| # P1368 Minimal Representation |
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|
| ## Abstract model |
|
|
| For a sequence $a_0,a_1,\ldots,a_{n-1}$, its cyclic rotation beginning at |
| position $p$ is |
| |
| $$ |
| (a_p,a_{p+1},\ldots,a_{n-1},a_0,a_1,\ldots,a_{p-1}). |
| $$ |
| |
| Compare two rotations lexicographically and choose the smallest one. If |
| several starting positions produce the same smallest rotation, choose the |
| smallest starting position. The C verification case uses a doubled sequence |
| and the linear-time two-candidate elimination algorithm. |
| |
| ## Problem statement |
| |
| Given a circular sequence of $n$ integers, output its lexicographically |
| smallest cyclic rotation. |
| |
| The verification function `minimal_representation` receives the sequence, its |
| length, and an output array. It writes the smallest rotation into the |
| output array and returns the corresponding zero-based starting position in the |
| input sequence. |
|
|
| ## Input and output |
|
|
| The original problem reads $n$ followed by $n$ integers and prints the |
| lexicographically smallest rotation, with adjacent values separated by spaces. |
|
|
| In the verification interface, `a` contains the $n$ input values and `out` has |
| capacity for $n$ values. The function declares a local buffer `b[2000]` and |
| copies the input twice into its first $2n$ cells. After |
| the function returns, `out` contains the smallest rotation and the return value |
| is an integer in $[0,n-1]$. |
|
|
| ## Constraints |
|
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| - Original problem: $1 \le n \le 300000$. |
| - Verification case: $1 \le n \le 1000$. |
| - Every sequence value is a signed C `int`. |
|
|
| ## Source |
|
|
| [Luogu P1368, "Minimal Representation"](https://www.luogu.com.cn/problem/P1368). |
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