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1. Find q and r as defined in the Division Algorithm when a = 549 and b = 236
2. Suppose N > 1 is a natural number and f: Z →N υ {0} is the function that associates with each a ε Z its remainder upon division by n; thus, if a = qn + r with 0 ≤ r < n, then f(a) = r.
(a.) Find the domain and range of f
(b.) Is f one-to-one?
(c.) Is f onto?
3. Find the binary, octal and hexadecimal representations for 2705.
4. Let Sbe the set of all people in the world. For a, b ε S, define a binary relation R as follows: (a, b) ε R if and only if a and b have visited the same webpage. Is this an example of a partially ordered set? Why or why not?
Sketch Dynamic Programming Tables (one for calculating optimal value and one for keeping track of items used in getting optimal value) for 0/1 Knapsack Problem given below and illustrate your final result.
Explain an O(m+n) algorithm which, given an initial infection of a computer Ca at time t determines for each other computer the earliest time at which it can become infected.
The Metropolitan Housing Agency is a non profit corporation that advocates the development and improvement of low income housing.
Use big-O notation to categorize traditional grade school algorithms for addition and multiplication. That is, if asked to add two numbers each having N digits, determine individual additions should be performed?
How is a Pert chart useful? How is a Gantt chart useful? What are the differences and similarities between both?
Design a linear-time algorithm that verifies that the height information in an AVL tree is correctly maintained and that the balance property is in order.
Construct an EER model for the given situation using the traditional EER notation, the Visio notation or the supertypes notation.
Illustrate how tree will expand (after inserting each Part#), and what the final tree would like. (b) Repeat item (a), but use a B-tree of order p = 4 instead of a B+-tree.
Give an algorithm that takes an n-node path G with weightsand returns an independent set of maximum total weight. The runningtime should be polynomial in n, independent of the values of theweights
Assume a flash storage device is used instead of disk, and it has seek time of 1 microsecond and transfer rate of 40 MB per second. Recompute the cost of sorting the relation in seconds.
Design a recursive linear-time algorithm that tests whether a binary tree satisfies the search tree order property at every node.
Identify at least two data structures that are used to organize a typical file cabinet. Why do you feel it is necessary to emulate these types of data structures in a computer program?
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