201341: [AtCoder]ARC134 B - Reserve or Reverse
Description
Score : $400$ points
Problem Statement
Given is a string $s$ of length $N$. Let $s_i$ denote the $i$-th character of $s$.
Snuke will transform $s$ by the following procedure.
- Choose an even length (not necessarily contiguous) subsequence $x=(x_1, x_2, \ldots, x_{2k})$ of $(1,2, \ldots, N)$ ($k$ may be $0$).
- Swap $s_{x_1}$ and $s_{x_{2k}}$.
- Swap $s_{x_2}$ and $s_{x_{2k-1}}$.
- Swap $s_{x_3}$ and $s_{x_{2k-2}}$.
- $\vdots$
- Swap $s_{x_{k}}$ and $s_{x_{k+1}}$.
Among the strings that $s$ can become after the procedure, find the lexicographically smallest one.
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
- $1 \leq N \leq 2 \times 10^5$
- $s$ is a string of length $N$ consisting of lowercase English letters.
Input
Input is given from Standard Input in the following format:
$N$ $s$
Output
Print the lexicographically smallest possible string $s$ after the procedure by Snuke.
Sample Input 1
4 dcab
Sample Output 1
acdb
- When $x=(1,3)$, the procedure just swaps $s_{1}$ and $s_{3}$.
- The $s$ after the procedure is
acdb, the lexicographically smallest possible result.
Sample Input 2
2 ab
Sample Output 2
ab
- When $x=()$, the $s$ after the procedure is
ab, the lexicographically smallest possible result. - Note that $x$ may have a length of $0$.
Sample Input 3
16 cabaaabbbabcbaba
Sample Output 3
aaaaaaabbbbcbbbc
Sample Input 4
17 snwfpfwipeusiwkzo
Sample Output 4
effwpnwipsusiwkzo