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

IntermediatePrefer not to say

May 2026

Summary

Got a Google SWE round that was basically a math/bit-manipulation problem dressed up as a counting question. Not the usual leetcode grind, more like competitive programming with a proof component. Walked out unsure if I'd even set up the approach correctly.

Questions Asked (1)

Given an array of N integers, define F(i, j) as the XOR of all elements from index i to j. Count the number of triples (x, y, z) with x ≤ y ≤ z such that F(x, y) XOR F(y, z) is strictly greater than F(x, z).

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

The problem looks deceptively like a prefix XOR warmup until you realize you're counting triples satisfying a strict inequality.

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AI HintsAI Generated

Suggested Approach

First, simplify the condition by expressing F(x,y) XOR F(y,z) in terms of prefix XORs, then analyze the inequality to derive necessary conditions on the prefix XOR values. Finally, count valid triples efficiently using a hash map or frequency array, considering the constraints on indices.

Pro tip: Always test your derived conditions with small examples to ensure no off-by-one errors, especially when dealing with inclusive indices and prefix XORs. Mentioning that you would verify with brute force for small N shows thoroughness.

1. Define Prefix XOR

Let P[k] = XOR of first k elements (P[0]=0). Then F(i,j) = P[j] XOR P[i-1]. Rewrite the condition using P.

2. Simplify the Inequality

Substitute F(x,y) = P[y] XOR P[x-1], F(y,z) = P[z] XOR P[y], F(x,z) = P[z] XOR P[x-1]. Simplify the XOR expression and the inequality to find conditions on P[x-1], P[y], P[z].

3. Analyze Conditions

Determine when the inequality holds. For example, show that it reduces to P[x-1] XOR P[z] > 0, i.e., P[x-1] != P[z], and possibly other constraints involving P[y]. Derive the exact condition.

4. Count Valid Triples

For each y, count pairs (x,z) with x<=y<=z such that the condition holds. Use prefix frequencies of P values to count efficiently in O(N) or O(N log N).

5. Handle Edge Cases and Complexity

Consider N=1, all elements equal, etc. Discuss time and space complexity, and potential optimizations.

Key Points to Mention

Prefix XOR array and its properties
XOR simplification: a XOR b XOR a = b, and inequality reduction
Derivation that condition simplifies to P[x-1] != P[z] (or similar)
Efficient counting using hash maps or frequency arrays
Time complexity O(N) or O(N log N) and space complexity O(N)
Verification with brute force for small N and edge cases

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