(5) T(n) = 2 T(n/2)+n/log n (6)T(n) a T(n/b) + n log n %3D (7) T(n) = log 1 + log2 + log3 + + log n + log (n+1)... + log n %3D ...

Give asymptotically tight upper and lower bounds for T (n) in each of the followingalgorithmic recurrences. Justify your answers.A. ?(?) = ?(7?/10) + ?

The possible solution to the recurrence relation T(n)= 2T(n/4) + 1     a θ(n)   b θ(n2)   c θ(nlgn)   d θ(√n)

Algorithms

Solve the first-order linear recurrence relation: Sn+1 = Sn + 2, with S0=1. You may use the general solution given on P.342.

Express the solution in big-O terms for the following recurrence relation: T(n) = 9*T(n/3) + n^3; T(1)=1; Answer: T(n) = O(......) .

Let ap = 1, an = an-1 + 3 be the recurrence relation of algorithm A and T(1) = 1, T(n) = T(n/5)+n be the recurrence relation of algorithm B. 1. Find the solution for both relations. Use any method.

Express the solution in big-O terms for the following recurrence relation: T(n) = 9*T(n/3) + n^3; T(1)=1; Answer: T(n) = O(......) .

Give asymptotically tight upper and lower bounds for T (n) in each of the followingalgorithmic recurrences. Justify your answers.E. ?(?) = 3?((?/3) - 2) + ?/2 (Hint: think about how you can use an assumptionabout the importance of the -2 to apply the Masters Theorem)

Develop a closed form solution for the recurrence relation: P(n) = 5 if n = 0, P(n) = P(n-1)+3 if n > 0 Prove the closed form solution is valid for all n