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:Question 47Select one:2(h+1)-1cross out2(h-1)-1cross out2h−1cross out2(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:Question 47Select one:2(h+1)-1cross out2(h-1)-1cross out2h−1cross out2(h+1)
Solution
The maximum number of nodes in a binary tree of height h is 2^(h+1) - 1.
Here's why:
- A binary tree of height 0 has 1 node (the root).
- A binary tree of height 1 has 2^1 = 2 nodes (the root and one child).
- A binary tree of height 2 has 2^2 = 4 nodes (the root, two children of the root, and one grandchild).
- And so on...
So, a binary tree of height h has 2^0 + 2^1 + 2^2 + ... + 2^h nodes. This is a geometric series with first term 1, common ratio 2, and h+1 terms. The sum of a geometric series is given by the formula a(r^n - 1) / (r - 1), where a is the first term, r is the common ratio, and n is the number of terms.
Substituting the values, we get 1(2^(h+1) - 1) / (2 - 1) = 2^(h+1) - 1.
So, the maximum number of nodes in a binary tree of height h is 2^(h+1) - 1.
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
Suppose you are given a binary tree with n nodes, such that each node has exactly either zero or two children. The maximum height of the tree will beQuestion 49Select one:(n+1)/2cross outn/2-1cross outn/2+1cross out(n-1)/2
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.
Tree: Height of a Binary Tree
The postorder traversal of a binary tree is 8, 9, 6, 7, 4, 5, 2, 3, 1. The inorder traversal of the same tree is 8, 6, 9, 4, 7, 2, 5, 1, 3. The height of a tree is the length of the longest path from the root to any leaf. The height of the binary tree above is ________ .
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