Problems 12.4 page 306 in the textbook introduction to algorithms by cormen 3rd

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Problems 12.4 page 306 in the textbook introduction to algorithms by cormen 3rd edition Quest) Let bn denote the number of different binary trees with n nodes. In this problem, you will find a formula for bn, as well as an asymptotic estimate. a. Show that b0 = 1 and that, for n = 1, bn=Sbk.bn-1-k for sigma running k=0 to n-1 b. Referring to Problem 4-4 for the definition of a generating function, let B(x) be the generating function Show that B(x) = xB(x)2 + 1, and hence one way to express B(x) in closed form is B(X)=1/2x(1-v(1-4x)) The Taylor expansion of f(x) around the point x = a is given by f(x)=(Sfk(a)/factorial(k)) * (x-a)k where f(k)(x) is the kth derivative of f evaluated at x. c. Show that bn=4n/(vtn3/2) *(1+O(1/n)) d. Show that

Explanation / Answer

this pdf file has a complete answer [PDF] Solution wwwmayr.in.tum.de/lehre/2007WS/fa-cse/.../tutorial06-solutions.pdf

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