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Suppose T is a multi-way tree in which each internal node has at least five and at most eight children. For what values of a and b is T a valid (a, b) tree? ANSWER: Since it has to satisfy the condition: 2 ? a ? (b+1)/2, the values are a = 4 and b = 8.
HERE ARE THE QUESTIONS: 1) For what values of d is the tree T of the previous exercise an order -d B-tree? HINT: The definition of an order-d deals with the minimum and maximum number of children an internal node can have.
2) Show each level of recursion in performing a four-way, external-memory merge-sort of the sequence given in the previous exercise. HINT: Draw the memory cache and manually process the requests using a pencil with a good erasure.
For inputs of size n, insertion sort runs in 8n 2 steps, where as merge sort runs in 64* nlog base 2 n steps. For which values of n odes insertion sort beat merge sort?
Let the algebraic expression E=(2x+y)(5a-b)^3. Create tree T which correspond to expression E and determine pre-order traversal of T.
Use separate chaining to store the following keys. Consider that each letter is a number corresponding to the sequence of English alphabets. That is, A->1,
Illustrate how to use depth-first search to find out in time O(|E|+|V |) whether undirected graph is 2-colorable. Describe and explain your strategy.
Create an E-R diagram with all appropriate notation for the following condition. In a particular fruit growing region there are a number of orchards.
In a program that uses a stack to check for balanced braces in an string, what condition indicates that the braces are balanced when the end of the string is reached
Sketch a flowchart or write psuedocode to represent logic of a program that alllows the user to enter three values .
Describe how the use of primitives helps remove ambiguities in an algorithm's representation.
On the basis of a linear-time algorithm for computing the strong component containing a given vertex v, describe a simple quadratic-time algorithm for computing the strong components of a digraph.
Think about a typical job order that might include the following information. Design a single table to hold all the data needed to store a job order including this information.
Calculate an arithmetic mean, median, and mode for up to fifty test scores. The information are contained in a text file. To determine the median, first sort the array.
Explain how will use a search tree to find the solution.
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