A binary tree is full if all of its vertices have either zero or two children. Let Bn denote the number of full binary trees with n vertices.

(a) By drawing out all full binary trees with 3, 5, or 7 vertices, determine the exact values of B3, B5, and B7. Why have we left out even numbers of vertices, like B4?
(b) For general n, derive a recurrence relation for Bn.
(c) Show by induction that Bn is (2n).

The following function returns a string of length n whose characters are all 'x'. give the order of growth (as a function of n) of the running time. recall that concatenating two strings in java takes time proportional to the sum of their lengths. public static string f(int n) { if (n == 0) return ""; if (n == 1) return "x"; return f(n/2) + f(n - n/2); } options: a) constant b) logarithmic c) linear d) linearithmic e)quadratic f)cubic g) exponential

The north and south regions had very diferent economies in the 1800s.

What is the name of the option in most presentation applications with which you can modify slide elements? 1. the option enables you to modify a slide element in most presentation applications.