May 23, 2024
May 23, 2024
May 23, 2024
###### Question 5321 – UGC NET CS 2013 Dec-paper-2
May 23, 2024

Consider a full binary tree with n internal nodes, internal path length i, and external path length e. The internal path length of a full binary tree is the sum, taken over all nodes of the tree, of the depth of each node. Similarly, the external path length is the sum, taken over all leaves of the tree, of the depth of each leaf. Which of the following is correct for the full binary tree?

Question 526 Explanation:
→ A node’s path length is the number of links (or branches) required to get back to the root.
→ The root has path length zero and the maximum path length in a tree is called the tree’s height.
→ The sum of the path lengths of a tree’s internal nodes is called the internal path length and the sum of the path lengths of a tree’s external nodes is called the external path length.
External Path Length:

The sum over all external (square) nodes of the lengths of the paths from the root of an extended binary tree to each node. For example, in the tree above, the external path length is 25 (Knuth 1997, pp. 399-400). The internal and external path lengths are related by
E = I + 2n,
where n is the number of internal nodes.
e = i+n
e = i+2n
e = 2i+n
e = 2n+i