I knew immediately it was a stack problem but fumbled the part where you unwind nested parentheses with multipliers.
Use a stack to handle nested parentheses, where each stack frame represents a scope with a multiplier and a map of element counts. Parse the string in a single pass, pushing new scopes on '(' and merging counts into the parent scope on ')', applying the multiplier. Finally, sort the elements lexicographically and concatenate counts.
Pro tip: Clarify edge cases upfront, such as single-element formulas, empty strings, or multipliers of 1, and mention that the stack approach naturally handles arbitrary nesting depth. Also, note that using a hash map for counts ensures O(1) updates, but sorting at the end adds O(k log k) where k is the number of distinct elements, which is acceptable since k is small.
Restate the problem: parse a chemical formula with nested parentheses and multipliers, return element counts in lexicographic order. Confirm that the solution must run in O(n) time and discuss potential edge cases.
Explain that you'll use a stack of maps, where each map stores element counts for the current scope. When encountering '(', push a new map; when encountering ')', pop the map, apply the multiplier, and merge into the parent map.
Detail how to parse element symbols (uppercase followed by lowercase letters) and numbers (multi-digit integers). Describe how to handle multipliers after ')' and how to accumulate counts.
Argue that each character is processed once, so time is O(n). Space is O(n) for the stack and maps, but in practice bounded by nesting depth and distinct elements.
After parsing, sort the elements lexicographically and concatenate each element with its count (omit count if 1). Walk through the example 'K4(ON(SO3)2)3' to verify the output 'K4N3O14S6'.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.