First, clarify the exact validation rules and priority order, then design a multi-pass algorithm that checks each error condition in the specified sequence. After validation, build the tree using a hash map for parent-child relationships, and serialize it recursively with children sorted alphabetically. Discuss time/space complexity and potential trade-offs.
Pro tip: Emphasize that the priority order is critical: you must short-circuit on the first error encountered, and explicitly state that you'll validate the input format before any structural checks. This shows attention to detail and prevents wasted computation.
Ask questions to confirm the exact format of input pairs, what constitutes an 'input format error', and the precise definition of each error condition. Also confirm the expected output format for the S-expression.
Plan separate checks for each error type, executed in the given order: input format, duplicate edge, too many children, multiple roots, cycle. Use appropriate data structures (e.g., sets for duplicates, maps for child counts) and short-circuit on first error.
If all validations pass, build the tree using adjacency lists. Detect cycles via DFS or by ensuring the number of edges equals nodes-1 and all nodes are reachable from the root.
Recursively serialize the tree, sorting children alphabetically at each node to ensure the lexicographically smallest string. Format as (root child1 child2 ...).
State the time and space complexity of your solution (likely O(n log n) due to sorting). Discuss alternative approaches, such as combining validation passes or using union-find for cycle detection, and their trade-offs.
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