Prove asymptotic bounds for recursion relations, Mathematics

Assignment Help:

1. (‡) Prove asymptotic bounds for the following recursion relations. Tighter bounds will receive more marks. You may use the Master Theorem if it applies.

1. C(n) = 3C(n/2) + n

2. G(n) = G(n - 1) + 1/n

3. I(n) = I(n/2) + n/ lg(n)

2. Define a (p,q)-tree as a rooted tree where every internal node has between p and q (inclusive) children. Use the Master Theorem to give asymptotic bounds for the height of the tree. You can assume both p and q are constants with 2 ≤ p ≤ q.

3. (‡) Dominos

853_domains.png

A 2 × 10 rectangle filled with ten dominos, and a 2 × 2 × 10 box filled with ten slabs.

1. A domino is a 2×1 or 1×2 rectangle. How many different ways are there to completely fill a 2 × n rectangle with n dominos?

2. A slab is a three-dimensional box with dimensions 1 × 2 × 2, 2 × 1 × 2, or 2 × 2 × 1. How many different ways are there to fill a 2 × 2 × n box with n slabs? Set up a recurrence relation and give reasonable exponential upper and lower bounds.


Related Discussions:- Prove asymptotic bounds for recursion relations

Shares and dividends, at what price a 6.25%rs 100 share be quoted when the ...

at what price a 6.25%rs 100 share be quoted when the money is worth 5%

Math, the size of my sitting room is 7metres by 6metres . i bought a rug fo...

the size of my sitting room is 7metres by 6metres . i bought a rug for covering the centre of its floor. one metre of the floor around the edge of the room is not to be covered by

X and Y Intercepts, Find the x and y intercepts for the following equations...

Find the x and y intercepts for the following equations: 3y=3x -y=-x-4 2x+3y=6 y=5

Advanced functions, writ the equation that describes the motion of a point ...

writ the equation that describes the motion of a point on the wheel that has a center of 4m off the ground, has radius of 15 cm, makes a full rotation every 10 seconds and starts a

Logarithmic functions- general properties, Logarithmic functi...

Logarithmic functions have the following general properties If y = log a x, a > 0 and a ≠1, then The domain of the function

Multiplication of two matrices, Need assignment help, Explain Multiplicatio...

Need assignment help, Explain Multiplication of two Matrices.

Saxon math, what is the are of a square that is 2 inches long and 2 inches...

what is the are of a square that is 2 inches long and 2 inches wide?

How much will it have depreciated after 2 years, The value of a computer is...

The value of a computer is depreciated over ?ve years for tax reasons (meaning that at the end of ?ve years, the computer is worth $0). If a business paid $2,100 for a computer, ho

Percentage, A person spent 12.5% of his money and then rs.1600 and then 40%...

A person spent 12.5% of his money and then rs.1600 and then 40% of the remaining,now left rs.960 with him.What is his original money?

Numerical methods, Consider the following interpolation problem: Find a q...

Consider the following interpolation problem: Find a quadratic polynomial p(x) such that p(x0) = y0 p’(x1) = y’1 , p(x2) = y2 where x0 is different from x2 and y0, y’1 , y2 a

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd