Expand algebraic expression with distribution
Problem Description
Given an algebraic expression composed of lowercase letters (representing variables), the addition operator +, the multiplication operators _ (underscore) and * (asterisk), and parentheses (), your task is to fully expand all products and return an equivalent expression containing only the + operator.
Initial Problem
Assume that the + operator will not appear outside any parentheses in the input expression.
Example:
(a+b)_(c+d) should expand to ac+ad+bc+bd.
Constraint: Achieve O(1) extra-space complexity.
Follow-up
Consider the case where the + operator may appear outside parentheses.
Example:
a+b_c_(d+e+f)+k+m*(g+h)+i should expand to a+bcd+bce+bcf+k+mg+mh+i.
Constraint: Provide working code that may use O(n) extra space (e.g., a stack), where n is the length of the input expression.
AI interview prep
Core dilemma
The central engineering conflict is designing an efficient expression parser and expander that correctly handles operator precedence and distribution, while navigating extremely tight memory constraints (O(1) auxiliary space) for the initial problem, which often conflicts with the recursive nature of expression parsing.
2 tradeoffs and 3 stress tests locked
Interview prep
Unlock the interviewer X-Ray rubric, tradeoff matrix, stress tests, clarifying questions, and key concepts.
Expand algebraic expression with distribution
Problem Description
Given an algebraic expression composed of lowercase letters (representing variables), the addition operator +, the multiplication operators _ (underscore) and * (asterisk), and parentheses (), your task is to fully expand all products and return an equivalent expression containing only the + operator.
Initial Problem
Assume that the + operator will not appear outside any parentheses in the input expression.
Example:
(a+b)_(c+d) should expand to ac+ad+bc+bd.
Constraint: Achieve O(1) extra-space complexity.
Follow-up
Consider the case where the + operator may appear outside parentheses.
Example:
a+b_c_(d+e+f)+k+m*(g+h)+i should expand to a+bcd+bce+bcf+k+mg+mh+i.
Constraint: Provide working code that may use O(n) extra space (e.g., a stack), where n is the length of the input expression.