Goldman Sachs·Software Engineer·Technical Phone Screen·Intermediate

Intermediate

Jun 2026

Summary

Goldman Sachs SWE interview with a greedy/sorting array problem. Pretty focused session, one question but they wanted clean code and a clear explanation of the approach.

Questions Asked (1)

Given an array of n integers and a number k, find the maximum number of elements whose sum is still less than k, and return that sum.

Algorithms & Data Structures

Author's notes

Sort ascending, greedily pick the smallest elements until adding the next one would hit or exceed k.

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AI HintsAI Generated

Suggested Approach

Sort the array in ascending order, then iterate through it while maintaining a running sum. Add each element to the sum as long as the sum remains less than k, and return the final sum. This greedy approach ensures we include as many elements as possible because smaller elements contribute less to the sum.

Pro tip: Clarify edge cases upfront, such as when the smallest element is already >= k (return 0) or when all elements can be included. Also, mention that sorting takes O(n log n) time, which is optimal for this problem.

1. Understand the problem

Restate the problem to ensure clarity: we need to select a subset of elements with the maximum count such that their sum is less than k, and return that sum. Confirm whether elements can be used only once and if the array can contain negative numbers.

2. Choose the right approach

Recognize that to maximize the number of elements, we should pick the smallest elements first. Sorting the array enables a greedy strategy where we add elements in increasing order until adding the next would exceed k.

3. Implement the algorithm

Sort the array. Initialize sum = 0 and count = 0. Iterate through the sorted array: if sum + current element < k, add it to sum and increment count; otherwise, break. Return sum.

4. Analyze complexity and edge cases

State that time complexity is O(n log n) due to sorting, and space complexity is O(1) if sorting in-place. Discuss edge cases: empty array, k <= 0, all elements >= k, and negative numbers (if allowed).

5. Test with examples

Walk through a small example, such as array [3,1,4,2] and k=6. Sorted: [1,2,3,4]. Sum=0: add 1 (sum=1), add 2 (sum=3), add 3 (sum=6) but 6 is not less than 6, so stop. Return 3. Verify correctness.

Key Points to Mention

Greedy strategy: selecting smallest elements first maximizes count.
Sorting is necessary to efficiently access smallest elements.
Time complexity: O(n log n) for sorting, O(n) for iteration.
Space complexity: O(1) if in-place sort, O(n) if using extra space.
Edge cases: k <= 0, empty array, all elements >= k, negative numbers.
The sum returned is the maximum possible sum with the maximum count of elements.

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.