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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.)
Consider the digraph G with three vertices P1,P2 and P3 and four directed edges, one each from P1 to P2, P1 to P3, P2 to P3 and P3 to P1. a. Sketch the digraph. b. Find the a
Step 1: Declare array 'k' of size 'n' i.e. k(n) is an array which stores all the keys of a file containing 'n' records Step 2: i←0 Step 3: low←0, high←n-1 Step 4: while (l
Data Structure and Algorithm 1. Explain linked list and its types. How do you represent linked list in memory? 2. List and elucidate the types of binary tree. 3. Descr
Q. The system allocates the memory for any of the multidimensional array from a big single dimensional array. Describe two mapping schemes that help us to store the two dimensi
Q. Illustrate the steps for converting the infix expression into the postfix expression for the given expression (a + b)∗ (c + d)/(e + f ) ↑ g .
tree is graph or not
Variable length codes (Niveau I) Code the following sequence of integers (2, 4, 2, 8, 3, 1, 4, 5, 13, 2) with • unary codes • ? codes • d codes • Rice codes (for a suitable l) and
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Maximum numbers of nodes a binary tree of depth d The maximum numbers of nodes a binary tree of depth d can have is 2 d+1 -1.
Explain an efficient way of storing two symmetric matrices of the same order in memory. A n-square matrix array is said to be symmetric if a[j][k]=a[k][j] for all j and k. For
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