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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.
Geometric Interpretation of the Cross Product There is as well a geometric interpretation of the cross product. Firstly we will let θ be the angle in between the two vectors a
encoded with the matrix -3 -7 and 4 9. what lights up a soccer stadium? ecoded message: {-3 - 7} {3 2 } {3 6} {57 127} {52 127} {77 173} {23 51)
Graph y = sin ( x ) Solution : As along the first problem in this section there actually isn't a lot to do other than graph it. Following is the graph. From this grap
Variable stars are ones whose brightness varies periodically. One of the most visible is R Leonis; its brightness is modelled by the function where t is measured in days.
A girl has 25 plants in all, 8 of them are tomatos. She has 10 more bean plants than pepper plants. How many pepper plants does she have?
A telephone dialled is numbered 0to9. if 0is dialled first the caller is connected to the international exchange system.find the number of local calls that can be rung if a local n
write a program C++ programming language to calculate simple interest, with it algorithm and it flowchart
sin 51+cos 81
The number of integral pairs (x,y) satisfying the equation x^2=y^2+1294 is a)2 b)3 c)4 d)None of these
reflection
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