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Which of the following permutations can be obtained in the output(in the same order),using a stack assuming that the input is the sequence A,B,C,D,E in that order?OptionsC,D,E,A,BC,D,E,B,AC,D,A,B,EC,D,A,E,B

Question

Which of the following permutations can be obtained in the output(in the same order),using a stack assuming that the input is the sequence A,B,C,D,E in that order?OptionsC,D,E,A,BC,D,E,B,AC,D,A,B,EC,D,A,E,B

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Solution

The stack is a Last-In-First-Out (LIFO) data structure. This means that the last element that is pushed into the stack is the first one that comes out. Given the input sequence A, B, C, D, E, we can push and pop elements in the following way:

  1. Push A
  2. Push B
  3. Push C
  4. Pop C
  5. Push D
  6. Pop D
  7. Push E
  8. Pop E
  9. Pop B
  10. Pop A

This gives us the sequence C, D, E, B, A. So, the first option is a possible output sequence.

For the second option, C, D, E, A, B, we can follow these steps:

  1. Push A
  2. Push B
  3. Push C
  4. Pop C
  5. Push D
  6. Pop D
  7. Push E
  8. Pop E
  9. Pop A
  10. Pop B

This gives us the sequence C, D, E, A, B. So, the second option is also a possible output sequence.

For the third option, C, D, A, B, E, there is no way to obtain this sequence using a stack with the given input sequence. Once E is pushed into the stack, it must be popped out before A and B, which contradicts the order in the third option. So, the third option is not a possible output sequence.

For the fourth option, C, D, A, E, B, there is also no way to obtain this sequence using a stack with the given input sequence. Once B is pushed into the stack, it must be popped out before A and E, which contradicts the order in the fourth option. So, the fourth option is not a possible output sequence.

In conclusion, the possible output sequences are C, D, E, B, A and C, D, E, A, B.

This problem has been solved

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