Prerequisite – Binary Tree Data StructureIn this article, we will comment on various cases for relationship between number of nodes and height of binary tree. Prior to understanding this article, you must have basic idea around binary trees and their properties.The **height** that the binary tree is the longest course from root **node to any kind of leaf** node in the tree. Because that example, the height of binary tree presented in figure 1(b) is 2 as longest path from root node to node 2 is 2. Also, the height of binary tree presented in number 1(a) is 4.

You are watching: What is the minimum number of nodes in a full binary tree with height 4?**Binary Tree –**In a binary tree, a node can have maximum 2 children.

Attention reader! Don’t stop learning now. Practice GATE exam well prior to the yes, really exam v the subject-wise and overall quizzes easily accessible in **GATE Test series Course**.Learn all **GATE CS concepts with free Live Classes** on ours youtube channel.**Calculating minimum and also maximum elevation from number of nodes –**If there space n nodes in binary tree, **maximum height** of the binary tree is **n-1** and also **minimum height** is **floor(log2n)**.

For example, left skewed binary tree presented in figure 1(a) with 5 nodes has actually height 5-1 = 4 and binary tree shown in figure 1(b) with 5 nodes has actually height floor(log25) = 2.**Calculating minimum and maximum number of nodes from height –**If binary tree has **height h**, minimum variety of **nodes is h+1** (in instance of left skewed and right it was crooked binary tree).For example, the binary tree presented in number 2(a) with height 2 has 3 nodes.If binary tree has height h, maximum variety of nodes will be when all level are fully full. Total variety of nodes will be 2^0 + 2^1 + …. 2^h = 2^(h+1)-1.For example, the binary tree displayed in figure 2(b) with height 2 has 2^(2+1)-1 = 7 nodes.**Binary search Tree –**In a binary find tree, left son of a node has actually value less than the parent and right child has actually value better than parent.**Calculating minimum and also maximum elevation from the variety of nodes –**If there are n nodes in a binary search tree, maximum elevation of the binary find tree is n-1 and minimum elevation is ceil(log2n).

**Calculating minimum and maximum variety of nodes from height –**If binary search tree has

**height h**, minimum number of

**nodes is h+1**(in case of left skewed and also right skewed binary find tree).If binary find tree has

**height h**, maximum variety of nodes will be once all level are totally full. Total number of nodes will be 2^0 + 2^1 + …. 2^h = 2^(h+1)-1.All the rules in BST are very same as in binary tree and also can it is in visualized in the very same way.

**Que-1.**The elevation 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:(A) 63 and also 6, respectively(B) 64 and 5, respectively(C) 32 and 6, respectively(D) 31 and also 5, respectively

**Solution:**follow to formula discussed,max number of nodes = 2^(h+1)-1 = 2^6-1 =63.min variety of nodes = h+1 = 5+1 = 6.

**Que-2.**

See more: The Hr Diagram Is Based On What Two Criteria, Introduction To The H

i beg your pardon of the following height is not possible for a binary tree through 50 nodes?(A) 4(B) 5(C) 6(D) None

See more: The Hr Diagram Is Based On What Two Criteria, Introduction To The H

**Solution:**follow to formula discussed,Minimum elevation with 50 nodes = floor(log250) = 5. Therefore, elevation 4 is not possible.