AtCoder Regular Contest 069 D

D - Menagerie

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Time limit : 2sec / Memory limit : 256MB

Score : 500 points

Problem Statement

Snuke, who loves animals, built a zoo.

There are N animals in this zoo. They are conveniently numbered 1 through N, and arranged in a circle. The animal numbered i(2≤i≤N−1) is adjacent to the animals numbered i−1 and i+1. Also, the animal numbered 1 is adjacent to the animals numbered 2 and N, and the animal numbered N is adjacent to the animals numbered N−1 and 1.

There are two kinds of animals in this zoo: honest sheep that only speak the truth, and lying wolves that only tell lies.

Snuke cannot tell the difference between these two species, and asked each animal the following question: "Are your neighbors of the same species?" The animal numbered i answered s_i. Here, if s_i is o, the animal said that the two neighboring animals are of the same species, and if s_i is x, the animal said that the two neighboring animals are of different species.

More formally, a sheep answered o if the two neighboring animals are both sheep or both wolves, and answered x otherwise. Similarly, a wolf answered x if the two neighboring animals are both sheep or both wolves, and answered o otherwise.

Snuke is wondering whether there is a valid assignment of species to the animals that is consistent with these responses. If there is such an assignment, show one such assignment. Otherwise, print -1.

Constraints

• 3≤N≤10⁵
• s is a string of length N consisting of o and x.

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Input

The input is given from Standard Input in the following format:

N
s

Output

If there does not exist an valid assignment that is consistent with s, print -1. Otherwise, print an string t in the following format. The output is considered correct if the assignment described by t is consistent with s.

• t is a string of length N consisting of S and W.
• If t_i is S, it indicates that the animal numbered i is a sheep. If t_i is W, it indicates that the animal numbered i is a wolf.

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Sample Input 1

6
ooxoox

Sample Output 1

SSSWWS

For example, if the animals numbered 1, 2, 3, 4, 5 and 6 are respectively a sheep, sheep, sheep, wolf, wolf, and sheep, it is consistent with their responses. Besides, there is another valid assignment of species: a wolf, sheep, wolf, sheep, wolf and wolf.

Let us remind you: if the neiboring animals are of the same species, a sheep answers o and a wolf answers x. If the neiboring animals are of different species, a sheep answers x and a wolf answers o.

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Sample Input 2

3
oox

Sample Output 2

-1

Print -1 if there is no valid assignment of species.

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Sample Input 3

10
oxooxoxoox

Sample Output 3

SSWWSSSWWS

题目链接：http://arc069.contest.atcoder.jp/tasks/arc069_b

题意：n只动物从1到n围成一个圈，每只动物要么是羊要么是狼。每只动物会说出一个字母，说'o'表示它两边动物种类相同，说'x'表示不同。但羊是说真话，狼是说反话。求出这n只动物的种类。

分析：模拟一下就可以了，不过这个模拟比较大！

下面给出AC代码：

 #include <bits/stdc++.h>
 using namespace std;
 const int N=;
 int gh(char *str,char *ch,int n) {
     for(int i=; i<n; i++) {
         if(i<n-) {
             if(str[i]=='o') {
                 if(ch[i]=='S') {
                     ch[i+]=ch[i-];
                 } else {
                     if(ch[i-]=='S') ch[i+]='W';
                     else ch[i+]='S';
                 }
             } else {
                 if(ch[i]=='S') {
                     if(ch[i-]=='S') ch[i+]='W';
                     else ch[i+]='S';
                 } else {
                     ch[i+]=ch[i-];
                 }
             }
         }
         else if(i==n-) {
             if(str[i]=='o') {
                 if(ch[i]=='S') {
                     if(ch[i+]!=ch[i-]) {
                         return ;
                     }
                 }
                 else {
                     if(ch[i+]==ch[i-]){
                         return ;
                     }
                 }
             }
             else{
                 if(ch[i]=='S'){
                     if(ch[i+]==ch[i-]){
                         return ;
                     }
                 }
                 else{
                     if(ch[i+]!=ch[i-]) {
                         return ;
                     }
                 }
             }
         }
         else if(i==n-){
             if(str[i]=='x'){
                 if(ch[i]=='S') {
                     if(ch[n-]==ch[]) return ;
                 }
                 else{
                     if(ch[n-]!=ch[]) return ;
                 }
             }
             else{
                 if(ch[i]=='S'){
                     if(ch[n-]!=ch[]) return ;
                 }
                 else{
                     if(ch[n-]==ch[]) return ;
                 }
             }
         }
     }
     return ;
 }
 int main() {
     char str[N];
     char ch[N];
     int n;
     int flag=;
     scanf("%d",&n);
     scanf("%s",str);
     ch[]='S';
     if(str[]=='o') {
         memset(ch,,sizeof(ch));
         ch[]='S';
         ch[]='S';
         ch[n-]='S';
         flag=gh(str,ch,n);
         if(flag==) {
             for(int i=; i<n; i++) printf("%c",ch[i]);
             puts("");
             return ;
         } else {
             memset(ch,,sizeof(ch));
             ch[]='S';
             ch[]='W';
             ch[n-]='W';
             flag=gh(str,ch,n);
             if(flag==){
                 for(int i=;i<n;i++) printf("%c",ch[i]);
                 puts("");
                 return ;
             }
         }
     }
     else{
         memset(ch,,sizeof(ch));
         ch[]='S';
         ch[]='S';
         ch[n-]='W';
         flag=gh(str,ch,n);
         if(flag==){
             for(int i=;i<n;i++) printf("%c",ch[i]);
             puts("");
             return ;
         }
         else{
             memset(ch,,sizeof(ch));
             ch[]='S';
             ch[]='W';
             ch[n-]='S';
             flag=gh(str,ch,n);
             if(flag==){
                 for(int i=;i<n;i++) printf("%c",ch[i]);
                 puts("");
                 return ;
             }
         }
     }
     ch[]='W';
     if(str[]=='o'){
         memset(ch,,sizeof(ch));
         ch[]='W';
         ch[]='S';
         ch[n-]='W';
         flag=gh(str,ch,n);
         if(flag==){
             for(int i=;i<n;i++) printf("%c",ch[i]);
             puts("");
             return ;
         }
         else{
             ch[]='W';
             ch[]='W';
             ch[n-]='S';
             flag=gh(str,ch,n);
             if(flag==){
                 for(int i=;i<n;i++) printf("%c",ch[i]);
                 puts("");
                 return ;
             }
         }
     }
     else{
         memset(ch,,sizeof(ch));
         ch[]='W';
         ch[]='S';
         ch[n-]='S';
         flag=gh(str,ch,n);
         if(flag==){
             for(int i=;i<n;i++) printf("%c",ch[i]);
             puts("");
         }
         else{
             ch[]='W';
             ch[]='W';
             ch[n-]='W';
             flag=gh(str,ch,n);
             if(flag==){
                 for(int i=;i<n;i++) printf("%c",ch[i]);
                 puts("");
                 return ;
             }
         }
     }
     puts("-1");
     return ;
 }