum of the t smallest inside elements.

Hint 3

Enumerate the left endpoint and extend the right endpoint while maintaining the inside and outside elements in order-statistics data structures that support counts, sums, and the sum of the smallest or largest t elements.

Hint 4

The marginal gains are non-increasing as t grows, so find the largest profitable t <= k and add its gain to the original subarray sum.

1:32:39

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

Starter codePython 3Spaces: 4

Examples

Case 1Case 2Case 3

Input

[1,-1,0,2]
1

Input

[4,3,2,4]
2

Input

[-1,-2]
0

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