Token Tree - Parse and Evaluate an Expression Tree from Tokens
Interview Experience
Problem
You are given a list of tokens representing a mathematical expression in prefix notation. Build the expression tree and evaluate it.
Tokens are either operators (+, -, *, /) or integer literals.
python
def evaluate_token_tree(tokens: List[str]) -> float:
...
Example:
**Input**: ["*", "+", "3", "4", "2"]
Expression: (* (+ 3 4) 2) = (3+4)*2 = 14
Output: 14
**Input**: ["+", "*", "2", "3", "/", "8", "4"]
Expression: (+ (* 2 3) (/ 8 4)) = 6 + 2 = 8
Output: 8
Approach
Use a recursive descent parser with a pointer into the token list. Each call to parse() consumes one operator and recursively parses its two operands.
python
def parse(tokens, idx):
token = tokens[idx]
if token not in "+-*/":
**return** float(token), idx + 1
left, idx = parse(tokens, idx + 1)
right, idx = parse(tokens, idx)
**return** apply(token, left, right), idx
Follow-ups
- Extend to handle unary operators (e.g., negation).
- How would you convert an infix expression to prefix notation first?
- Add support for variables (e.g.,
x,y) with a substitution map. - How does this change if tokens are streamed one at a time?
Full Details
Problem
You are given a list of tokens representing a mathematical expression in prefix notation. Build the expression tree and evaluate it.
Tokens are either operators (+, -, *, /) or integer literals.
python
def evaluate_token_tree(tokens: List[str]) -> float:
...
Example:
**Input**: ["*", "+", "3", "4", "2"]
Expression: (* (+ 3 4) 2) = (3+4)*2 = 14
Output: 14
**Input**: ["+", "*", "2", "3", "/", "8", "4"]
Expression: (+ (* 2 3) (/ 8 4)) = 6 + 2 = 8
Output: 8
Approach
Use a recursive descent parser with a pointer into the token list. Each call to parse() consumes one operator and recursively parses its two operands.
python
def parse(tokens, idx):
token = tokens[idx]
if token not in "+-*/":
**return** float(token), idx + 1
left, idx = parse(tokens, idx + 1)
right, idx = parse(tokens, idx)
**return** apply(token, left, right), idx
Follow-ups
- Extend to handle unary operators (e.g., negation).
- How would you convert an infix expression to prefix notation first?
- Add support for variables (e.g.,
x,y) with a substitution map. - How does this change if tokens are streamed one at a time?
About This Question
This is a candidate experience report from a sigma computing interview during the phone round.
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About Sigma Computing Interview Reports
This question was reported by a candidate who interviewed at Sigma Computing. LeakCode aggregates interview reports from 10+ sources, including 1Point3Acres, Glassdoor, LeetCode Discuss, Blind, Reddit, Indeed, and Nowcoder. Each report is translated where necessary, deduplicated against existing entries, and tagged by company, role, round type, and reporting date.
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 Sigma Computing are the higher-signal extractions to take from this report.
For broader preparation context, the Sigma Computing interview process typically includes a recruiter screen, one or two technical phone screens, and a 4-5 round on-site loop covering coding, system design (at L4+ levels), and behavioral. Reports tagged on LeakCode show the round-by-round distribution and typical difficulty calibration. To browse questions filtered by round type and seniority, use the company hub linked above.
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 Sigma Computing reports consistently are the ones worth investing in; one-off niche problems are not.
During Your Sigma Computing 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 Sigma Computing 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.