Google·Machine Learning Engineer·Technical Phone Screen·Senior

Senior

Apr 2026

Summary

Google ML Engineer interview with a tricky string problem that looks deceptively simple. The necklace question was the kind of thing where you either see the insight or you spin your wheels forever.

Questions Asked (1)

Given a circular string of D's and R's where the count of D's equals the count of R's, find a way to cut and split it between two people so both halves have an equal number of D's and R's.

Algorithms & Data Structures

Author's notes

The key thing I kept missing early on was that you don't need more than two cuts.

Create a free account to read the full note

AI HintsAI Generated

Suggested Approach

Model the circular string as a sequence of +1 (for D) and -1 (for R) values, then find a cut point where the prefix sum equals half the total sum. Since the total sum is zero, this reduces to finding an index where the prefix sum is zero, which can be done in O(n) time by scanning the string once.

Pro tip: Clarify that the cut must be a single contiguous split into two arcs, and mention that if multiple valid cuts exist, any one is acceptable. This shows you understand the problem constraints and avoids overcomplicating the solution.

1. Understand the problem

Restate the problem: given a circular string with equal numbers of D and R, find a cut that splits it into two contiguous substrings each having equal numbers of D and R. Confirm that the cut can be at any position between characters.

2. Transform to prefix sums

Assign +1 to D and -1 to R. Compute the total sum, which is 0. The goal is to find an index i such that the sum of the first i characters (in the linearized string) is 0, because then the remaining part also sums to 0.

3. Find a zero-sum cut

Scan the string from left to right, maintaining a running sum. Whenever the running sum becomes 0, that index is a valid cut point. If no such point exists before the end, the entire string is the only cut (but since total sum is 0, the end is always a valid cut, though trivial).

4. Handle circularity

Since the string is circular, any cut point found in the linear scan corresponds to a valid cut in the circle. If the scan reaches the end without finding a non-trivial cut, consider that the cut at the end is the same as the start, which is trivial; however, because the total sum is 0, there must be at least one index where the running sum is 0 (other than the start) if the string is not already balanced in a trivial way.

5. Verify and return

Once a cut index is found, verify that both resulting substrings have equal numbers of D and R by checking their sums are 0. Return the cut position or the two substrings.

Key Points to Mention

Prefix sum technique for balanced parentheses or equal counts.
Time complexity O(n) and space complexity O(1) for the scan.
The problem is equivalent to finding a zero-sum contiguous subarray in a circular array.
Edge cases: all D's and R's alternating, or already balanced halves.
Proof that a valid cut always exists when total counts are equal.
Connection to the 'maximum subarray' or 'equilibrium index' problem.

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