3. Use a stack to evaluate the following postfix expression.\[3 \, 5 \, 7 \, + \, 2 \, 1 \, - \, * \, 1 \, + \, +\]To evaluate this postfix expression, follow these steps using a stack:1. **Read** the expression from left to right.2. **Push operands** (numbers) onto the stack.3. **Apply operators** to the top elements on the stack and push the result back on the stack.Detailed Steps:- **Push** 3: Stack [3]- **Push** 5: Stack [3, 5]- **Push** 7: Stack [3, 5, 7]- **Apply '+'**: Pop 7 and 5, push 12: Stack [3, 12]- **Push** 2: Stack [3, 12, 2]- **Push** 1: Stack [3, 12, 2, 1]- **Apply '-'**: Pop 1 and 2, push 1: Stack [3, 12, 1]- **Apply '*'**: Pop 1 and 12, push 12: Stack [3, 12]- **Push** 1: Stack [3, 12, 1]- **Apply '+'**: Pop 1 and 12, push 13: Stack [3, 13]- **Apply '+'**: Pop 13 and 3, push 16: Stack [16]Final result in the stack is 16. Thus, the evaluation of the postfix expression \(3 \, 5 \, 7 \, + \, 2 \, 1 \, - \, * \, 1 \, + \, +\) is 16.

Evaluation rule of a Postfix Expression states: While reading the expression from left to right, push the element in the stack if it is an operand.Pop the two operands from the stack, if the element is an operator and then evaluate it.Expression:- 357+21-*1++ Step Input Symbol Operation Stack Calculation 1 3 Push 3 2 5 Push 3,5 3 7 Push 3,5,7 4 plus Pop(2 elements) and Evaluate 3 5+7=12 5 Push result (12) 3,12 6 2 Push 3,12,2 7 1 Push 3,12,2,1 8 munus Pop(2 elements) and Evaluate 3,12 2-1=1 9 Push result (1) 3,12,1 10 multiplication Pop(2 elements) and Evaluate 3 12*1=12 11 Push result (12) 3,12 12 1 Push 3,12,1 13 plus Pop(2 elements) and Evaluate 3 12+1 =13 14 Push result(13) 3,13 15 plus Pop(2 elements) and Evaluate Empty 3+13 = 16 16 Push result(16) 16 17 no-more elements(pop) Empty 16(Result)

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3. Use a stack to evaluate the following postfix expression. 3 5 7 + 2 1 - * 1 + +

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Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

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Question

3. Use a stack to evaluate the following postfix expression.

\[3 \, 5 \, 7 \, + \, 2 \, 1 \, - \, * \, 1 \, + \, +\]

To evaluate this postfix expression, follow these steps using a stack:

1. **Read** the expression from left to right.
2. **Push operands** (numbers) onto the stack.
3. **Apply operators** to the top elements on the stack and push the result back on the stack.

Detailed Steps:

- **Push** 3: Stack [3]
- **Push** 5: Stack [3, 5]
- **Push** 7: Stack [3, 5, 7]
- **Apply '+'**: Pop 7 and 5, push 12: Stack [3, 12]
- **Push** 2: Stack [3, 12, 2]
- **Push** 1: Stack [3, 12, 2, 1]
- **Apply '-'**: Pop 1 and 2, push 1: Stack [3, 12, 1]
- **Apply '*'**: Pop 1 and 12, push 12: Stack [3, 12]
- **Push** 1: Stack [3, 12, 1]
- **Apply '+'**: Pop 1 and 12, push 13: Stack [3, 13]
- **Apply '+'**: Pop 13 and 3, push 16: Stack [16]

Final result in the stack is 16. Thus, the evaluation of the postfix expression \(3 \, 5 \, 7 \, + \, 2 \, 1 \, - \, * \, 1 \, + \, +\) is 16.

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