Question: Problem 4 (20 points). Given the recurrence relation of the running time for a recursive algorithm, prove by induction that T(n) O(n), i.e. T(n) Scnloga(n)

Problem 4 (20 points). Given the recurrence relation of the running

Problem 4 (20 points). Given the recurrence relation of the running time for a recursive algorithm, prove by induction that T(n) O(n), i.e. T(n) Scnloga(n) for some positive constants c and initial input no T(n)- 2T(n/3)+n, T(3) 10 n>3 Problem 5 (20 points). Given the recurrence relation of the running time for a recursive algorithm, prove by induction that T(n) o(n), i.e. T(n) s cn for some positive constants c and initial input no T(n) 3T(n/2)+n3, T(1) 1 n> 1 Problem 6 (15 points). Given a recurrence relation, use a recursion tree to analyze the running time: T(n) 2T(n/3)+n T(3)-10 n>3 Problem 7 (15 points). Given a recurrence relation, use a recursion tree to analyze the running time: T(n) 2T(n/2)+n, T(1) 1 n> 1

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