Mell What is the minimum number of nodes in a binary tree can have?
Maximum number of nodes of complete binary tree of height “h” is 2h+1 – 1. Minimum number of nodes of complete binary tree of height “h” – 2….Complete Binary Tree.
| Max Nodes | Min Nodes | |
|---|---|---|
| Binary Tree | 2h+1 – 1 | h+1 |
| Full Binary Tree | 2h+1 – 1 | 2h+1 |
| Complete Binary Tree | 2h+1 – 1 | 2h |
What is the minimum number of nodes?
If binary search tree has height h, minimum number of nodes is h+1 (in case of left skewed and right skewed binary search tree). If binary search tree has height h, maximum number of nodes will be when all levels are completely full.
Can a binary tree have 0 nodes?
For a binary tree, each node can have zero, one, or two children. If a tree has only a root node and no other node then it is called a NULL tree.
What is the minimum depth of a binary tree?
Given a binary tree, find its minimum depth. The minimum depth is the number of nodes along the shortest path from the root node down to the nearest leaf node. For example, minimum height of below Binary Tree is 2.
What is the minimum height of complete binary tree?
If there are n nodes in binary tree, maximum height of the binary tree is n-1 and minimum height is floor(log2n). For example, left skewed binary tree shown in Figure 1(a) with 5 nodes has height 5-1 = 4 and binary tree shown in Figure 1(b) with 5 nodes has height floor(log25) = 2.
How do we find the height of a binary tree?
To find the height of the binary tree we will recursively calculate the height of the left and right subtree of a node. To find the heights of left and right subtrees we use in-order traversal. After finding the height of both left and right subtree we will store the height of the subtree which has maximum value and add 1 to it to include the current level of tree.
How do you balance a binary tree?
A binary tree is balanced if for each node it holds that the number of inner nodes in the left subtree and the number of inner nodes in the right subtree differ by at most 1. A binary tree is balanced if for any two leaves the difference of the depth is at most 1.