InterviewDB Question

Formula Numbers: Evaluate Arithmetic Expressions with Named Variables

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Question Details

Problem

You are given a list of variable definitions of the form "name = expr" where expr is an arithmetic expression involving integer literals, +, -, *, /, parentheses, and previously defined variable names. Evaluate each definition in order and return the final value of a queried variable.

python
def evaluate_formula(definitions: list[str], query: str) -> float:
    """
    definitions: ["x = 3", "y = x + 2", "z = (x * y) - 1"]
    query: "z"
    """
    pass


**Input**:
  definitions = ["a = 4", "b = a * 2", "c = (a + b) / 3"]
  query = "c"

**Output**: 4.0
# a=4, b=8, c=(4+8)/3=4.0

**Input**:
  definitions = ["n = 10", "m = n - 3", "r = m * m"]
  query = "r"

**Output**: 49.0

Follow-ups

  1. How would you build a recursive descent parser for arithmetic expressions with operator precedence?
  2. What data structure holds the evaluated variable context during parsing?
  3. How do you detect and report undefined variable references?
  4. Extend to support built-in functions like sqrt(x) and abs(x) in expressions.

Full Details

Problem

You are given a list of variable definitions of the form "name = expr" where expr is an arithmetic expression involving integer literals, +, -, *, /, parentheses, and previously defined variable names. Evaluate each definition in order and return the final value of a queried variable.

python
def evaluate_formula(definitions: list[str], query: str) -> float:
    """
    definitions: ["x = 3", "y = x + 2", "z = (x * y) - 1"]
    query: "z"
    """
    pass


**Input**:
  definitions = ["a = 4", "b = a * 2", "c = (a + b) / 3"]
  query = "c"

**Output**: 4.0
# a=4, b=8, c=(4+8)/3=4.0

**Input**:
  definitions = ["n = 10", "m = n - 3", "r = m * m"]
  query = "r"

**Output**: 49.0

Follow-ups

  1. How would you build a recursive descent parser for arithmetic expressions with operator precedence?
  2. What data structure holds the evaluated variable context during parsing?
  3. How do you detect and report undefined variable references?
  4. Extend to support built-in functions like sqrt(x) and abs(x) in expressions.
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About This Question

This is a reported interview question from a zoox interview during the onsite round.

It covers the following topics: Recursion, Coding, Onsite .

Topics

Recursion Coding Onsite

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About Zoox Interview Reports

This question was reported by a candidate who interviewed at Zoox. 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 Zoox are the higher-signal extractions to take from this report.

For broader preparation context, the Zoox 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 Zoox reports consistently are the ones worth investing in; one-off niche problems are not.

During Your Zoox 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 Zoox 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.