Basic Calculator IV

Basic Calculator IV

What is this problem about?

The "Basic Calculator IV interview question" is a significantly more complex variation that moves from arithmetic to algebra. In this problem, the expression contains not just numbers and operators, but also variables (like a or b). You are also given "mapped" values for some variables. Your goal is to evaluate the expression and return the result as a list of strings, representing the polynomial in a specific canonical order (sorted by degree and then lexicographically).

Why is this asked in interviews?

Companies like Roblox and Google ask the "Basic Calculator IV coding problem" to see how candidates handle symbolic computation and custom data structures. It’s no longer about simple integers; it’s about managing "terms" (coefficient and variable combinations). It tests your ability to implement polynomial addition, subtraction, and multiplication from scratch.

Algorithmic pattern used

This problem requires a Custom Polynomial Class and the Recursive Descent Parsing pattern.

1. Polynomial Representation: Store each polynomial as a hash map where the key is a sorted list of variables (the "monomial") and the value is the coefficient.
2. Operations:
   • Addition/Subtraction: Merge the two hash maps by adding/subtracting coefficients for identical variable lists.
   • Multiplication: For every term in Polynomial A and every term in Polynomial B, multiply the coefficients and concatenate the variable lists (then sort the variables).
3. Parsing: Use a stack-based or recursive parser to handle parentheses and operator precedence, returning a Polynomial object at each step instead of a simple number.

Example explanation

Expression: (e + 8) * (e - 8), mapped values: {}

1. Polynomial 1: 1*e + 8
2. Polynomial 2: 1*e - 8
3. Multiply:
   • $(1e imes 1e) = 1e^2$
   • $(1e imes -8) = -8e$
   • $(8 imes 1e) = 8e$
   • $(8 imes -8) = -64$
4. Simplify: $1e^2 - 64$ Final Output: ["e*e", "-64"]

Common mistakes candidates make

• Sorting Monomials: Forgetting that a*b and b*a are the same term and must be stored in a consistent sorted order.
• Term Ordering: Failing to sort the final output by degree (highest degree first) and then by variable name.
• Complexity: This is a very long problem to code. Candidates often run out of time or get lost in the nested loops required for polynomial multiplication.

Interview preparation tip

Don't panic! Break the problem into small, testable units: a function to multiply two polynomials, a function to add them, and a parser. If you can clearly define these interfaces, even if you don't finish every line of code, you show strong "Design interview pattern" skills.