benchmarks/Algorithms/minimal_representation/problem.md

P1368 Minimal Representation

Abstract model

For a sequence $a_0,a_1,\ldots,a_{n-1}$, its cyclic rotation beginning at position $p$ is

$$(a_p,a_{p+1},\dots ,a_{n-1},a_0,a_1,\dots ,a_{p-1})\mathrm{.}(a\_p,a\_\{p+1\},\backslash ldots,a\_\{n-1\},a\_0,a\_1,\backslash ldots,a\_\{p-1\}).$$

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

• 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".