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 _______.
Question
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 _______.
Solution
The height of the binary tree is 4.
Here's how we can determine this:
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From the postorder traversal, we know that the last element is the root of the tree, which is 1.
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From the inorder traversal, we know that the elements to the left of 1 (8, 6, 9, 4, 7, 2, 5) are in the left subtree, and the elements to the right of 1 (3) are in the right subtree.
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We can then split these elements into their respective subtrees and repeat the process. For the left subtree, 5 is the root, 8, 6, 9, 4, 7, 2 are on the left, and there are no elements on the right. For the right subtree, there are no elements on the left or right of 3.
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We continue this process until we have processed all elements. The height of the tree is the maximum number of steps we have taken from the root to a leaf, which in this case is 4.
Similar Questions
The height of a binary search tree is the length of the ________ path from the root to a leaf.
Tree: Height of a Binary Tree
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.
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)
t a binary tree using inorder and level order traversal given below.Inorder Traversal: 4, 5, 3, 2, 6, 9, 10Level Order Traversal: 2, 5, 6, 10, 9, 3, 4Options
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