This is the generalized version of a two-subsequence problem and it's a lot nastier.
Model the problem as finding a shortest common supersequence (SCS) of the given subsequences, but note that for subsequences (not substrings), the order constraints are partial. Use a graph-based approach: create a DAG where edges represent required order between characters, then topologically sort to get a valid parent sequence. If cycles exist, no common parent exists.
Pro tip: Clarify with the interviewer whether the parent sequence must be minimal or any valid sequence is acceptable. Often, a simple concatenation with deduplication works if you respect order constraints, but discussing minimality shows depth.
Ask about input size, character set, whether the parent must be minimal, and if multiple valid parents are acceptable. This guides algorithm choice.
Create a directed graph where each character occurrence is a node, and edges represent required order from each subsequence. For repeated characters, use indices to distinguish occurrences.
If the graph has a cycle, no common parent exists. Otherwise, a topological sort gives a valid parent sequence. Use Kahn's algorithm or DFS.
If minimal parent is needed, this becomes NP-hard in general (shortest common supersequence for multiple strings). Discuss approximation or special cases (e.g., two sequences via DP).
Output the topological order as the parent sequence. Verify by checking each input subsequence is indeed a subsequence of the parent.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.