Let the postfix expression 3, 2, +, 7, *, 6, 5, +, 4, *, is being evaluated using a stack. What are the values on top and bottom of stack respectively, just before second + operator is evaluated?

Question

Accepted Answer

The correct option is (4):
The evaluation of a postfix expression using a stack follows a clear LIFO (Last-In, First-Out) principle, where operands are pushed onto the stack, and operators pop the required number of operands, perform the operation, and push the result back. Following the expression $3, 2, +, 7, \*, 6, 5, +, 4, *$: First, '3' and '2' are pushed, then the first '+' is encountered, resulting in $3 + 2 = 5$, which is pushed back. The stack is now $$5$$ (bottom: 5, top: 5). Next, '7' is pushed, making the stack $$5, 7$$. The '*' operator is then processed: $5 \* 7 = 35$, which is pushed back. The stack becomes $$35$$ (bottom: 35, top: 35). Finally, '6' and '5' are pushed, so the stack state **just before the second '+' operator is evaluated** is $$35, 6, 5$$. In this state, the top of the stack is 5, and the bottom is 35, which precisely matches the choice (5, 35).

The incorrect option is (1):
This option suggests the stack values are 27 (top) and 5 (bottom). This result is premature and incorrect because 27 is not an intermediate result in this specific calculation sequence up to the point of the second '+' operator. The value 5 is the correct bottom-most element only after the first operation $3+2$ is completed, but this option ignores the subsequent multiplication. The value 27 would be obtained only if the expression was $(3+2) \times 7 - 6$ or a similar combination, which is not what the given postfix notation implies at this step. Therefore, 27, 5 does not reflect the stack's state just before the second addition.

The incorrect option is (2):
This option gives values of 11 (top) and 35 (bottom). The bottom value, 35, is correct as it is the result of the first main calculation $(3+2) \times 7$. However, the value 11 for the top is incorrect. The value 11 would only be present if the operator were evaluated right away (e.g., $6+5=11$) or if the expression involved 11 as a number to be pushed. Since both '6' and '5' are separate operands that are pushed onto the stack before the operator is processed, the top element must be 5, not the result of their addition.

The incorrect option is (3):
The values 11 (top) and 27 (bottom) are incorrect for the state of the stack. As established, the bottom-most value should be 35, which is the result of the first product operation. The value 27 is not the result of any intermediate operation at this stage of the evaluation. Furthermore, the top value is incorrect because 11 is the *result* of the operation $6+5$, which has not yet been performed at the point requested by the question. Both values fail to represent the actual operands residing on the stack just prior to the second addition.