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
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
Find and solve a recurrence relation for the number of ways to stack n poker
chips using red, white and blue chips such that no two red chips are together.
Use your solution to compute the number of ways to stack 15 poker chips.
find a
recurrence relation for the number of bit strings of length n that
contain the string 10. What are the initial conditions? How many
bit strings of length eight contain the string 10