An Alogrithmn for Efficient Closest Pairs of Points has a recurrence: T(h) = 2 T (n / 2) + f (n) , F(n) episilon theta (n) . Find the complexity of T(n)
An Alogrithmn for Efficient Closest Pairs of Points has a recurrence: T(h) = 2 T (n...
FOR ALGORITHM A WORST CASE TIME COMPLEXITY IS DESCRIBED BY RECURRENCE FORMULA T(n)= n/ T (n )thi T (c)=1 if c < 100 FOR ALGORITHM B WORST TIME COMPLEXITY IS DESCRIBED BY RECURRENCE FORMULA T(n) = 2T (2/2) + n/logn ; (c) = 1 fc 2100 WHICH ALGORITHM IS ASYMPTOTICALLY FASTER? WHY?
given the following recurrence find the growth rate of t(n) using master theorem T(n) = 16(T) n/2 + 8n^4 + 5n^3 + 3n+ 24 with T(1) = Theta(1)
Consider the following recurrence T(n) = 3T(n/5) + c What is the complexity of T(n) in Big O? ___________.
1. (25 points) Given the recurrence relations. Find T(1024). 2 T(n) = 2T(n/4) + 2n + 2 for n> 1 T(1) = 2
Consider the algorithm to find the closest pair of points in the plane. Let's say you wanted to generalize the algorithm to find the two closest pairs of points in the plane given a set of (unsorted) points (p1, py. Give an algorithm for finding the two distances for this pair. In the step to conquer the two subproblems, you must explain why your algorithm is guaranteed to find the correct result. You do not need to specify the best...
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.
(15 pts) 1. Create the recursion tree for the recurrence T(n)-T(2n/5)T3n/5) O(n). Show total complexity
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...
4. Suppose T (n) satisfies the recurrence equations T(n) = 2 * T( n/2 ) + 6 * n, n 2 We want to prove that T (n)-o(n * log(n)) T(1) = 3 (log (n) is log2 (n) here and throughout ). a. compute values in this table for T (n) and n*log (n) (see problem #7) T(n) | C | n * log(n) 2 4 6 b. based on the values in (a) find suitable "order constants" C and...
7. What is the worst-case running time complexity of an algorithm with the recurrence relation T(N) = 2T(N/4) + O(N2)? Hint: Use the Master Theorem.