Use the method of forward substitutions to solve the recurrence
T(n) = 1 + 3 T(n − 1) for n ≥ 1 , T(0) = 0.
T(n) = 3T(n-1) + 1 = 3(3T(n-2) + 1) + 1 = 3(3(3T(n-3) + 1) + 1) + 1 = 3^3T(n-3) + 3^2 + 3^1 + 1 = 3^nT(1) + 3^n-1 + ... + 1 = 3^n + 3^n-1 + ... + 1 = (3^(n+1) - 1) / 2 so, T(n) = O(3^n) Answer: T(n) = O(3^n)
Use the method of forward substitutions to solve the recurrence T(n) = 1 + 3 T(n...
Solve the following recurrence using the master method: 1))2, with T(0) = 2 T(n) (T(n
solve the recurrence relation using the substitution method: T(n) = 12T(n-2) - T(n-1), T(1) = 1, T(2) = 2.
Use generating functions to solve the following recurrence. T(0) = 0, T(1) = 1. T(n) = 7 T(n-1) – 12 T(n-2)
Solve the recurrence relation using a recursion tree AND substitution method: T(n) = T(n-1) + 10n
Solve the recurrence relation using a recursion tree AND substitution method: T(n) = 2T(n - 1) + 10n.
Solve exactly using the iteration method the following recurrence T(n) = 2T(n/2) + 6n, with T(8) = 12. You may assume that n is a power of two. Please explain your answer. (a) (20 points) Solve exactly using the iteration method the following recurrence T(n) - 2T(n/2) + 6n, with T(8)-12. You may assume that n is a power of two.
Algorithm Question: Problem 3. Solve the recurrence relation T(n) = 2T(n/2) + lg n, T(1) 0.
Let T(1) = 2, T(n) = 4T(n/2) + 2n use subsition to solve this recurrence problem.
19. Solve the following recurrence equations using the characteristic equation o) T(n)2T(3o n> 1, n a powver of 3 T(1) 0 (b) T(n)-0n> 1, n a per of 5 T(1) =0 (c) nT (n)- (n 1)T(n-1)+3 for > 1 T (1) 1 (d) 'aT (n) = 3 (n-1 )T (n-1)-2 (n-2)T (n-2) + 4n T (0) = 0 T(1)=0 for n > 1 ##Solve for D only 19. Solve the following recurrence equations using the characteristic equation o) T(n)2T(3o n>...
1. Solve the recurrence relation T(n) = 2T(n/2) + n, T(1) = 1 and prove your result is correct by induction. What is the order of growth? 2. I will give you a shortcut for solving recurrence relations like the previous problem called the Master Theorem. Suppose T(n) = aT(n/b) + f(n) where f(n) = Θ(n d ) with d≥0. Then T(n) is: • Θ(n d ) if a < bd • Θ(n d lg n) if a = b...