Question

A full binary tree with n non leaf nodes contain

• A. ${\log }_{2}n$ nodes
• B. n+1 nodes
• C. 2n nodes
• D. 2n+1 nodes

Answer 1

Answer: (D)

2n+1 nodes

A full binary tree with n non leaf nodes contain 2n+1 nodes.

In a binary tree each non-leaf node provides two edges. The full tree contains 2*n nodes. Each non-leaf node connected to an ancestor consumes one edge, which is tree of all nodes except the root node of the tree. Henceforth it leaves * n+1 edges connected to leaves.

In a binary tree, a tree where each non-leaf node has exactly two sons - number of leaves is n+1. Total number of nodes is 2n+1.

A full binary tree is a tree in which every node other than the leaves has two children. A complete binary tree is a binary tree in which every level, except possibly the last, is completely filled, and all nodes are as far left as possible.