Arithmetic Evaluation

Use the AStack class defined in Page 122 to implement the below expression evaluation algorithm in the main() function. In addition to the final evaluation result, you also need to print out contents of the two stacks each time when any stack's content changes. Please hard code "2 * 3 - 48/4 4 * 5" in your implementation as the input to the algorithm and generate the outputs.

Algorithm for Parsing Arithmetic Expression

Two stacks are required, one for numbers and the other for operators. The algorithm is:

For each item in the infix expression (no parenthesis) from the left to the right:

• If the item is a number then push it on the number stack and go to pick a new item (back to the 'for' loop);
• While the item is an operator (+,-,, or /) and the operator stack is not empty and the operator on the top of the stack is not lower in priority than the item (+ or -are lower in priority than and /), then
  • Pop an operator from the operator stack.
  • Pop two numbers off the number stack.
  • Calculate using second number-operator-first number.
  • Push the result on the number stack.
• Push the item on the operator stack.

After the loop, while the operator stack is not empty

• Pop an operator from the operator stack.
• Pop two numbers off the number stack.
• Calculate using second number-operator-first number.
• Push the result on the number stack.

The answer is the last item in the number stack.