Recall that an application of the Stack ADT is postfix expression evaluation. As a reminder, here is pseudocode for the algorithm: scan given postfix expression; for each symbol in postfix if operand then push its value onto a stack S; if operator then ( pop operand2; pop operand1; apply operator to compute operand1 op operand2; push result back onto stack S; return value at top of stack; Evaluate the following postfix expression: 6 5 3 + 2 12 5 % +

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### Postfix Expression Evaluation Using Stack ADT

An application of the Stack ADT (Abstract Data Type) is the evaluation of postfix expressions. The following is a pseudocode algorithm for the postfix expression evaluation:

1. **Scan the given postfix expression.**
2. **For each symbol in the postfix expression:**
   - If the symbol is an operand, push its value onto a stack (Stack S).
   - If the symbol is an operator, perform the following steps:
     - Pop the top value from the stack; assign it to `operand2`.
     - Pop the next top value from the stack; assign it to `operand1`.
     - Apply the operator to `operand1` and `operand2` (i.e., compute `operand1 op operand2`).
     - Push the result back onto the stack.
3. **Return the value that is on the top of the stack.**

#### Pseudocode:
```
scan given postfix expression;
for each symbol in postfix
    if operand
        then push its value onto a stack S;
    if operator
        then {
            pop operand2;
            pop operand1;
            apply operator to compute operand1 op operand2;
            push result back onto stack S;
        }
return value at top of stack;
```

#### Example:
Evaluate the following postfix expression: `6 5 3 + 2 12 * + 5 % +`

To solve this expression using the stack algorithm:
1. **Scan** `6` and push to the stack.

   Stack: `[6]`

2. **Scan** `5` and push to the stack.

   Stack: `[6, 5]`

3. **Scan** `3` and push to the stack.

   Stack: `[6, 5, 3]`

4. **Scan** `+` (operator); pop `3` and `5`, compute `5 + 3 = 8`, then push the result `8` back to the stack.

   Stack: `[6, 8]`

5. **Scan** `2` and push to the stack.

   Stack: `[6, 8, 2]`

6. **Scan** `12` and push to the stack.

   Stack: `[6, 8, 2, 12]`

7. **Scan** `*` (operator); pop `12` and `2`,
Transcribed Image Text:### Postfix Expression Evaluation Using Stack ADT An application of the Stack ADT (Abstract Data Type) is the evaluation of postfix expressions. The following is a pseudocode algorithm for the postfix expression evaluation: 1. **Scan the given postfix expression.** 2. **For each symbol in the postfix expression:** - If the symbol is an operand, push its value onto a stack (Stack S). - If the symbol is an operator, perform the following steps: - Pop the top value from the stack; assign it to `operand2`. - Pop the next top value from the stack; assign it to `operand1`. - Apply the operator to `operand1` and `operand2` (i.e., compute `operand1 op operand2`). - Push the result back onto the stack. 3. **Return the value that is on the top of the stack.** #### Pseudocode: ``` scan given postfix expression; for each symbol in postfix if operand then push its value onto a stack S; if operator then { pop operand2; pop operand1; apply operator to compute operand1 op operand2; push result back onto stack S; } return value at top of stack; ``` #### Example: Evaluate the following postfix expression: `6 5 3 + 2 12 * + 5 % +` To solve this expression using the stack algorithm: 1. **Scan** `6` and push to the stack. Stack: `[6]` 2. **Scan** `5` and push to the stack. Stack: `[6, 5]` 3. **Scan** `3` and push to the stack. Stack: `[6, 5, 3]` 4. **Scan** `+` (operator); pop `3` and `5`, compute `5 + 3 = 8`, then push the result `8` back to the stack. Stack: `[6, 8]` 5. **Scan** `2` and push to the stack. Stack: `[6, 8, 2]` 6. **Scan** `12` and push to the stack. Stack: `[6, 8, 2, 12]` 7. **Scan** `*` (operator); pop `12` and `2`,
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