Google·Software Engineer·Onsite - Coding / Algorithms·Intermediate

IntermediatePrefer not to say

May 2026

Summary

Google SWE coding round, one problem the whole session. The question was a heap-based subset sum thing that I'd never seen before and the brute force approach definitely wasn't going to cut it.

Questions Asked (1)

Given an array of distinct non-negative integers and an integer k, find the k-th largest subset sum across all 2^n possible subsets (including the empty subset with sum 0).

Algorithms & Data Structures

Author's notes

I started with brute force because my brain went to 'enumerate all subsets' immediately, which is obviously 2^n and they were not impressed.

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AI HintsAI Generated

Suggested Approach

Start by clarifying the problem: subsets are defined by indices, and we need the k-th largest sum among all 2^n subset sums. Then discuss approaches: brute force is infeasible for large n, so consider meet-in-the-middle to generate all sums for n up to ~40, or a heap-based best-first search that generates subset sums in descending order without enumerating all. Finally, analyze time and space complexity and edge cases.

Pro tip: Mention that the problem is NP-hard in general (related to subset sum), so for large n you must rely on constraints; Google interviewers value recognizing intractability and proposing practical solutions like meet-in-the-middle or approximation. Also, clarify whether k is 1-indexed and whether subsets are considered distinct by indices.

1. Clarify the problem

Confirm that subsets are defined by indices (so duplicate sums from different subsets count separately), that k is 1-indexed, and that the empty subset is included. Ask about constraints on n and k to determine feasible approaches.

2. Discuss brute force and its limitations

Acknowledge that enumerating all 2^n subset sums and sorting is O(2^n log 2^n), which is only feasible for n ≤ ~20. This sets the stage for more efficient methods.

3. Propose meet-in-the-middle for moderate n

Split the array into two halves, generate all subset sums for each half (2^(n/2) each), sort one half, and use binary search to count how many pairs sum to at least a target. Then binary search on the answer to find the k-th largest sum. This works for n up to ~40.

4. Propose heap-based best-first search for small k

If k is small, use a max-heap to generate subset sums in descending order. Start with the full set sum, and repeatedly replace included elements with excluded ones to generate next largest sums, avoiding duplicates. This is O(k log k) but may miss some sums if not careful.

5. Analyze complexity and edge cases

Compare time and space complexities of the approaches. Discuss edge cases: k=1 (largest sum), k=2^n (smallest sum, often 0), empty array, and large k relative to 2^n.

Key Points to Mention

Meet-in-the-middle technique to reduce exponential time to O(2^(n/2) log 2^(n/2)).
Binary search on the answer combined with counting pairs that sum to at least a target.
Heap-based best-first search for generating k largest subset sums without full enumeration.
Time and space complexity trade-offs: O(2^n) vs O(2^(n/2)) vs O(k log k).
Edge cases: k=1, k=2^n, empty subset, and constraints on n and k.
The problem is NP-hard in general, so constraints dictate the approach.

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