Question

In the same driver class, create a binary tree for the following arithmetic expression:

((7 (4 x 12)) - ((8 - 4) x (3 2))) ((3 (4 x 2)) x (7 1));
then evaluate the value of the arithmetic expression tree. your evaluation must be based on the expression tree. your implementation should:
a. display the inorder representation of the tree
b. display the postorder representation of the tree
c. use a stack to evaluate the value of the tree based on the postorder representation of the expression. you may assume that the tree has only integer numbers.

Answer 1

To create a binary tree for the given arithmetic expression, we follow specific steps, and to evaluate the value of the expression, we can use a stack.

Step-by-step explanation:

To create a binary tree for the given arithmetic expression, we can follow these steps:

1. Create a tree node for each operand and operator of the expression.
2. Make the operand nodes leaf nodes.
3. Use the operator nodes as internal nodes and connect them to their respective operands.
4. Create the binary tree with the expression rooted at the top.

The inorder representation of the tree would be: 7 * 4 - 12 + 8 - 4 * 3 - 2 * 3 * 4 * 2 * 7 * 1. The postorder representation of the tree would be: 7 4 12 x * 8 4 - 3 2 - x 3 4 2 x * * 2 7 1 x * * *.

To evaluate the value of the arithmetic expression tree using a stack, we can follow these steps:

1. Traverse the postorder representation of the tree from left to right.
2. If the element is a number, push it onto the stack.
3. If the element is an operator, pop the top two elements from the stack, perform the operation, and push the result back onto the stack.
4. After traversing the entire postorder representation, the top element on the stack will be the final result.

In this case, the value of the arithmetic expression tree is 91.