Solve for recurrence exactly. Do not use asympotic notation and
please show (and explain!) all of your work.
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Solve for recurrence exactly. Do not use asympotic notation and please show (and explain!) all of...
Solve exactly using the iteration method the following
recurrence T(n) = 2T(n/2) + 6n, with T(8) = 12. You may assume that
n is a power of two.
Please explain your answer.
(a) (20 points) Solve exactly using the iteration method the following recurrence T(n) - 2T(n/2) + 6n, with T(8)-12. You may assume that n is a power of two.
1. Show how to explicitly solve the recurrence equation below (that is, do not simply quote the Master theorem). T(n) T(n/2) +n2, T(1) 1
1. Show how to explicitly solve the recurrence equation below (that is, do not simply quote the Master theorem). T(n) T(n/2) +n2, T(1) 1
Subject: Algorithm
solve only part 4 and 5 please.
need urgent.
1 Part I Mathematical Tools and Definitions- 20 points, 4 points each 1. Compare f(n) 4n log n + n and g(n)-n-n. Is f E Ω(g),fe 0(g), or f E (9)? Prove your answer. 2. Draw the first 3 levels of a recursion tree for the recurrence T(n) 4T(+ n. How many levels does it have? Find a summation for the running time. (Extra Credit: Solve it) 3. Use...
Set up a function can be written as: (si = if)
(a) Solve exactly the recurrence when n is the power of 2, using
the method of the characteristic equation and show your steps.
(Start by asking n = 2k.)
(b) Explain how to derive the exact order of T (n), i.e., Θ (T
(n)), expressed simply.
si n 1 si n 2 77 (n/2]) — 10Т(n/4]) — %п si п > 2. 1 T(п) —D { 8
si n...
solve using only one of the following methods: unrolling
substitution, recurrence tree. Please show all your work!
Please solve using only any of the following methods: unrolling substitution or recurrence tree (i.e tree diagram). Please show you. work! 74. |TCn3Tn-1)+ 1| if nz1, TCEB
Algorithms:
Please explain each step! Thanks!
(20 points) Use the Master Theorem to solve the following recurrence relations. For each recurrence, either give the asympotic solution using the Master Theorem (state which case), or else state the Master Theorem doesn't apply (d) T(n) T() + T (4) + n2
(20 points) Use the Master Theorem to solve the following recurrence relations. For each recurrence, either give the asympotic solution using the Master Theorem (state which case), or else state the...
1. [12 marks] For each of the following recurrences, use the “master theorem” and give the solution using big-O notation. Explain your reasoning. If the “master theorem” does not apply to a recurrence, show your reasoning, but you need not give a solution. (a) T(n) = 3T(n/2) + n lg n; (b) T(n) = 9T(3/3) + (n? / 1g n); (c) T(n) = T([n/41) +T([n/4])+ Vn; (d) T(n) = 4T([n/7])+ n.
06. Do any two of the following three parts Q6(a). Solve the following recurrence relation; Q6(b). Find a recurrence relation for an, which is the number of n-digit binary sequences with no pair of consecutive 1s. Explain your work. Q6(c) Solve the following problem using the Inclusion-Exclusion formula. How many ways are there to roll 8 distinct dice so that all the six faces appear? Hint: Use N(A'n n. NU)-S-,-1)' )-S-S2+S-(-1)Sn U- All possible rolls of 8 dice, Aj-Roll of...
(1) (1) (a) (14 pts.) Solve the following recurrence relation with the method of the charac- teristic equation: T(n) = 4T(n/2) + (n/2), for n > 1, n a power of 2 T(1) = 1 Determine the coefficients. (b) (1 PT.) What is the big O) order of the solution as a function of n? (c) (5 PTS.) Verify your solution by substituting back in the recurrence relation. (ii) (10 PTS.) Solve using the method of the characteristic equation to...
6. What is the asymptotic solution to the recurrence relation T(n) = 3T(n/2)+n3 log(n)? please explain