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The height of a binary tree is the maximum number of edges in any root to leaf path. The maximum number of nodes in a binary tree of height h is:a.2^(h+1) -1b.2^h -1c.2^(h-1) – 1d.2*(h+1)

Question

The height of a binary tree is the maximum number of edges in any root to leaf path. The maximum number of nodes in a binary tree of height h is:a.2^(h+1) -1b.2^h -1c.2^(h-1) – 1d.2*(h+1)

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Solution

The maximum number of nodes in a binary tree of height h is 2^(h+1) -1.

Here's why:

  1. A binary tree of height 0 has 1 node (the root).
  2. A binary tree of height 1 can have up to 3 nodes (the root, and two children).
  3. A binary tree of height 2 can have up to 7 nodes (the root, two children of the root, and four grandchildren).

In general, each level of the tree can have twice as many nodes as the level above it. So, the total number of nodes is the sum of a geometric series:

1 + 2 + 4 + 8 + ... + 2^h

This sum can be calculated using the formula for the sum of a geometric series, which gives us 2^(h+1) - 1.

So, the correct answer is a. 2^(h+1) -1.

This problem has been solved

Similar Questions

Consider a binary tree with n nodes, where each node can have at most two children. The height of the tree is defined as the maximum number of edges between the root node and any leaf node. Which of the following statements is true regarding the height h of this binary tree?*The height of the tree is always equal to n-1The height of the tree is always equal to log₂(n)The height of the tree can be greater than or equal to n-1

The height of a binary tree is the number of edges between the tree's root and its furthest leaf. For example, the following binary tree is of height :Function DescriptionComplete the getHeight or height function in the editor. It must return the height of a binary tree as an integer.getHeight or height has the following parameter(s):root: a reference to the root of a binary tree.Note -The Height of binary tree with single node is taken as zero.Input FormatThe first line contains an integer , the number of nodes in the tree.Next line contains space separated integer where th integer denotes node[i].data.Note: Node values are inserted into a binary search tree before a reference to the tree's root node is passed to your function. In a binary search tree, all nodes on the left branch of a node are less than the node value. All values on the right branch are greater than the node value.ConstraintsOutput FormatYour function should return a single integer denoting the height of the binary tree.

what is height of complete binary tree

Tree: Height of a Binary Tree

The height of a binary search tree is the length of the ________ path from the root to a leaf.

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