My first instinct was to just look for the node that nobody points to as a child, which is the right idea, but I fumbled explaining it cleanly.
Clarify that the root is the only node that is never a child of another node. Use a hash set to track all child nodes, then find the node that is not in the set. Alternatively, compute the difference between the sum of all node values and the sum of all child values to find the root's value.
Pro tip: Mention that this approach works in O(n) time and O(n) space, and discuss trade-offs with other methods like using in-degree counts or XOR if node values are unique. Also, handle edge cases like a single node or empty list.
Restate that the root is the only node not appearing as a child. Confirm assumptions about node structure and uniqueness of values.
Select a method: hash set of children, sum difference, or XOR. Explain why it's efficient and correct.
Describe step-by-step: iterate through nodes, collect child references, then find the node not in the set. Use a simple example to illustrate.
State time and space complexity: O(n) time and O(n) space for hash set; O(1) space for sum difference if values are numeric.
Discuss empty list, single node, and potential duplicate values. Mention that if values are not unique, sum/XOR methods fail, so hash set is safer.
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