(1) Solve following recurrence using substitution method: nT(n-1), if n > 1 if n = 1...

 

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(1) Solve following recurrence using substitution method: nT(n-1), if n > 1 if n = 1 T(n-1)+logn, if n> 1 T(n) = 1, T(n): = 1, if n = 1 3T (n/2)+n, if n>1 T(n) = 1, if n = 1 (2) Solve following recurrence using Master Theorem: T(n) = Tn)+logn, ifn>1 if n = 1 (3) Solve following recurrence using recursion tree method: .T(n) = 2T(n/2) + cn (4) We had a detailed analysis of select(A,k) problem in this module. Based on what you learned from this problem, analyse the complexity of Quick Sort Algorithm. Note, quick sort will lead to unbalanced sub-problems (much like select(A,k)) problem. You are expected to use either Akra-Baazi or induction method to solve the recurrence. (1) Solve following recurrence using substitution method: nT(n-1), if n > 1 if n = 1 T(n-1)+logn, if n> 1 T(n) = 1, T(n): = 1, if n = 1 3T (n/2)+n, if n>1 T(n) = 1, if n = 1 (2) Solve following recurrence using Master Theorem: T(n) = Tn)+logn, ifn>1 if n = 1 (3) Solve following recurrence using recursion tree method: .T(n) = 2T(n/2) + cn (4) We had a detailed analysis of select(A,k) problem in this module. Based on what you learned from this problem, analyse the complexity of Quick Sort Algorithm. Note, quick sort will lead to unbalanced sub-problems (much like select(A,k)) problem. You are expected to use either Akra-Baazi or induction method to solve the recurrence.