Question

Suppose we are given a binary tree t whose nodes are labeled with numbers. describe an algorithm to find the largest binary-search-ordered rooted minor 3 of t.

A) Initialize max_minor to the root value, perform BFS traversal, and update max_minor whenever a BST is encountered.

B) Perform DFS traversal, update max_minor if a BST of size at least 3 is found, and return the final max_minor.

C) Use a breadth-first search (BFS) algorithm to find the largest minor 3 rooted at any node in the binary tree.

D) Perform DFS traversal, update max_minor if a BST of size exactly 3 is found, and return the final max_minor.

Answer 1

To find the largest binary-search-ordered rooted minor 3 in a binary tree, a depth-first search (DFS) traversal should be used to check each node for BST properties of size at least 3.

Step-by-step explanation:

To find the largest binary-search-ordered rooted minor 3 of a given binary tree t, you need a reliable algorithm. The goal is to identify the biggest subtree that is also a valid binary search tree (BST) with at least 3 nodes. Under the provided options, the correct approach is:

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Answer option B effectively encapsulates this process. It is crucial because a breadth-first search (BFS) would not efficiently identify a binary search tree within the larger tree, as the hierarchy and ordering of nodes are critical for a subtree to be a BST.

The DFS algorithm is preferred because it allows us to check the properties of a BST (left < root < right) as we traverse the tree. This method can find the largest BST within a binary tree, not just any BST that happens to be of size 3.