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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.)
characteristics of a good algorithm
Normally a potential y satisfies y r = 0 and 0 ³ y w - c vw -y v . Given an integer K³0, define a K-potential to be an array y that satisfies yr = 0 and K ³ y w - c vw -y v
If a Dequeue is implemented via arrays, then this will suffer with the similar problems which a linear queue had suffered. Program 8 gives the array implementation of Dequeue.
How to construct a data flow diagram for a college assignment and marking systemA
Merge sort is also one of the 'divide & conquer' classes of algorithms. The fundamental idea in it is to split the list in a number of sublists, sort each of these sublists & merge
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what is folding method?
Q. Implement a stack making use of the linked list. Show the PUSH and POP operations both. A n s . Stack implemantation using linked list # include # include
Q. Perform implementation of a queue using a singly linked list L. The operations INSER and DELETE should take O (1) time.
implement multiple stacks in an array and write different algorithms to perform operations on it
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