Reduce List - Repeatedly Remove Elements by Rule Until One Remains
Interview Experience
Problem
Given a list of integers and a reduction rule, repeatedly apply the rule until only one element remains.
Return that element.
Rule: In each pass, scan left to right. Remove any element that is smaller than its right neighbor. If no element is removed in a pass, stop.
Return the last remaining element.
python
def reduce_list(nums: List[int]) -> int:
...
Example:
**Input**: [3, 1, 4, 1, 5, 9, 2, 6]
Pass 1: remove 3 (3<4)? No, 3>1. Remove 1 (1<4) -> [3,4,1,5,9,2,6]
remove 1 (1<5) -> [3,4,5,9,2,6]
remove 2 (2<6) -> [3,4,5,9,6]
Pass 2: no element < right neighbor that qualifies -> stops at [3,4,5,9,6]
**Note**: clarify exact rule with interviewer.
Simpler variant: nums=[5,3,1], remove smallest each pass
[5,3,1] -> remove 1 -> [5,3] -> remove 3 -> [5] ->
**output** 5
Follow-ups
- Prove the invariant: what property does the remaining list always satisfy after each pass?
- What is the worst-case number of passes for a list of length n?
- How does the answer change if you remove elements larger than their right neighbor instead?
- How would you parallelize the reduction using a segment tree?
Full Details
Problem
Given a list of integers and a reduction rule, repeatedly apply the rule until only one element remains.
Return that element.
Rule: In each pass, scan left to right. Remove any element that is smaller than its right neighbor. If no element is removed in a pass, stop.
Return the last remaining element.
python
def reduce_list(nums: List[int]) -> int:
...
Example:
**Input**: [3, 1, 4, 1, 5, 9, 2, 6]
Pass 1: remove 3 (3<4)? No, 3>1. Remove 1 (1<4) -> [3,4,1,5,9,2,6]
remove 1 (1<5) -> [3,4,5,9,2,6]
remove 2 (2<6) -> [3,4,5,9,6]
Pass 2: no element < right neighbor that qualifies -> stops at [3,4,5,9,6]
**Note**: clarify exact rule with interviewer.
Simpler variant: nums=[5,3,1], remove smallest each pass
[5,3,1] -> remove 1 -> [5,3] -> remove 3 -> [5] ->
**output** 5
Follow-ups
- Prove the invariant: what property does the remaining list always satisfy after each pass?
- What is the worst-case number of passes for a list of length n?
- How does the answer change if you remove elements larger than their right neighbor instead?
- How would you parallelize the reduction using a segment tree?
About This Question
This is a candidate experience report from a grammarly interview during the phone round.
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Use this question as one calibration data point, not a memorization target. Companies typically rotate their question pools every 2-4 months; the exact wording of a 2024 question may differ from what you encounter today. The underlying pattern, difficulty level, and follow-up depth at Grammarly are the higher-signal extractions to take from this report.
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How To Practice This Type of Question
Solve similar problems on LeetCode under timed conditions (25-35 minutes per medium difficulty). The goal is pattern recognition: recognize the underlying technique (sliding window, two-pointer, BFS, memoized recursion, etc.) within 60-90 seconds of reading. Strong candidates verbalize their hypothesis out loud before coding, then iterate based on feedback. Weak candidates dive into implementation immediately, lose time on the wrong approach, and run out of time for follow-ups.
Companies update their question pools every 2-4 months. The exact wording of any given question may have been retired by the time you interview. Focus your prep on the pattern, not the specific problem. The patterns that appear in Grammarly reports consistently are the ones worth investing in; one-off niche problems are not.
During Your Grammarly Round
Apply the standard interview round template: clarify requirements (2-3 minutes), state your approach out loud and confirm direction with the interviewer (3-5 minutes), code with narration (15-25 minutes), test with concrete examples including edge cases (5 minutes), discuss optimization or trade-offs if time permits (5 minutes). This template is universally accepted across FAANG and adjacent companies; deviating from it produces weaker interviewer feedback signal.
The single most predictive failure mode in Grammarly reports tagged "no hire": not asking clarifying questions. Interviewers are explicitly trained to weight this. Strong candidates ask 3-5 clarifying questions even on problems that look obvious; weak candidates dive into code immediately. The clarifying-question check is often the first signal recorded in the interviewer's written notes.