Prerequisite – Binary Tree Data StructureIn this article, we will comment on various instances for relationship between variety of nodes and also height the binary tree. Prior to understanding this article, you must have basic idea about binary trees and their properties.The **height** of the binary tree is the longest path from root **node to any leaf** node in the tree. Because that example, the height of binary tree presented in figure 1(b) is 2 as longest course from root node to node 2 is 2. Also, the elevation of binary tree displayed 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 have the right to have maximum two children.

Attention reader! Don’t stop finding out now. Exercise GATE test well prior to the actual exam through the subject-wise and overall quizzes obtainable in **GATE Test series Course**.Learn all **GATE CS principles with free Live Classes** on our youtube channel.**Calculating minimum and also maximum height from number of nodes –**If there room n nodes in binary tree, **maximum height** that the binary tree is **n-1** and also **minimum height** is **floor(log2n)**.

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

**Calculating minimum and also maximum number of nodes from elevation –**If binary find tree has

**height h**, minimum number of

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

**height h**, maximum variety of nodes will be when all level are completely full. Total number of nodes will certainly 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 be visualized in the same way.

**Que-1.**The elevation of a tree is the length of the longest root-to-leaf path in it. The maximum and also the minimum number of nodes in a binary tree of elevation 5 are:(A) 63 and also 6, respectively(B) 64 and also 5, respectively(C) 32 and also 6, respectively(D) 31 and also 5, respectively

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

**Que-2.**

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which of the complying with height is not possible for a binary tree through 50 nodes?(A) 4(B) 5(C) 6(D) None

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**Solution:**follow to formula discussed,Minimum height with 50 nodes = floor(log250) = 5. Therefore, height 4 is no possible.