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The following postfix expression with single digit operands is evaluated using a stack:
8 2 3 ^ / 2 3 * + 5 1 * -
Note that ^ is the exponentiation operator. The top two elements of the stack after the first * is evaluated are:
Note that ^ is the exponentiation operator. The top two elements of the stack after the first * is evaluated are:
- a)6, 1
- b)5, 7
- c)3, 2
- d)1, 5
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
The following postfix expression with single digit operands is evaluat...
Answer:
To evaluate this postfix expression, we will use a stack to keep track of the intermediate results. Let's go step by step to understand the process:
1. Push 8, 2, and 3 onto the stack:
Stack: [8, 2, 3]
2. Evaluate the exponentiation operation ^:
2 ^ 3 = 8
Replace the top two elements on the stack with the result:
Stack: [8, 8]
3. Evaluate the division operation /:
8 / 8 = 1
Replace the top two elements on the stack with the result:
Stack: [1]
4. Push 2 and 3 onto the stack:
Stack: [1, 2, 3]
5. Evaluate the multiplication operation *:
2 * 3 = 6
Replace the top two elements on the stack with the result:
Stack: [1, 6]
6. Push 5 and 1 onto the stack:
Stack: [1, 6, 5, 1]
7. Evaluate the multiplication operation *:
5 * 1 = 5
Replace the top two elements on the stack with the result:
Stack: [1, 6, 5]
8. Evaluate the subtraction operation -:
6 - 5 = 1
Replace the top two elements on the stack with the result:
Stack: [1, 1]
After the first * operation is evaluated, the top two elements on the stack are 1 and 6. Therefore, the correct answer is option 'A': 6, 1.
To evaluate this postfix expression, we will use a stack to keep track of the intermediate results. Let's go step by step to understand the process:
1. Push 8, 2, and 3 onto the stack:
Stack: [8, 2, 3]
2. Evaluate the exponentiation operation ^:
2 ^ 3 = 8
Replace the top two elements on the stack with the result:
Stack: [8, 8]
3. Evaluate the division operation /:
8 / 8 = 1
Replace the top two elements on the stack with the result:
Stack: [1]
4. Push 2 and 3 onto the stack:
Stack: [1, 2, 3]
5. Evaluate the multiplication operation *:
2 * 3 = 6
Replace the top two elements on the stack with the result:
Stack: [1, 6]
6. Push 5 and 1 onto the stack:
Stack: [1, 6, 5, 1]
7. Evaluate the multiplication operation *:
5 * 1 = 5
Replace the top two elements on the stack with the result:
Stack: [1, 6, 5]
8. Evaluate the subtraction operation -:
6 - 5 = 1
Replace the top two elements on the stack with the result:
Stack: [1, 1]
After the first * operation is evaluated, the top two elements on the stack are 1 and 6. Therefore, the correct answer is option 'A': 6, 1.
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Community Answer
The following postfix expression with single digit operands is evaluat...
The algorithm for evaluating any postfix expression is fairly straightforward:
1. While there are input tokens left
o Read the next token from input.
o If the token is a value
+ Push it onto the stack.
o Otherwise, the token is an operator
(operator here includes both operators, and functions).
* It is known a priori that the operator takes n arguments.
* If there are fewer than n values on the stack
(Error) The user has not input sufficient values in the expression.
* Else, Pop the top n values from the stack.
* Evaluate the operator, with the values as arguments.
* Push the returned results, if any, back onto the stack.
2. If there is only one value in the stack
o That value is the result of the calculation.
3. If there are more values in the stack
o (Error) The user input has too many values.
o Read the next token from input.
o If the token is a value
+ Push it onto the stack.
o Otherwise, the token is an operator
(operator here includes both operators, and functions).
* It is known a priori that the operator takes n arguments.
* If there are fewer than n values on the stack
(Error) The user has not input sufficient values in the expression.
* Else, Pop the top n values from the stack.
* Evaluate the operator, with the values as arguments.
* Push the returned results, if any, back onto the stack.
2. If there is only one value in the stack
o That value is the result of the calculation.
3. If there are more values in the stack
o (Error) The user input has too many values.
Let us run the above algorithm for the given expression.
First three tokens are values, so they are simply pushed. After pushing 8, 2 and 3, the stack is as follows
First three tokens are values, so they are simply pushed. After pushing 8, 2 and 3, the stack is as follows
8, 2, 3
When ^ is read, top two are popped and power(2^3) is calculated
8, 8
When / is read, top two are popped and division(8/8) is performed
1
Next two tokens are values, so they are simply pushed. After pushing 2 and 3, the stack is as follows
1, 2, 3
When * comes, top two are popped and multiplication is performed.
1, 6
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The following postfix expression with single digit operands is evaluated using a stack:8 2 3 ^ / 2 3 * + 5 1 * -Note that ^ is the exponentiation operator. The top two elements of the stack after the first * is evaluated are:a)6, 1b)5, 7c)3, 2d)1, 5Correct answer is option 'A'. Can you explain this answer?
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