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

Calculate the height of the tunnel and the perimeter, The adjoining figure...

The adjoining figure shows the cross-section of a railway tunnel. The radius of the tunnel is 3.5m (i.e., OA=3.5m) and ∠AOB=90 o . Calculate : i.       the height of the

Calcilate the height of the cone of which the bucket , A bucket of height 8...

A bucket of height 8 cm and made up of copper sheet is in the form of frustum of right circular cone with radii of its lower and upper ends as 3 cm and 9 cm respectively. Calculate

Word problems fraction, Savannah''s mom made a fruit smoothie that tasted s...

Savannah''s mom made a fruit smoothie that tasted so good. She put in one-fourth of a cup of diced apples, one-fifth of a cup of sliced oranges, along with half of a cup of yogurt

Montel''s Theorem, In 5 pages, please try to prove Theorem 3 based on Monte...

In 5 pages, please try to prove Theorem 3 based on Montel''s Theorem. please use "Latex" Knuth Donald to write this paper. It is known that Theorem 3 on page 137 of the attached

Standard basis vectors - calculus, Standard Basis Vectors The vector th...

Standard Basis Vectors The vector that is, i = (1, 0,0) is called a standard basis vector.  In three dimensional (3D) space there are three standard basis vectors, i → = (1

LINEAR EQUATIONS, SOLVE THE inequation 0>-5 -X AND X Belongs TO R .Represen...

SOLVE THE inequation 0>-5 -X AND X Belongs TO R .Represent THE SOLUTION SET ON THE NUMBER LINE

Who made clothes for, on april 26, jonh dough wrote a check#374 to Miller P...

on april 26, jonh dough wrote a check#374 to Miller Pharmacy for $16.00 , is this a deposit or withdrawal

Permutations and combinations, number of ways that a mixed doubles tennis g...

number of ways that a mixed doubles tennis game can be arranged from 7 couples if no husband and wife play in the same game is??

SURFACE AREA AND VOLUMES, Metallic spheres of radii 6 centimetre, 8 centime...

Metallic spheres of radii 6 centimetre, 8 centimetre and 10 centimetres respectively are melted to form a single solid sphere. Find the radius of the resulting sphere.

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