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Assume a complete binary tree T with n nodes where each node has an item (value). Label the nodes of the complete binary tree T from top to bottom & from left to right 0, 1, ..., n-1. Relate with T the array A where the ith entry of A is the item in the node labeled i of T, i = 0, 1, ..., n-1. Table illustrates the array representation of a Binary tree of Figure
Given the index i of a node, we can efficiently & easily compute the index of its parent and left & right children:
Index of Parent: (i - 1)/2, Index of Left Child: 2i + 1, Index of Right Child: 2i + 2.
Node #
Item
Left child
Right child
0
A
1
2
B
3
4
C
-1
D
5
6
E
7
8
G
H
I
J
9
?
Table: Array Representation of a Binary Tree
First column illustrates index of node, second column contain the item stored into the node & third & fourth columns mention the positions of left & right children
(-1 shows that there is no child to that specific node.)
Adjacency list representation An Adjacency list representation of Graph G = {V, E} contains an array of adjacency lists mentioned by adj of V list. For each of the vertex u?V,
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One can change a binary tree into its mirror image by traversing it in Postorder is the only proecess whcih can convert binary tree into its mirror image.
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merging 4 sorted files containing 50 10 25 and 15 records will take time
Q. Describe what do you understand by the term array? How does an array vary from an ordinary variable? How are the arrays represented in the specific memory?
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