Assignment#2-100426154 (dhavalkumar patel)

# Assignment#2-100426154 (dhavalkumar patel) - Dhavalkumar...

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Dhavalkumar Patel 100426154 Assignment #2 Discrete Mathematics 3.3 Complexity of Algorithms (p. 199): Exercise 2. 3.4 The Integers and Division (p. 209): Exercise 16. 3.5 Primes and Greatest Common Divisors (p. 217): Exercise 10. 3.8 Matrices (p. 256): Exercise 20.

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2. Write the algorithm that puts the first four terms of a list of arbitrary length in increasing order. Show that this algorithm has time complexity O (1) in terms of the number of comparisons used. Answer: bubble sort (al, . .., an: real numbers with n :::: 2) For i: = 1 to n – 1 For j: = 1 to n – i If aj > aj+l then interchange aj and aj+l {aI, . .. , an is in increasing order} It has O(1) complexity
16. Evaluate these quantities. a)-17 mod 2 b) 144 mod 7 c) -101 mod 13 d)199 mod 19 a) -17 mod 2 Solution: Note: The remainder cannot be negative -9 2 -17 - (-18) +1 (-9)*2= -18, then the remainder would be +1 Therefore, -17 mod 2= +1 Proof: To verify the answer we can multiply 2 by -9, and add it with the remainder +1

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## This note was uploaded on 03/11/2012 for the course LSDHFA 234 taught by Professor Sdaf during the Spring '12 term at UOIT.

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Assignment#2-100426154 (dhavalkumar patel) - Dhavalkumar...

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