Question

design an algorithm that given two expression trees determines whether one represents a subexpression of the other. a subexpression is a part of an expression that is by itself a correct expression

Answer 1

To determine if one expression tree contains another as a subexpression, perform a depth-first traversal of the first tree, and at each node, initiate a matching procedure with the second tree. If a match is found, return true, otherwise, return false after the traversal.

Step-by-step explanation:

To design an algorithm that given two expression trees determines whether one represents a subexpression of the other, you must traverse both trees and compare their structures and node values. A subexpression is a part of an expression that is, by itself, a correct expression, and it can occur as any subtree within the larger expression tree.

Algorithm:

1. Perform a depth-first traversal of the first expression tree.
2. At each node, initiate a matching procedure with the root of the second expression tree.
3. The matching procedure involves comparing the current node of the first tree to the current node of the second tree and recursively checking if the children match as well.
4. If a complete match is found, return true indicating that the second tree is a subexpression of the first tree.
5. If the traversal of the first tree is complete without a match, return false.

This algorithm checks all possible subtrees of the first tree to see if they match the second tree, ensuring that a subexpression, if it exists, will be identified.