Consider a complete binary tree of n levels, with the root node at level 0. How many nodes are present in level n-2 (the level before the last level) of such a binary tree? Choose one answer.[INPUT] a.??.[LINK: https://csemoodle.ucsd.edu/filter/tex/displaytex.php?2%5E%7Bn-1%7D] [IMG: 2^{n-1}] [INPUT] b. [LINK: https://csemoodle.ucsd.edu/filter/tex/displaytex.php?n-2][IMG: n-2] [INPUT] c. [LINK: https://csemoodle.ucsd.edu/filter/tex/displaytex.php?n-1] [IMG: n-1] [INPUT] d. [LINK: https://csemoodle.ucsd.edu/filter/tex/displaytex.php?2%5E%7Bn-2%7D] [IMG: 2^{n-2}]Question2 Marks: 1 Which one of these functions has the fastest asymptotic growth? Choose one answer.[INPUT] a. [LINK: https://csemoodle.ucsd.edu/filter/tex/displaytex.php?log_2+n] [IMG: log_2 n] [INPUT] b. [LINK: https://csemoodle.ucsd.edu/filter/t??.ex/displaytex.php?log_3+n] [IMG: log_3 n] [INPUT] c. [LINK: https://csemoodle.ucsd.edu/filter/tex/displaytex.php?log_%7B100%7D+n] [IMG: log_{100} n] [INPUT] d. They all have the same asymptotic growthQuestion3 Marks: 1 Which one of the following functions growths the fastest? Choose one answer.[INPUT] a. [LINK: https://csemoodle.ucsd.edu/filter/tex/displaytex.php?log%282%5En%29] [IMG: log(2^n)] [INPUT] b.??.[LINK: https://csemoodle.ucsd.edu/filter/tex/displaytex.php?log%283%5En%29] [IMG: log(3^n)] [INPUT] c. [LINK: https://csemoodle.ucsd.edu/filter/tex/displaytex.php?log%28n%5E2%29] [IMG: log(n^2)] [INPUT] d. [LINK:https://csemoodle.ucsd.edu/filter/tex/displaytex.php?n%5E2] [IMG: n^2]Question4 Marks: 1 Solving the recurrence relation [LINK: https://csemoodle.ucsd.edu/filter/tex/displaytex.php?T%28+n+%29+%3D+4+T%28%5Cfrac%7Bn%7D2%29+%2B+2n] [IMG: T( n ) = 4 T(frac{n}2) + 2n] and??.[LINK: https://csemoodle.ucsd.edu/filter/tex/displaytex.php?T%281%29+%3D+1] [IMG: T(1) = 1] , we get [LINK:https://csemoodle.ucsd.edu/filter/tex/displaytex.php?T%28+n+%29+%3D+] [IMG: T( n ) =]Choose one answer.[INPUT] a. [LINK: https://csemoodle.ucsd.edu/filter/tex/displaytex.php?%5CTheta%28n%5E2%29] [IMG: Theta(n^2)] [INPUT] b. [LINK:https://csemoodle.ucsd.edu/filter/tex/displaytex.php?%5CTheta%28n%5E2+log+n%29] [IMG: Theta(n^2 log n)] [INPUT] c. [LINK: https://csemoodle.ucsd.edu/filter/tex/displaytex.php?%5CTheta%28n+log+n%29] [IMG: Theta(n log n)] [INPUT] d. [LINK: https://csemoodle.ucsd.edu/filter/tex/displaytex.php?%5CTheta%28n%5E3%29] [IMG: Theta(n^3)]??.Question5 Marks: 1 Solving the recurrence relation [LINK: https://csemoodle.ucsd.edu/filter/tex/displaytex.php?T%28+n+%29+%3D+3T%28%5Cfrac%7Bn%7D2%29+%2B+n] [IMG: T( n ) = 3T(frac{n}2) + n] and [LINK: https://csemoodle.ucsd.edu/filter/tex/displaytex.php?T%281%29+%3D+3] [IMG: T(1) = 3] , we get [LINK:https://csemoodle.ucsd.edu/filter/tex/displaytex.php?T%28+n+%29+%3D+] [IMG: T( n ) =]Choose one answer.[INPUT] a. [LINK: https://csemoodle.ucsd.edu/filter/tex/displaytex.php?%5CTheta%28n%5E%7B1.79%7D%29] [IMG: Theta(n^{1.79})] [INPUT] b.??.[LINK:https://csemoodle.ucsd.edu/filter/tex/displaytex.php?%5CTheta%28n+log+n%29] [IMG: Theta(n log n)] [INPUT] c. [LINK: https://csemoodle.ucsd.edu/filter/tex/displaytex.php?%5CTheta%28n%5E2%29] [IMG: Theta(n^2)] [INPUT] d. [LINK: https://csemoodle.ucsd.edu/filter/tex/displaytex.php?%5CTheta%28n%5E%7Blog+3%7D%29] [IMG: Theta(n^{log 3})]Question6 Marks: 1 Solving the recurrence relation [LINK: https://csemoodle.ucsd.edu/filter/tex/displaytex.php?T%28+n+%29+%3D+2+T%28%5Cfrac%7Bn%7D3%29+%2B+n] [IMG: T( n ) = 2 T(frac{n}3) + n] and [LINK: https://csemoodle.ucsd.edu/filter/tex/displaytex.php?T%281%29+%3D+1] [IMG: T(1) = 1] , we get [LINK:https://csemoodle.ucsd.edu/filter/tex/displaytex.php?T%28+n+%29+%3D+] [IMG: T( n ) =]Choose one answer.[INPUT] a.??.[LINK: https://csemoodle.ucsd.edu/filter/tex/displaytex.php?%5CTheta%28+n+%29] [IMG: Theta( n )] [INPUT] b. [LINK: https://csemoodle.ucsd.edu/filter/tex/displaytex.php?%5CTheta%28n+log+n%29] [IMG: Theta(n log n)] [INPUT] c. [LINK: https://csemoodle.ucsd.edu/filter/tex/displaytex.php?%5CTheta%28log+n%29] [IMG: Theta(log n)] [INPUT] d. [LINK:https://csemoodle.ucsd.edu/filter/tex/displaytex.php?%5CTheta%28n%5E2%29] [IMG: Theta(n^2)]Question7 Marks: 1 What is the time complexity of the merge sort algorithm? Choose one answer.[INPUT] a. [LINK: https://csemoodle.ucsd.edu/filter/tex/displaytex.php?%5CTheta%28+n+%29] [IMG: Theta( n )]??.[INPUT] b. [LINK: https://csemoodle.ucsd.edu/filter/tex/displaytex.php?%5CTheta%28n%5E2%29] [IMG: Theta(n^2)] [INPUT] c. [LINK: https://csemoodle.ucsd.edu/filter/tex/displaytex.php?%5CTheta%28n+log+n%29] [IMG: Theta(n log n)] [INPUT] d. None of the other threeQuestion8 Marks: 1 What is the time complexity to merge two sorted arrays having m and n elements respectively? Choose one answer.[INPUT] a. [LINK: https://csemoodle.ucsd.edu/filter/tex/displaytex.php?O%28m%2Bn%29] [IMG: O(m+n)] [INPUT] b. [LINK: https://csemoodle.ucsd.edu/filter/tex/displaytex.php?O%28mn%29] [IMG: O(mn)] [INPUT] c.??.[LINK: https://csemoodle.ucsd.edu/filter/tex/displaytex.php?O%28m%29] [IMG: O(m)] [INPUT] d. [LINK:https://csemoodle.ucsd.edu/filter/tex/displaytex.php?O%28+n+%29] [IMG: O( n )]Question9 Marks: 1 Assume you have a method to merge two sorted arrays with n elements each and it takes [LINK: https://csemoodle.ucsd.edu/filter/tex/displaytex.php?n%5E2][IMG: n^2] steps. What is the new time complexity of the merge sort algorithm using the new method to merge? Choose one answer.[INPUT] a.??.[LINK: https://csemoodle.ucsd.edu/filter/tex/displaytex.php?%5CTheta%28n%5E2%29] [IMG: Theta(n^2)] [INPUT] b. [LINK:https://csemoodle.ucsd.edu/filter/tex/displaytex.php?%5CTheta%28n+log+n%29] [IMG: Theta(n log n)] [INPUT] c. [LINK: https://csemoodle.ucsd.edu/filter/tex/displaytex.php?%5CTheta%28n%5E2+log+n%29] [IMG: Theta(n^2 log n)] [INPUT] d. [LINK: https://csemoodle.ucsd.edu/filter/tex/displaytex.php?%5CTheta%28+n+%29] [IMG: Theta( n )]Question10 Marks: 1 A Rubik?s cube cosists of a 3x3x3 cube with colored sides. The goal is the twist the cube such that each of the 6 sides of the cube consist of only one color. What is the time complexity to solve a Rubik?s cube? Choose one answer.[INPUT] a.??.[LINK: https://csemoodle.ucsd.edu/filter/tex/displaytex.php?%5CTheta%282%5En%29] [IMG: Theta(2^n)] [INPUT] b. [LINK:https://csemoodle.ucsd.edu/filter/tex/displaytex.php?%5CTheta%28+n%5E2+log+log+n%29] [IMG: Theta( n^2 log log n)] [INPUT] c. [LINK:https://csemoodle.ucsd.edu/filter/tex/displaytex.php?%5CTheta%28n%21%29] [IMG: Theta(n!)] [INPUT] d. [LINK: https://csemoodle.ucsd.edu/filter/tex/displaytex.php?%5CTheta%281%29] [IMG: Theta(1)]??.
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