The following postfix expression with single-digit operands is evaluated using…
2022
The following postfix expression with single-digit operands is evaluated using a stack: 8 2 3 ^ / 2 4 + 5 1 * - Note that ^ is exponentiation. The top two elements of the stack after the first * is evaluated, are —
- A.
8,1
- B.
5,6
- C.
3,2
- D.
1,5
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Correct answer: B
Evaluate the postfix expression until the first *:
Expression: 8 2 3 ^ / 2 4 + 5 1 * -
Push 8 → stack = [8]
Push 2 → stack = [8, 2]
Push 3 → stack = [8, 2, 3]
^ → 2^3 = 8, pop 3 and 2, push 8 → stack = [8, 8]
/ → 8 / 8 = 1, pop 8 and 8, push 1 → stack = [1]
Push 2, push 4 → stack = [1, 2, 4]
+ → 2 + 4 = 6, pop 4 and 2, push 6 → stack = [1, 6]
Push 5, push 1 → stack = [1, 6, 5, 1]
First * → 5 * 1 = 5, pop 1 and 5, push 5 → stack = [1, 6, 5]
Therefore, after the first * is evaluated the stack is [1, 6, 5]. The top element is 5 and the next element is 6.
Note: None of the provided options list the correct top-two pair (5, 6). The original solution contained arithmetic and transcription errors (for example, 2 + 4 was incorrectly given as 7).