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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.)
Readjusting for tree modification calls for rotations in the binary search tree. Single rotations are possible in the left or right direction for moving a node to the root position
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In the last section, we discussed regarding shortest path algorithm that starts with a single source and determines shortest path to all vertices in the graph. In this section, we
This notation bounds a function to in constant factors. We say f(n) = Θ(g(n)) if there presents positive constants n 0 , c 1 and c 2 such that to the right of n 0 the value of f
Explain how two dimensional arrays are represented in memory. Representation of two-dimensional arrays in memory:- Let grades be a 2-D array as grades [3][4]. The array will
3633(mod 11)
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write aprogram for random -search to implement if a[i]=x;then terminate other wise continue the search by picking new randon inex into a
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