Suppose that you start with an empty stack and interpret a letter to mean push and – to mean pop. Mark the sequences below that leave e at the bottom of the stack.1 pointa – b c – – d – e f g – ha – b c – d – e – f g – ha – b – c – d – e f g – ha b c d – – – – e f g – ha – b c – – d – e f g h –
Question
Suppose that you start with an empty stack and interpret a letter to mean push and – to mean pop. Mark the sequences below that leave e at the bottom of the stack.1 pointa – b c – – d – e f g – ha – b c – d – e – f g – ha – b – c – d – e f g – ha b c d – – – – e f g – ha – b c – – d – e f g h –
Solution
The sequences that leave 'e' at the bottom of the stack are:
- a – b c – – d – e f g – h
- a b c d – – – – e f g – h
Here's why:
-
a – b c – – d – e f g – h
- Push 'a', pop 'a'
- Push 'b', push 'c', pop 'c', pop 'b'
- Push 'd', pop 'd'
- Push 'e', push 'f', push 'g', pop 'g'
- Push 'h', pop 'h'
- Now, 'e' is at the bottom of the stack.
-
a b c d – – – – e f g – h
- Push 'a', push 'b', push 'c', push 'd'
- Pop 'd', pop 'c', pop 'b', pop 'a'
- Push 'e', push 'f', push 'g', pop 'g'
- Push 'h', pop 'h'
- Now, 'e' is at the bottom of the stack.
The other sequences do not leave 'e' at the bottom of the stack.
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