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
1. For each of the following, prove using the definition of
O(·):
(a) 7n + log(n) = O(n)
(b) n2 + 4n + 7 = O(n2 )
(c) n! = O(nn)
(d) 2n = O(22n)
Please explain the procedure clearly for all (They are of the
same question)
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
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
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). a. T(n) = 2T(n/2) + √n b. T(n) = 8T(n/2) +
n2 c. T(n) = 16T(n/2) + n4 d. T(n) = 7T(n/3)
+ n e. T(n) = 9T(n/3) + n3.1