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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.)
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
Write an algorithm in the form of a flowchart that: inputs top speeds (in km/hr.) of 5000 cars Outputs fastest speed and the slowest speed Outputs average (mean) s
Create main method or a test class that creates 2 Element objects that are neighbours of each other, the first element temperature set at 100, the 2nd at 0 and use an appropriate h
data structure for multiqueue
Which data structure is required to change infix notation to postfix notation? Stack function is used to change infix notation to postfix notatio n
Polynomials like 5x 4 + 2x 3 + 7x 2 + 10x - 8 can be represented by using arrays. Arithmetic operations such as addition & multiplication of polynomials are com
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
How many recursive calls are called by the naïve recursive algorithm for binomial coefficients, C(10, 5) and C(21, 12) C(n,k){c(n-1,k)+c(n-1,k-1) if 1 1 if k = n or k = 0
#question.show that the following inequality is correct or incorrect. n!=O(n^n)
Q. Write down any four applications or implementation of the stack. Ans. (i) The Conversion of infix to postfix form (ii)
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