Implement expression expansion to plus-only form

Q: Implement expression expansion to plus-only form

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Question

Given a string expression consisting only of lowercase letters (variables), '+', '', '(', and ')', return an equivalent expression that uses only '+' by fully distributing multiplication over addition. Concatenation denotes multiplication and there are no spaces. Maintain variable order within each product according to their left-to-right appearance, and output terms in the natural left-to-right expansion order. Part 1 (no '+' outside parentheses): Expand expressions where '+' appears only inside parentheses. Examples: (a+b)(c+d) -> ac+ad+bc+bd; a*(b+c)*(d+e+f)*g -> abdg+abeg+abfg+acdg+aceg+acfg. Implement an O(n) time solution using O(

extra space beyond the output (no stack), and explain why it works. Part 2 (general case): Expand expressions that may also contain '+' outside parentheses. Example: a+b c (d+e+f)+k+m*(g+h)+i -> a+bcd+bce+bcf+k+mg+mh+i. Implement working code that handles nested parentheses using an appropriate data structure (e.g., a stack) to track the current multiplication result segments, targeting O(n) time and O(n) extra space beyond the output. Analyze time and space complexities and discuss key edge cases.

Implement expression expansion to plus-only form

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