All of the problems listed below are from the text Discrete Mathematical Structures for Computer Science by Judith Gersting. Problems should be done immediately after the class in which the relevant material was covered. Homework will not be collected or graded. The date after the assignment number is the date the homework was assigned. Assignment #1 (June 30, 1998):
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Your answers will be graded both on the correctness of the mathematics and on the way in which you have written it down. Always explain what you are doing.
IMPORTANT:Answers to "True or False" and "Show that. " problems MUST include a full justification.
For example. If you are given the statement "all odd integers are prime," first determine whether it is true or false. Then make the resulting claim, and give its justification. The following is acceptable:
CLAIM: Not all odd integers are prime. PROOF: Even though 9 is odd, it is not prime, since 9 = (3)(3).
(This is not the only possible answer -- you could use, say, 15 or 25 instead of 9. The point is that this is the level of precision expected in your answer.)
If you are given the statement "the product of two odd integers is odd," first determine whether it is true or false. Then make the resulting claim, and give its justification. The following is acceptable:
CLAIM: The product of any two odd integers is odd. PROOF: If m and n are odd integers, then m=2k+1 and n=2l+1 for some integers k and l, so mn = (2k+1)(2l+1) = 4kl+2k+2l+1 = 2(2kl+k+l)+1. Therefore mn is odd.
However, the following is NOT acceptable:
CLAIM: The product of any two odd integers is odd. PROOF: 5 and 7 are odd. (5)(7)=35, and 35 is odd.
(Since the claim concerns ANY pair of odd integers, not just 5 and 7, checking the statement for just one pair of odd integers does not constitute a valid answer.)
The only difference between a "True or False" problem and a "Show that. " problem is that with the latter, you are given a statement which is KNOWN to be true and then asked to justify it.
The number of your particular task is the value of the expression faculty_number%7.
Write a complete program with at least one example in main function.(0) [P-9.3] Extend class BinarySearchTree. shown in Code Fragmant 9.3 through 9.5 to support the functions of the orderd dictionary ADT, listed in Section 8.3.1.
(1) [P-9.5] Implement a class RestructableNodeBinaryTree that supports the functions of the binary tree ADT, plus a function restructure() for performing a rotation operation. This class is a component of the implementation of an AVL tree given in Section 9.2.2.
(2) [P-9-7] Implement the functions of the ordered dictionary ADT using AVL tree.
(3) [P-9.9] Write a C++ class that implements all the functions of an ordered dictionary given in Chapter 8 using (2,4) tree.
(4)[P-9.10a] Write a C++ class that can take any red-black tree and convert it into its corresponding (2,4) tree.
(5)[P-9.10b] Write a C++ class that can take any(2,4)tree and convert it into its correspondingred-blacktree.
(6) [P-9-11]Write a C++ class that implements all the functions of a dictionary given in Chapter 8 by means of red-black tree.
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