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Explanation: A binary tree, which is completely filled, with the possible exception of the bottom level, which is filled from left to right is called complete binary tree. A Tree in which each node has exactly zero or two children is called full binary tree.

Theorem: Let T be a nonempty, full binary tree Then: (a) If T has I internal nodes, the number of leaves is L = I + 1. (b) If T has I internal nodes, the total number of nodes is N = 2I + 1. (c) If T has a total of N nodes, the number of internal nodes is I = (N – 1)/2.

Search Operation Whenever an element is to be searched, start searching from the root node. Then if the data is less than the key value, search for the element in the left subtree. Otherwise, search for the element in the right subtree. Follow the same algorithm for each node.

In a full binary tree every node has either 0 or 2 child nodes. In a complete binary tree, all levels are completely filled except possibly the last level. There is no particular sequence for filling in nodes. All nodes should be on the left. This means that there is no node that has a right child but not a left child.

A binary search tree is a rooted binary tree in which nodes are arranged in strict total order in which the nodes with keys greater than any particular node A is stored on the right sub-trees to that node A and the nodes with keys equal to or less than A are stored on the left sub-trees to A, satisfying the binary ...

A full binary tree is defined as a binary tree in which all nodes have either zero or two child nodes. Conversely, there is no node in a full binary tree, which has one child node.

To be a binary search tree, for every node, all of the nodes in its left tree must be <= the node, and all of the nodes in its right subtree must be > the node.