Let B(n) represent the number of different binary trees with n nodes. a. Define B(0) to
Chapter 6, Problem 53(choose chapter or problem)
Let B(n) represent the number of different binary trees with n nodes. a. Define B(0) to have the value 1 (there is one binary tree with 0 nodes). Prove that B(n) is given by the recurrence relation B(1) = 1 B(n) = n1 k=0 B(k)B(n 1 k) b. Compare the sequence B(n) to the sequence of Catalan numbers (Exercise 97, Section 4.4). Write the closed-form expression for B(n). c. Compute the number of different binary trees with 3 nodes. Draw all these trees. d. Compute the number of different binary trees with 6 nodes.
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