In a simple binary tree with n nodes, how many edges does it contain?

In a simple binary tree with n nodes, how many edges does it contain?

• A. n - 1
• B. n
• C. n + 1
• D. 2n - 2

Answer: (A)

A tree with n nodes has exactly n-1 edges. In a binary tree, every node except the root is connected to its parent by one edge, so the total number of edges equals the number of non-root nodes, which is n-1. This reflects that a connected acyclic graph with n nodes always needs exactly n-1 connections to tie all the nodes together. The other options would require extra edges that would either create cycles or unnecessary connections, which a tree structure prohibits.

A tree with n nodes has exactly n-1 edges. In a binary tree, every node except the root is connected to its parent by one edge, so the total number of edges equals the number of non-root nodes, which is n-1. This reflects that a connected acyclic graph with n nodes always needs exactly n-1 connections to tie all the nodes together. The other options would require extra edges that would either create cycles or unnecessary connections, which a tree structure prohibits.