Table of Contents
- 1 What is the height of a complete binary tree with n nodes?
- 2 What is the sum of all node heights?
- 3 What is height of a binary tree?
- 4 What will be the height H of a complete binary tree if we construct from N number of nodes?
- 5 What is the height of binary tree shown in Figure 1?
- 6 What is the maximum number of nodes in a binary tree?
What is the height of a complete binary tree with n nodes?
Detailed Solution Concept: In a binary tree, a node can have maximum two children. If there are n nodes in binary tree, maximum height of the binary tree is n-1.
What is the sum of all node heights?
Theorem: For a complete binary tree of height h containing 2^(h+1) – 1 nodes, the sum of the heights is 2^(h+1) -1 -(h+1).
How do you find the sum of all nodes in a binary tree?
If the tree is not empty, traverse through left subtree, calculate the sum of nodes and store it in sumLeft. Then, traverse through the right subtree, calculate the sum of nodes and store it in sumRight. Finally, calculate total sum = temp. data + sumLeft + sumRight.
How do you find the sum of heights?
sum-of-heights Σh = n – h – 1.
What is height of a binary tree?
The height of a binary tree is the height of the root node in the whole binary tree. In other words, the height of a binary tree is equal to the largest number of edges from the root to the most distant leaf node. A similar concept in a binary tree is the depth of the tree.
What will be the height H of a complete binary tree if we construct from N number of nodes?
If there are n nodes in binary tree, maximum height of the binary tree is n-1 and minimum height is floor(log2n).
How do you find the height of a node in BST?
Recursion:
- Take a variable called height =0.
- Search for that given node in the tree using recursion.
- Each time you left or right , increase the height by 1.
- Once you found the given node, return the height.
- If till the end you wont find the node, return 0.
What is height of a node?
A node’s height is the number of edges to its most distant leaf node. On the other hand, a node’s depth is the number of edges back up to the root. So, the root always has a depth of while leaf nodes always have a height of.
What is the height of binary tree shown in Figure 1?
Also, the height of binary tree shown in Figure 1 (a) is 4. In a binary tree, a node can have maximum two children. If there are n nodes in binary tree, maximum height of the binary tree is n-1 and minimum height is floor (log2n).
What is the maximum number of nodes in a binary tree?
If binary tree has height h, minimum number of nodes is n+1 (in case of left skewed and right skewed binary tree). For example, the binary tree shown in Figure 2 (a) with height 2 has 3 nodes. If binary tree has height h, maximum number of nodes will be when all levels are completely full.
What are the rules of binary tree and BST?
All the rules in BST are same as in binary tree and can be visualized in the same way. Que-1. The height of a tree is the length of the longest root-to-leaf path in it. The maximum and the minimum number of nodes in a binary tree of height 5 are: max number of nodes = 2^ (h+1)-1 = 2^6-1 =63.
What is the time complexity of a binary tree?
Time Complexity: O (nh) where n is the total number of nodes and h is the height of the binary tree. The idea is to compute heights and sum them up in the same recursive call. Time Complexity: O (n) where n is the total number of nodes of the binary tree.