a) Find the recurrence relation for the number of ways to
arrange flags on an n...
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.
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
find a
recurrence relation for the number of bit strings of length n that
contain two consecutive 1s. What are the initial conditions? How
many bit strings of length eight contain two consecutive
1s
1Set up and solve a recurrence relation for the number of times
the algorithm’s basic operation is executed.
2 How does this algorithm compare with the straightforward
nonrecursive algorithm for computing this function?
Consider the following recurrence relation defined only for n =
2^k for integers k such that k ≥ 1: T(2) = 7, and for n ≥ 4, T(n) =
n + T(n / 2). Three students were working together in a study group
and came up with this answer for this recurrence: T(n) = n * log2
(n) − n − log2 (n) + 8. Determine if this solution is correct by
trying to prove it is correct by induction.
1a. Consider the sequence {?? }n≥0 which starts
1,2,7,20,61,122,..., defined by the recurrence relation ?? = 2??−1
+ 3??−2 and initial conditions ?0 = 1, ?1 = 2. Solve the recurrence
relation. That is, find a closed formula for ??. Show your
work.
The abandoned field behind your house is home to a large prairie
dog colony. Each week the size of the colony triples. However,
sadly 4 prairie dogs die each week as well (after the tripling
occurs). Consider...