A complete binary tree is a full binary tree in which every leaf is at the same

Question

A complete binary tree is a full binary tree in which every leaf is at the same level. The set of complete binary trees is defined recursively by: Basis step: A single vertex is a complete binary tree. Recursive step. A complete binary tree T-T-T2 consists of a new root r together with edges connecting the r to each of the roots, r1 and r2, of two complete binary trees, T, (the left subtree) and T2 (the right subtree) respectively, where Ti and T2 have the same height. A balanced binary tree is a binary tree in which every leaf is either at level I or 1-1 for some positive integer I. The set of balanced binary trees is defined recursively by: Basis step: A single vertex is a balanced binary tree. The tree with two vertices, namely a root and a left child (a leaf) is a balanced binary tree. The tree with two vertices, namely a root and a right child (a leaf) is a balanced binary tree Recursive step. A balanced binary tree T-T1·T2 consists of a new root r together with edges connecting the r to each of the roots, ri and r2, of two balanced binary trees, T1 (the left subtree) and T2 (the right subtree), respectively, where the leaves of Ti and T2 are at either level lor -1 for some positive integer I.

Explanation / Answer

Full binary tree: Binary tree in which each node has either zero or two children

Basic step: A single vertex is a full & balanced binary tree. A tree with three vertices, namely a root and a left child(a leaf) and a right child(a leaf) is also a full & balanced binary tree.

Recursive step: A full & balanced binary tree T = T1 * T2 consists of a new root r together with edges connecting the r to the each roots r1 and r2 of two full & balanced binary trees, T1(the left subtree) and T2(the right subtree), respectively, where the leaves of T1 and T2 are either level l or l-1 for some positive integer l.

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