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3. (10 marks) Suppose an intermixed sequence of stack push and pop operations are performed. The pushes push into the stack the integers 0 through 9 in order; popped values are printed in the order they are popped. Which of the below sequences c...

To determine which sequence could occur as the printed output, we can simulate the stack operations. Here is a step-by-step analysis:

  1. The integers 0 through 9 are pushed into the stack in order.
  2. The first value to be popped must be 0 since it was the first one pushed.
  3. After popping 0, any number from 1 to 9 can be popped next depending on subsequent operations.

Analyzing the given options: A) 1 2 3 0 6 5 4 7 8 9: This sequence is not possible because after popping 3, only numbers greater than or equal to it can be popped. So, popping of numbers like 1 and 2 before popping higher values is not possible.

B) 2 3 4 5 6 7 8 9: This sequence is possible. After popping the initial value of zero (0), all other values can be popped in ascending order.

C) 6 7 8 9 : This sequence is not possible because after popping a number, subsequent pops should have higher values. However, after popping any number less than or equal to five (5), it would not be possible to pop six (6).

D)7,8,9: This sequence is not possible because there are missing numbers that should have been popped before reaching these values.

Based on this analysis, the correct answer is B)2,3,4,5,6,7,8,9,0 ,1


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