GATE CS 1991 Q01 — Trees

The Weighted External Path Length (WEPL) of a binary tree is defined as the sum of the products of the weights of the external nodes (leaves) and their respective depths (distance from the root):

From the given binary tree, we identify the weights of the leaf nodes and their corresponding depths:

• Leaves at depth $4$: weights $2$ and $4$
• Leaves at depth $3$: weights $5$, $7$, $8$, and $10$
• Leaf at depth $2$: weight $15$

Substituting these values into the formula: