Question: Question 1: (20 Marks] There are two algorithms for a problem. The running time of Algorithm I is expressed as T(n) = 3T(n 2) +

Question 1: (20 Marks] There are two algorithms for a problem.

Question 1: (20 Marks] There are two algorithms for a problem. The running time of Algorithm I is expressed as T(n) = 3T(n 2) + 0(1) and the running time of Algorithm II is expressed as T(n) = 3T (n/2) + O(n). Is the running time of Algorithm II smaller than that of Algorithm I for large values of n? Justify. (Here, n represents the size of the input and we can assume that T(1) = 0(1).) Question 1: (20 Marks] There are two algorithms for a problem. The running time of Algorithm I is expressed as T(n) = 3T(n 2) + 0(1) and the running time of Algorithm II is expressed as T(n) = 3T (n/2) + O(n). Is the running time of Algorithm II smaller than that of Algorithm I for large values of n? Justify. (Here, n represents the size of the input and we can assume that T(1) = 0(1).)

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