A binomial tree is a special kind of rooted tree used for various data structure

Question

A binomial tree is a special kind of rooted tree used for various data structures in computer science. A degree d binomial tree can be defined recursively as follows. A degree 0 binomial tree is a single vertex with no edges. A degree d binomial tree has a root vertex with out-degree d. The first (that is, leftmost) subtree is a degree d - 1 binomial tree. The second (that is. second to left) subtree is a degree d - 2 binomial tree. Continue on in this way so that the last (rightmost) subtree is a degree 0 binomial tree. Draw binomial trees of degree 1, 2, 3, and 4. What is the height h(d) of a degree d binomial tree? Prove your result by induction on d. Write a recurrence for the number of nodes n(d) in a binomial tree of degree d. Use the guess-and-check method to guess a formula for n(d). Prove that your formula holds by induction on d.

Explanation / Answer

There is a theorem which proves that the height of a degree d in a binomial tree by applying iduction on d

The height of Bk, the binomial tree of order k, is k.

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