Expression Trees: Understanding Binary Tree Structures

What is an expression tree?

Expression trees are considered to be a:

a. full binary tree

b. perfect binary tree

c. binary tree

d. balanced tree

Answer:

The correct answer is c. binary tree.

Expression trees are binary trees that represent arithmetic expressions. They allow us to evaluate expressions by following the order of operations defined by the tree structure.

Binary trees are trees in which each node has at most two children. In an expression tree, each node represents an operator or an operand of an arithmetic expression.

For example, let's consider the expression "3 + 4 * 2". To create the expression tree for this expression, we would start by placing the operators in their appropriate positions. The "+" operator would be at the root of the tree, with "3" as its left child and "*" as its right child. The "4" would be the left child of the "*", and "2" would be the right child. This expression tree represents the order of operations in the expression.

The "*" operator has a higher precedence than the "+" operator, so it is higher in the tree. This allows us to evaluate the expression correctly by performing the multiplication before the addition.

In summary, expression trees are binary trees that represent arithmetic expressions. They allow us to evaluate expressions by following the order of operations defined by the tree structure. So, the correct answer is c. binary tree.