Instacart·Software Engineer·Technical Phone Screen·Intermediate

IntermediatePrefer not to say

May 2026Remote

Summary

Technical phone screen for a software engineer role at Instacart. One meaty parsing question that took up most of the time, and the discussion around it went pretty deep into tokenization and complexity analysis.

Questions Asked (1)

Given a symbolic arithmetic expression as a string (with integer constants, up to two named variables, binary + and - operators, optional whitespace, and optional nested parentheses), evaluate it and return the result as a canonical reduced form like `ax + by + c`. Walk through your tokenization approach, parsing strategy, and time complexity.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

This one took me a second to even understand what 'canonical form' meant in context.

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AI HintsAI Generated

Suggested Approach

Start by clarifying the problem constraints (e.g., variable names, operator precedence, parentheses) and then outline a two-phase approach: tokenization and parsing. For parsing, use a recursive descent parser or shunting-yard algorithm to handle operator precedence and parentheses, building an expression tree. Finally, evaluate the tree by representing each subexpression as a linear combination of variables and a constant, then simplify to canonical form.

Pro tip: Mention that you can represent each subexpression as a tuple (coefficient of x, coefficient of y, constant) and perform addition/subtraction component-wise, which simplifies evaluation and avoids symbolic manipulation overhead. Also, discuss how to handle unary minus and implicit multiplication (e.g., '2x' meaning 2*x) if applicable, and clarify assumptions with the interviewer.

1. Clarify requirements and constraints

Ask about variable names, allowed operators, whitespace handling, and whether implicit multiplication (like '2x') is allowed. Confirm the expected output format and edge cases (e.g., empty string, single constant).

2. Design tokenization

Scan the input string to produce tokens: numbers, variables, operators (+, -), and parentheses. Skip whitespace. Handle multi-digit numbers and possibly unary minus by context.

3. Choose parsing strategy

Use recursive descent or shunting-yard to parse tokens into an abstract syntax tree (AST) respecting operator precedence and parentheses. Explain how you handle left-associativity of + and -.

4. Evaluate AST to canonical form

Traverse the AST, representing each node as a linear combination (coeff_x, coeff_y, constant). Combine children according to the operator. At the root, output the canonical form like 'a*x + b*y + c'.

5. Analyze complexity and edge cases

State time complexity O(n) for tokenization and parsing, and O(n) for evaluation, where n is the length of the string. Discuss space complexity O(n) for the AST or stack. Mention edge cases like nested parentheses, negative coefficients, and zero coefficients.

Key Points to Mention

Tokenization approach: scanning left-to-right, handling whitespace, numbers, variables, and operators.
Parsing strategy: recursive descent or shunting-yard, with operator precedence and parentheses handling.
Representation of subexpressions as linear combinations (coefficients for variables and constant) to simplify evaluation.
Handling of unary minus and implicit multiplication (if applicable) by context or preprocessing.
Time and space complexity: O(n) time for tokenization, parsing, and evaluation; O(n) space for AST or stack.
Edge cases: empty input, single constant, nested parentheses, multiple variables, and zero coefficients in output.

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