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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.)
Warnock's Algorithm An interesting approach to the hidden-surface problem was presented by Warnock. His method does not try to decide exactly what is happening in the scene but
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Ask question find frequency count of function- {for(i=1;i {for(j=1;j {for(k=1;k } } }
what is algorithim?
Explain the Abstract data type assertions Generally, ADT assertions translate into assertions about the data types which implement ADTs, which helps insure that our ADT impleme
Best Case: If the list is sorted already then A[i] T (n) = c1n + c2 (n -1) + c3(n -1) + c4 (n -1) = O (n), which indicates that the time complexity is linear. Worst Case:
Painter's Algorithm As the name suggests, the algorithm follows the standard practice of a painter, who would paint the background (such as a backdrop) first, then the major d
Write a recursive function the computes the number of digits in a positive integer n. For example if n = 6598, the function should return 4. Find a variant expression and a thresho
As we have seen, as the traversal mechanisms were intrinsically recursive, the implementation was also easy through a recursive procedure. Though, in the case of a non-recursive me
A depth-first traversal of a tree visits a nodefirst and then recursively visits the subtrees of that node. Similarly, depth-first traversal of a graph visits a vertex and then rec
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