QUESTION 24What is the time complexity function of the following algorithm?1. Input string 11,.. ,In.2. For i = 1 to n- 1 do2.1 For j i + 1 to n do2.1.1 If ri = Ij then2.1.1.1 Return "There is duplicate integer in the str ng.3. Return "There are no duplicate integers in the string."n2 -na.f(n) =%3DOb. f(n) = n?O c. f(n) = 2nO d. f(n) =n

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Answered: QUESTION 24 What is the time complexity…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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1.3.2 also attached
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6. Discover the recursive formula for Hn. Find Hn for n=1,2,3...6. Based on these values you will be able tosee the recursive pattern. proving the formula is optional for extra credit. Consider all subsets of N={1, 2, 3,..., n). How many of these subsets, SC N, satisfy the property that (i) Vx (x ES → x +1 ¢ S) ? Denote the number of subsets satisfying this property (i) by Hn. (a) Find the first 6 values of Hn . I have calculated n=1 and n=2, so you need to do n=3, 4, 5, 6 (b) Find and prove the recursive formula for the sequence Hn . Example: Let n=1. Then N={1} and the subsets satisfying property (i) are {1} and O so H1=2. Let n=2. Then N={1,2} and the subsets satisfying property (i) are {1}, {2}, and Ø, i.e. H3=3. Note: {1,2} is also subset of {1,2} but since for x=1, x+1=2 and both 1 and 2 are contained in {1,2} therefore the set {1,2} fails to satisfy property (i). 7. Prove by induction that the number of subsets for a set with n elements is 2^n.
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