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Stack A has the entries a, b, c (with a on top). Stack B is empty. An entry popped out of stack A can be printed immediately or pushed to stack B. An entry popped out of the stack B can be only be printed. In this arrangement, which of the following permutations of a, b, c are not possible?

Question

Stack A has the entries a, b, c (with a on top). Stack B is empty. An entry popped out of stack A can be printed immediately or pushed to stack B. An entry popped out of the stack B can be only be printed. In this arrangement, which of the following permutations of a, b, c are not possible?

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Solution

The permutation that is not possible is "c, a, b".

Here's why:

  1. "c, a, b" would require 'c' to be the first one to be printed. But 'c' is at the bottom of stack A and we can't get to it without first popping 'a' and 'b'.

  2. We could push 'a' and 'b' to stack B, but according to the rules, once an entry is popped out of stack B, it can only be printed.

  3. So, we can't push 'a' and 'b' to stack B to get to 'c' because we would have to print 'b' before we could print 'a'.

  4. Therefore, the permutation "c, a, b" is not possible under these rules.

This problem has been solved

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