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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.
Frequently, tests that yield abnormal results are repeated for confirmation. What is the probability that for a usual person a test will be at least 1.5 times as high as the upper
Assumptions and Application of T Distribution Assumptions of t distribution 1. The sample observations are random 2. Samples are drawn from general distribution 3.
I have a maths assignment as- Use a newspaper to study and give a report on shares and dividends.
The curve (y+1) 2 =x 2 passes by the points (1, 0) and (- 1, 0). Does Rolle's Theorem clarify the conclusion that dy dx vanishes for some value of x in the interval -1≤x≤1?
terminology and requirements of linear programming
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?
COMMUNICATING THE MEANING OF ADDITION : One of the characters in a novel written by the Malayalam writer Vaikom Muhammed Basheer was asked by his teacher, "How much is one and on
There are k baskets and n balls. The balls are put into the baskets randomly. If k
How can I submit a sample of my work in either teaching online or checking homework as I am retired and doing this for the first time?
3^2=8
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