Prove by structural induction that a 2–3 tree of height h has at least 2h leaves and at most 3h leaves. (Therefore a 2–3 tree that contains n leaf nodes has height between log3 n and log2 n.) A 2–3–4...

Prove by structural induction that a 2–3 tree of height h has at least 2h leaves and at most 3h leaves. (Therefore a 2–3 tree that contains n leaf nodes has height between log3 n and log2 n.)

A 2–3–4 tree is a similar data structure to a 2–3 tree, except that a tree can be a single node or a node with 2, 3, or 4 subtrees. Give a formal recursive definition of a 2–3–4 tree, and prove that a 2–3–4 tree of height h has at least 2h leaves and at most 4h leaves