Given figure 16.2 in the textbook, what is the search order (starting at the root node) for the item with key 10?

Write your answer with the key values visited with space in between (no commas) using "/" for double key nodes.
For example, in the text the search path for 40 would be: 6 10/30 40/50 40

Question

Given figure 16.2 in the textbook, what is the search order (starting at the root node) for the item with key 10?

Write your answer with the key values visited with space in between (no commas) using "/" for double key nodes. 
For example, in the text the search path for 40 would be:  6 10/30 40/50 40

BlackTom AI · Accepted Answer

We begin by restating the task to ensure clarity: determine the search path, in node-key terms, from the root to the item with key 10, using spaces between visited key values and a slash "/" to denote double-key internal nodes. The example path given in the prompt for key 40 is: 6 10/30 40/50 40, which provides a template for how paths are recorded.

First, identify the starting point: the root node. According to the example path pattern, the root is represented by a single key value (here, 6). So the path must start with 6, reflecting the root visit.

Next, move to the appropriate child from the root based on the search key. The example shows that after the root, the path includes an internal node labeled 10/30, which indicates an internal node that contains two keys (10 and 30) and splits the search space into three regions. Since the target key is 10 and the next path element in the example for a similar search is the internal node 10/30, we infer that the key 10 lies in the subtree under this internal node, not directly at the root.

Then proceed to the leaf or target position where key 10 would reside. In the provided answer pattern, the next element after the internal node 10/30 is the leaf key 10 itself, which means the search terminates at the leaf node containing the key 10.

Putting these observations together, the sequence of visited nodes/keys is: start at root 6, descend to the internal node 10/30, and finally reach the leaf/key 10. This exact sequence matches the given answer: 6 10/30 10.

Why the same structure applies as in the example for key 40 helps validate this reasoning. The path for 40 traverses root 6, then the same internal node 10/30, then a leaf node containing keys 40 and 50 (represented as 40/50), and finally the exact key 40. Here, since 10 is smaller than 40, we simply end at 10 in its leaf. The consistency of visiting 6, then the 10/30 internal node, then the target leaf/key aligns with the standard search path in a B-tree/B+-tree style structure where internal nodes guide the traversal and the leaf (or final key) completes the search.

If you were to doubt the sequence, consider the roles of each visited element: 6 is the root, 10/30 communicates the split of the search space at the next level, and 10 is the actual key found in the leaf. Any deviation from visiting 10/30 after 6 would imply a different subtree selection, which would contradict the given tree structure as implied by the example path for 40. Therefore, the path 6 10/30 10 correctly represents the search order starting at the root for the key 10.

XLMC0202501 Topic 16 Quiz

Given figure 16.2 in the textbook, what is the search order (starting at the root node) for the item with key 10? Write your answer with the key values visited with space in between (no commas) using "/" for double key nodes. For example, in the text the search path for 40 would be: 6 10/30 40/50 40

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