Question

How many null links does an arbitrary binary tree with $n$ nodes have?

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

Hint:

Always remember: a tree with $n$ nodes has $n-1$ edges. In a binary tree, subtract these from the total $2n$ child pointers to find the number of null links.

Answer 1

The Correct Option is A

Step 1: Understanding binary tree links.
In a binary tree, each node has exactly two child pointers: one left child pointer and one right child pointer. Therefore, for a tree with $n$ nodes, the total number of child pointers is $2n$.
Step 2: Counting non-null links.
In any tree with $n$ nodes, there are exactly $n-1$ edges (links connecting parent and child nodes). These edges correspond to the non-null child pointers in the binary tree.
Step 3: Calculating null links.
Out of the total $2n$ child pointers, $n-1$ are non-null. Hence, the number of null links is: \[ 2n - (n-1) = n+1 \]
Step 4: Final conclusion.
Thus, an arbitrary binary tree with $n$ nodes contains exactly $n+1$ null links.