Question

Given the postfix expression: 562+∗124/ - What is the value obtained after the evaluation is performed using the stack implementation? A. 37 B. −37 C. 40 D. 3

Answer 1

To evaluate the given postfix expression using a stack, follow the steps of scanning the expression, pushing numbers onto the stack and performing operations on the top two elements when encountering operators. The result is obtained by evaluating the postfix expression using a stack implementation.

Step-by-step explanation:

To evaluate the given postfix expression using a stack implementation, we follow these steps:

1. Create an empty stack.
2. Scan the postfix expression from left to right.
3. If the current element is a number, push it onto the stack.
4. If the current element is an operator (+, -, *, /), pop the top two elements from the stack and perform the operation on them.
5. Push the result back onto the stack.
6. Repeat steps 3-5 until all elements have been processed.
7. The final result will be the top element of the stack.

Applying these steps to the given postfix expression:

1. Starting with an empty stack, we encounter '5' and '6'. We push them onto the stack.
2. We encounter '+'. We pop '6' and '5' from the stack, perform the addition '6 + 5', and push the result '11' onto the stack.
3. We encounter '2' and '4'. We push them onto the stack.
4. We encounter '/'. We pop '4' and '2' from the stack, perform the division '4 / 2', and push the result '2' onto the stack.
5. We encounter '*'. We pop '2' and '11' from the stack, perform the multiplication '2 * 11', and push the result '22' onto the stack.
6. We encounter '1' and '2'. We push them onto the stack.
7. We encounter '/'. We pop '2' and '1' from the stack, perform the division '2 / 1', and push the result '2' onto the stack.
8. We encounter '-'. We pop '2' and '22' from the stack, perform the subtraction '2 - 22', and push the result '-20' onto the stack.

The final result of the evaluation is '-20'.

Answer 2

Based on the above, the value obtained after evaluating the postfix expression 5 6 2 + ∗ 12 4 / - using the stack implementation is option B-37.

In postfix evaluation, the operation is scanned from left to right. The first operator encountered is '+'. Applying this to the two preceding operands, we obtain the expression:

`\(5 * (6 + 2) * 12 / 4 -\)`

So, by Simplifying further:

`\(40 * 12 / 4 -\)`

Now, the first operator encountered is '/'. Applying this to the preceding operands, we obtain the expression:

`\(40 / 3 -\)`

Therefore, The result is:

-
`\(37\)`

See text below

Given the postfix expression:

5 6 2 + ∗ 12 4 / -

What is the value obtained after the evaluation is performed using the stack implementation? A. 37 B. −37 C. 40 D. 3