P1044 Stack
Abstract model
Start with the ordered input sequence $1,2,\ldots,n$, an empty stack, and an empty output sequence. A legal execution repeatedly pushes the next input item or pops the stack top. Count the distinct complete output sequences. This count is the $n$-th Catalan number. The verification case computes the same count by dynamic programming on the numbers of unprocessed inputs and stacked items; it restricts $n$ to at most $7$.
Problem statement
Stack A has capacity greater than $n$. Two operations are allowed: move the first remaining operand to the stack top, or move the stack top to the end of the output sequence. Given the initial operand sequence $1,2,\ldots,n$, output the number of different output sequences obtainable after all operands have been processed.
Input and output
The input contains one integer $n$. Output the number of possible output sequences.
Constraints
- Original problem: $1 \le n \le 18$.
- Verification entry point: $0 \le n \le 7$.