Solve the following recurrence relations: (find an asymptotic upper bound O(?) for each one) a. T(n)...

Solve the following recurrence relations: (find an asymptotic upper bound O(?) for each one)

a. T(n) = T(2n/3)+T(n/3) + n^2

b. T(n) = √nT(√n) + n

c. T(n) = T(n-1)+T(n/2) + n

The base case is that constant size problems can be solved in constant time (O(1)). You can use the induction, substitution or recursion tree method

Expert Solution

venereology answered 1 month ago

Use a recursion tree to determine a good asymptotic upper bound on the recurrence T(n) =...

Use a recursion tree to determine a good asymptotic upper bound on the recurrence T(n) = 2T(n/3) + 2n. Use the substitution method to verify your answer

Use a recursion tree to determine a good asymptotic upper bound on the recurrence ?(?) =...

Use a recursion tree to determine a good asymptotic upper bound on the recurrence ?(?) = 3?(?/3) + ?. Use the substitution method to verify your answer.

6. Solve the following recurrence relations t(n) = t(n-1) + 3 for n>1 t(1) = 0...

6. Solve the following recurrence relations t(n) = t(n-1) + 3 for n>1 t(1) = 0 t(n) = t(n-1) + n for n>1 t(1) = 1 t(n) = 3t(n/2) + n for n>1, n is a power of 2 t(1) = ½ t(n) = 6t(n-1) – 9t(n-2) for n>1 t(0) = 0 t(1) = 1

Prove the upper and lower bound of T(n) = T(n/3) + T(2n/3) + O(n)

1. Using domain and range transformations, solve the following recurrence relations: a) T(1) = 1, T(n)...

1. Using domain and range transformations, solve the following recurrence relations: a) T(1) = 1, T(n) = 2T(n/2) + 6n - 1 b) T(1) = 1, T(n) = 3T(n/2) + n^2 - n

Solve the following recurrence relations. a. x(n) = x(n − 1) + 3 for n >...

Solve the following recurrence relations. a. x(n) = x(n − 1) + 3 for n > 1, x(1) = 0 b. x(n) = 5x(n − 1) for n > 1, x(1) = 6 c. x(n) = x(n/5) + 1 for n > 1, x(1) = 1 (solve for n = 5k )

Give asymptotic upper and lower bounds for T(n). Assume that T(n) is constant for n <=...

Give asymptotic upper and lower bounds for T(n). Assume that T(n) is constant for n <= 2. Make your bounds as tight as possible, and justify your answers. T(n) = T(n-2) + n^2

Give upper and lower bounds for T(n) in the following recurrence: T(n) = 3T(n/4) + n

- Solve the following recurrence relation : T(n) = T(αn) + T((1 − α)n) + n

Show for the following recurrence that T(n) = T(n/3) + nlog(n) is O(nlog(n)) (not using the...

Show for the following recurrence that T(n) = T(n/3) + n*log(n) is O(n*log(n)) (not using the Master theorem please)

Question