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 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.
a) Find the recurrence relation for the number of ways to
arrange flags on an n foot flagpole with 1 foot high red flags, 2
feet high white flags and 1 foot high blue flags.
b) solve the recurrence relation of part a
consider the linear non-homogeneous recurrence relation of order
three x(n)+x(n-1)-4x(n-2)-4x(n-3)=16
find the eigenvalues of the recurrence relation, the closed form
solution, and based on the dominant Eigen value determine if x(n)
has longterm exponential growth