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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.)
Huffman Encoding is one of the very simple algorithms to compress data. Even though it is very old and simple , it is still widely used (eg : in few stages of JPEG, MPEG etc). In t
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Game trees An interesting application of trees is the playing of games such as tie-tac-toe, chess, nim, kalam, chess, go etc. We can picture the sequence of possible moves by m
Evaluate the frequency counts for all statements in the following given program segment. for (i=1; i ≤ n; i ++) for (j = 1; j ≤ i; j++) for (k =1; k ≤ j; k++) y ++;
What data structure would you mostly likely see in a nonrecursive execution of a recursive algorithm? Stack
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Easy algorithm for beginner for quicksort with explanation
Linked lists are among the most common and easiest data structures. They may be used to implement various other common abstract data types, including queues, stacks, symbolic expre
This algorithm inputs number of hours of sunshine recorded every day for a week (7 days). Output is the highest value for hours of sunshine and average (mean) value for numbers of
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