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國立臺灣大學 2025 · 考試 · 第 10 題

(5 points) Select all the correct statement(s) from the following statements regarding binary trees and binary search trees.

(A)
Every binary tree is a binary search tree.
(B)
Every binary search tree on $n$ nodes has height $O(\log n)$ .
(C)
In a binary search tree, we can find the next smallest element to a given element in $O(1)$ time.
(D)
Let $A_1, A_2$ , and $A_3$ be three sorted arrays of $n$ distinct real numbers. Constructing a balanced binary search tree of the set $A_1 \cup A_2 \cup A_3$ requires $O(n)$ time.
(E)
Let $T$ be a complete binary tree with $n$ nodes. Finding a path from the root of $T$ to a given vertex $v \in T$ using breadth-first search takes $\Omega(n \lg n)$ time.

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