What is the solution to the following recurrence? T(n) = 16T(3/4)+ n T(1) = 1 T(n)...
20. (4 pts) Consider the following recurrence. an = 2an-1 + 2an-2 ao = 0 Q1 = 2V3 For what values of a and B is the following expression a solution of that recurrence? a;=a (1+ v3)*+B (1 - v3)' a = -1 and B 1 O a = = { and B :- O a = 2 and B = -2 the four other possible answers are incorrect O a = 1 and B = -1
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>...
Recurrence equations using the Master Theorem: Characterize each of the following recurrence equations using the master method (assuming that T(n) = c for n < d, for constants c > 0 and d > = 1). T(n) = c for n < d, for constants c > 0 and d greaterthanorequalto 1). a. T(n) = 2T(n/2) + log n b. T(n) = 8T(n/2) + n^2 c. T(n)=16T(n/2) + (n log n)^4 d. T(n) = 7T(n/3) + n
Using the Master Theorem discussed in class, solve the following recurrence relations asymptotically. Assume T(1) = 1 in all cases. (a) T(n) = T(9n/10) + n (b) T(n) = 16T(n/4) + n^2 (c) T(n) = 7T(n/3) + n^2 (d) T(n) = 7T(n/2) + n^2 (e) T(n) = 2T(n/4) + √n log^2n.
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...
22. (4 pts) Which one of the following recurrences is linear and homogeneous? o T(n) =T(n 2020) + 1 T(n) =T(n+1) - T(m - 2) +T(n – 3) 3 the four other possible answers are incorrect T(n) = 2T(n/2) + 4n ап = am-1 + An-1
Prove that the solution of the recurrence T(n) = T(n/2) +6(logk n) with T(1-6(1), for any integer k 2 0, is T(n) = Θ(logk+1 n) (Hint: the upper bound T(n) = O(logk+1 n) is easy; the lower bound T(n) = Ω(logk +1 n) is harder.) Prove that the solution of the recurrence T(n) = T(n/2) +6(logk n) with T(1-6(1), for any integer k 2 0, is T(n) = Θ(logk+1 n) (Hint: the upper bound T(n) = O(logk+1 n) is easy;...
6. What is the asymptotic solution to the recurrence relation T(n) = 3T(n/2)+n3 log(n)? please explain
22. (4 pts) Which one of the following recurrences is linear and homogeneous? T(n) = 2(n+1)- T(m - 2)+T(– 3) An = an-1 + an-1 T(n) = 2T(n/2) + 4n () T(n) =T(m - 2020)+1 the four other possible answers are incorrect
(1) (1) (a) (14 pts.) Solve the following recurrence relation with the method of the charac- teristic equation: T(n) = 4T(n/2) + (n/2), for n > 1, n a power of 2 T(1) = 1 Determine the coefficients. (b) (1 PT.) What is the big O) order of the solution as a function of n? (c) (5 PTS.) Verify your solution by substituting back in the recurrence relation. (ii) (10 PTS.) Solve using the method of the characteristic equation to...