Solve the recurrence relation T (n) = T ( √n) + c. n > 4

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)

In recurrence relation T(n) = T(n/3)+Θ(n2), the number of sub-problems are   a 2   b n/2   c 1   d 3

Consider the following recurrence relation: T(0) = 2, T(1) = 5, T(n) = 27(n – 1) – T(n – 2) for n>1 Write out the first few values T(0), T(1), T(2),...,. Make a guess about the closed form of T(n) and then prove that it is a closed form for T(n) using induction.

Solve the recurrence relation by substitution: T(n) = T(n-1) + 2^n

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.

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

Use the substitution method to identify the big-Oh of the represented by the following recurrence relation. Note: c is a constant. T(n) = cn + T(n/2) + T(n/2), T(1) = c

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.