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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
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.
Describe Multiplication and Division Equations? Multiplication Equations : To solve multiplication equations, divide both sides of the equation by the number being multiplie
If d is the HCF of 30, 72, find the value of x & y satisfying d = 30x + 72y. (Ans:5, -2 (Not unique) Ans: Using Euclid's algorithm, the HCF (30, 72) 72 = 30 × 2 + 12
Terminology related to division : A good way to remedy this situation is to familiarise children with these concepts in concrete, contexts, to start with. For instance, if a chi
Using R function nlm and your code from Exercise E1.2, write an R function called pois.mix.mle to obtain MLEs of the parameters of the Poisson mixture model.
LAST COST METHOD
a ,b,c are complex numbers such that a/1-b=b/1-c=c-1-a=k.find the value of k
The students at Norton School were asked to name their favorite type of pet. Of the 430 students surveyed, 258 said in that their favorite type of pet was a dog. Assume that only 1
Ask question #Minimum 100 words accepted what is a ratio
What are Factor Trees explain? In algebra, we often need to factor a number into its prime factors. One way to do this is to use a factor tree. This is a network of numbers, st
Q. What is set theory? Define universal set? Ans. The universe , or universal set , written as U , is the set that contains all elements being considered in a given dis
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