Implement expression expansion to plus-only form
Expression Expansion to Plus-Only Form
Given a string expression composed solely of lowercase letters (representing variables), +, _, (, and ), your task is to return an equivalent expression that exclusively uses + by fully distributing multiplication over addition.
Key Rules:
- Concatenation of variables or parenthesized expressions denotes multiplication.
- There are no spaces in the input expression.
- Maintain the original left-to-right order of variables within each product term.
- Output terms in the natural left-to-right expansion order.
Part 1: Expressions with Plus Only Inside Parentheses
In this part, the + operator will only appear within parentheses.
Examples:
(a+b)_(c+d)->ac+ad+bc+bda_(b+c)_(d+e+f)_g->abdg+abeg+abfg+acdg+aceg+acfg
Constraints:
- Implement an
O(n)time solution. - Use
O(1)extra space beyond the output (i.e., no stack or similar data structure for parsing). - Provide an explanation for why your solution meets the space complexity requirement.
Part 2: General Case with Plus Outside Parentheses
This part extends to expressions where + may also appear outside parentheses, allowing for more complex structures and nested parentheses.
Example:
a+b_c_(d+e+f)+k+m_(g+h)+i->a+bcd+bce+bcf+k+mg+mh+i
Constraints:
- Implement working code that handles nested parentheses.
- Utilize an appropriate data structure (e.g., a stack) to track current multiplication result segments.
- Target
O(n)time complexity. - Target
O(n)extra space complexity beyond the output. - Analyze the time and space complexities of your solution.
- Discuss key edge cases.
AI interview prep
Core dilemma
Managing the state of intermediate products and sums during expression parsing, especially given operator precedence and the distributive property, while adhering to strict space constraints (O(1) for Part 1, O(N) for Part 2) where the output size can grow exponentially relative to the input, creating a tension between memory usage for intermediate results and the stated complexity requirements.
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Interview prep
Unlock the interviewer X-Ray rubric, tradeoff matrix, stress tests, clarifying questions, and key concepts.
Implement expression expansion to plus-only form
Expression Expansion to Plus-Only Form
Given a string expression composed solely of lowercase letters (representing variables), +, _, (, and ), your task is to return an equivalent expression that exclusively uses + by fully distributing multiplication over addition.
Key Rules:
- Concatenation of variables or parenthesized expressions denotes multiplication.
- There are no spaces in the input expression.
- Maintain the original left-to-right order of variables within each product term.
- Output terms in the natural left-to-right expansion order.
Part 1: Expressions with Plus Only Inside Parentheses
In this part, the + operator will only appear within parentheses.
Examples:
(a+b)_(c+d)->ac+ad+bc+bda_(b+c)_(d+e+f)_g->abdg+abeg+abfg+acdg+aceg+acfg
Constraints:
- Implement an
O(n)time solution. - Use
O(1)extra space beyond the output (i.e., no stack or similar data structure for parsing). - Provide an explanation for why your solution meets the space complexity requirement.
Part 2: General Case with Plus Outside Parentheses
This part extends to expressions where + may also appear outside parentheses, allowing for more complex structures and nested parentheses.
Example:
a+b_c_(d+e+f)+k+m_(g+h)+i->a+bcd+bce+bcf+k+mg+mh+i
Constraints:
- Implement working code that handles nested parentheses.
- Utilize an appropriate data structure (e.g., a stack) to track current multiplication result segments.
- Target
O(n)time complexity. - Target
O(n)extra space complexity beyond the output. - Analyze the time and space complexities of your solution.
- Discuss key edge cases.