B - String Shifting
B - String Shifting
Score : $200$ points
Problem Statement
On a non-empty string, a left shift moves the first character to the end of the string, and a right shift moves the last character to the beginning of the string.
For example, a left shift on abcde results in bcdea, and two right shifts on abcde result in deabc.
You are given a non-empty $S$ consisting of lowercase English letters. Among the strings that can be obtained by performing zero or more left shifts and zero or more right shifts on $S$, find the lexicographically smallest string and the lexicographically largest string.
What is the lexicographical order?
Simply speaking, the lexicographical order is the order in which words are listed in a dictionary. As a more formal definition, here is the algorithm to determine the lexicographical order between different strings $S$ and $T$.
Below, let $S_i$ denote the $i$-th character of $S$. Also, if $S$ is lexicographically smaller than $T$, we will denote that fact as $S \lt T$; if $S$ is lexicographically larger than $T$, we will denote that fact as $S \gt T$.
- Let $L$ be the smaller of the lengths of $S$ and $T$. For each $i=1,2,\dots,L$, we check whether $S_i$ and $T_i$ are the same.
- If there is an $i$ such that $S_i \neq T_i$, let $j$ be the smallest such $i$. Then, we compare $S_j$ and $T_j$. If $S_j$ comes earlier than $T_j$ in alphabetical order, we determine that $S \lt T$ and quit; if $S_j$ comes later than $T_j$, we determine that $S \gt T$ and quit.
- If there is no $i$ such that $S_i \neq T_i$, we compare the lengths of $S$ and $T$. If $S$ is shorter than $T$, we determine that $S \lt T$ and quit; if $S$ is longer than $T$, we determine that $S \gt T$ and quit.
Constraints
- $S$ consists of lowercase English letters.
- The length of $S$ is between $1$ and $1000$ (inclusive).
Input
Input is given from Standard Input in the following format:
Output
Print two lines. The first line should contain $S_{\min}$, and the second line should contain $S_{\max}$. Here, $S_{\min}$ and $S_{\max}$ are respectively the lexicographically smallest and largest strings obtained by performing zero or more left shifts and zero or more right shifts on $S$.
aaba
aaab
baaa
By performing shifts, we can obtain four strings: aaab, aaba, abaa, baaa. The lexicographically smallest and largest among them are aaab and baaa, respectively.
z
z
z
Any sequence of operations results in z.
abracadabra
aabracadabr
racadabraab