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Suppose a binary tree is constructed with n nodes, such that each node has exactly either zero or two children. The maximum height of the tree will be

Question

Suppose a binary tree is constructed with n nodes, such that each node has exactly either zero or two children. The maximum height of the tree will be

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Solution

The maximum height of a binary tree with n nodes, where each node has either zero or two children, will be n. This is because in the worst-case scenario, each node (except for the root) is the left or right child of the node above it, creating a "chain" of nodes. This results in a tree with a maximum height of n.

Here's a step-by-step explanation:

  1. A binary tree is a tree data structure in which each node has at most two children, referred to as the left child and the right child.

  2. In this case, each node in the binary tree has either zero or two children. This means that each node is either a leaf node (with no children) or an internal node with two children.

  3. The height of a binary tree is the maximum number of edges from the root node to the furthest leaf node.

  4. In the worst-case scenario, each internal node has only one child node that is not a leaf node. This creates a "chain" of nodes from the root to a leaf

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