Tree basics

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 A graph is called a tree having no cycles, no self loops, no parallel edges.


full binary tree

all nodes with 0 or 2 childs

if n leaf nodes, total nodes=2n-1;

total internal nodes=total nodes-leaf nodes-one root node


complete binary tree

each level must be completely filled, except the last level, and all leaf nodes must be as left as possible.

nodes at level i=(2^i) except last 


a full binary tree is not complete binary tree and a complete binary tree is not a full binary tree

except only one condition, in which full binary tree<-> complete binary tree when each node has either 0 or 2 child nodes and

on last level the child must be as left as possible, also called perfect binary tree.



Array representation and linked list representation.


Array representation

No. of levels must be known to us at beginning.

maximum no. of nodes at a level l = 2^(l+1)-1.

hence for array representation an array of size 2^(l+1)-1 must be taken.

for any node i the left child will be at 2i+1 and right node=2i+1 (note: indexing is zero based)



Linked list representation

In normal binary tree (not BST) the time complexity to find a node is 

we can increase the speed of binary tree traversals by using threaded binary trees.


Drawbacks of Binary search tree

Its time comp. should be O(log n), but if the data is in sorted order, then its complexity will become O(n).





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