When we perform the operation search(14) on the binary search tree shown below, what are the keys in the nodes examined during the search (in order they are examined)?

Question

BlackTom AI · Accepted Answer

A binary search tree (BST) property: at each node compare the search key k with the node’s key v; if k = v you stop, if k < v go to the left child, if k > v go to the right child. Use that rule starting from the root. 1) Relevant concepts - BST invariant (left subtree keys < node key < right subtree keys). - Search begins at the root and follows comparisons to left or right child until key is found or a null child is reached. 2) Step-by-step reasoning and comparisons - Start at the root with key 17. - Compare 14 to 17: 14 < 17, so go to the left child. - Nodes examined so far: 17. - At the left child with key 6: - Compare 14 to 6: 14 > 6, so go to the right child. - Nodes examined so far: 17, 6. - At that right child with key 11: - Compare 14 to 11: 14 > 11, so go to the right child. - Nodes examined so far: 17, 6, 11. - At the right child of 11 with key 14: - Compare 14 to 14: equal, found the node. - Nodes examined (final): 17, 6, 11, 14. 3) Intermediate “calculations” (comparisons shown) - 14 < 17 → left - 14 > 6 → right - 14 > 11 → right - 14 = 14 → found 4) Why the correct answer is correct These comparisons follow the BST search rule; each decision uniquely determines the next node, yielding the exact examined sequence 17 → 6 → 11 → 14. 5) Why other options are incorrect - “The only node examined is 14”: wrong because search always starts at the root and requires comparisons down the tree. - “First key 4, then 6, then 9, then 11, then 14”: visiting 4 first would require going left from 17, but 14 < 17 so left is correct, yet 4 < 6 and 14 > 6 so we go right from 6, not left to 4; also 9 is the left child of 11, but 14 > 11 so we go right to 14, not to 9. - “First key 9, then 14”: 9 is reached from 11’s left child; however 14 > 11 so the search goes to 11’s right child (14), not to 9. 6) Conclusion The nodes examined in order are 17, then 6, then 11, then 14 — which matches the provided correct answer.

When we perform the operation search(14) on the binary search tree shown below, what are the keys in the nodes examined during the search (in order they are examined)?单项选择题

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