Use the recursion tree method to determine the asymptoticupper
bound of T(n).T(n) satisfies the recurrence T(n)=2T(n-1)+ c, where
c is a positive constant, andT(0)=0.
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
Solve the recurrence equations by Substitution
a) T(n) = 4T (n/2) + n, T (1) = 1
b) T(n) = 4T (n/2) + n2 , T (1) = 1
c) T(n) = 4T (n/2) + n3 , T (1) = 1
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
Use a recursion tree to determine a good asymptotic upper bound
on the recurrence ?(?) = 3?(?/3) + ?. Use the substitution method
to verify your answer.
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