Logarithm Properties

 


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Circular Queue implementation

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Tree terminologies

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 Tree : Tree is collection of nodes and edges. Or, it's collection of nodes where one node is taken as root node and rest of the nodes are divided into disjoint subsets and each subset is tree or subtree.  Tree terminologies :  Level starts from 1 onwards (we count nodes) and height starts from 0 onwards (we counts edges).  Binary Tree : A tree that can have 0, 1 or 2 sub trees, is called binary tree. How many binary trees can be generated from given number of nodes (n)? 1. Unlabelled Nodes : How many trees with maximum height? 2. Labelled Nodes :  Height vs Nodes Formula :  1. If height of binary tree is given? Minimum No. of Nodes (n) = h + 1 Maximum No. of Nodes (n) = 2^(n+1) - 1 2. If nodes of binary tree is given? Minimum Height (h) = log(n+1) - 1 Maximum  Height (h)  = n-1 Relationship b/w nodes with degree 0 and degree 2: Number of nodes with degree(0) = Number of nodes with degree(2) + 1
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