Table of Contents
- 1 What is the minimum and maximum number of nodes in AVL tree of height 6?
- 2 What is the maximum number of nodes in an AVL tree of height 6?
- 3 What is the maximum number of nodes in AVL tree?
- 4 What is the minimum and maximum number of nodes in a complete binary tree of height h?
- 5 What is the maximum number of nodes in a binary tree at level 6?
- 6 What is the maximum possible number of nodes in a binary tree at level 8 and also tell that BST from Array is possible?
- 7 What are the different types of questions based on AVL trees?
- 8 How to find the maximum height of a node in a tree?
What is the minimum and maximum number of nodes in AVL tree of height 6?
the minimum number of nodes in an AVL tree for a tree with a height of 6 is not 20, it should be 33. The following equation should demonstrate the recursive call of the N(h) function.
What is the maximum number of nodes in an AVL tree of height 6?
If there are n nodes in AVL tree, maximum height can’t exceed 1.44*log2n. If height of AVL tree is h, maximum number of nodes can be 2h+1 – 1.
What is the minimum and maximum number of nodes in a full tree of height 6?
Solution: According to formula discussed, max number of nodes = 2^(h+1)-1 = 2^6-1 =63. min number of nodes = h+1 = 5+1 = 6.
What is the maximum number of nodes in AVL tree?
If there are n nodes in AVL tree, maximum height can’t exceed 1.44*log 2n. If height of AVL tree is h, maximum number of nodes can be 2 h+1 – 1. Minimum number of nodes in a tree with height h can be represented as: N(h) = N(h-1) + N(h-2) + 1 for n>2 where N(0) = 1 and N(1) = 2.
What is the minimum and maximum number of nodes in a complete binary tree of height h?
Maximum number of nodes of full binary tree of height “h” is 2h+1 – 1. Minimum number of nodes of full binary tree of height “h” is 2h+1.
What can be the minimum number of nodes of an AVL tree with height 4?
So, minimum number of nodes required to construct AVL tree of height-4 = 12. But given number of nodes = 10 which is less than 12. Thus, maximum height of AVL tree that can be obtained using 10 nodes = 3.
What is the maximum number of nodes in a binary tree at level 6?
Discussion Forum
| Que. | What is the maximum possible number of nodes in a binary tree at level 6? |
|---|---|
| b. | 6 |
| c. | 1 |
| d. | 64 |
| Answer:64 |
What is the maximum possible number of nodes in a binary tree at level 8 and also tell that BST from Array is possible?
1) The maximum number of nodes at level ‘l’ of a binary tree is 2l. Here level is the number of nodes on the path from the root to the node (including root and node). Level of the root is 0. This can be proved by induction.
What is the maximum number of nodes in an AVL tree?
If there are n nodes in AVL tree, maximum height can’t exceed 1.44*log 2n. If height of AVL tree is h, maximum number of nodes can be 2 h+1 – 1. Minimum number of nodes in a tree with height h can be represented as: N (h) = N (h-1) + N (h-2) + 1 for n>2 where N (0) = 1 and N (1) = 2.
What are the different types of questions based on AVL trees?
We have discussed types of questions based on AVL trees. Given number of nodes, the question can be asked to find minimum and maximum height of AVL tree. Also, given the height, maximum or minimum number of nodes can be asked. Que – 1. What is the maximum height of any AVL-tree with 7 nodes?
How to find the maximum height of a node in a tree?
That height is the minimum. To find the maximum, do the same as for the minimum, but then go back one step (remove the last placed node) and see if adding that node to the opposite sub-tree (from where it just was) violates the AVL tree property. If it does, your max height is just your min height.
What is AVL tree in DBMS?
AVL tree is binary search tree with additional property that difference between height of left sub-tree and right sub-tree of any node can’t be more than 1. Here are some key points about AVL trees: