AtCoder Regular Contest 069 D

D - Menagerie

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 si. Here, if si is o, the animal said that the two neighboring animals are of the same species, and if si 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.

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 ti is S, it indicates that the animal numbered i is a sheep. If ti is W, it indicates that the animal numbered i is a wolf.

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.

Sample Input 2

3
oox

Sample Output 2

-1

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

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：

  1 #include <bits/stdc++.h>
  2 using namespace std;
  3 const int N=123456;
  4 int gh(char *str,char *ch,int n) {
  5     for(int i=1; i<n; i++) {
  6         if(i<n-2) {
  7             if(str[i]=='o') {
  8                 if(ch[i]=='S') {
  9                     ch[i+1]=ch[i-1];
 10                 } else {
 11                     if(ch[i-1]=='S') ch[i+1]='W';
 12                     else ch[i+1]='S';
 13                 }
 14             } else {
 15                 if(ch[i]=='S') {
 16                     if(ch[i-1]=='S') ch[i+1]='W';
 17                     else ch[i+1]='S';
 18                 } else {
 19                     ch[i+1]=ch[i-1];
 20                 }
 21             }
 22         }
 23         else if(i==n-2) {
 24             if(str[i]=='o') {
 25                 if(ch[i]=='S') {
 26                     if(ch[i+1]!=ch[i-1]) {
 27                         return 1;
 28                     }
 29                 }
 30                 else {
 31                     if(ch[i+1]==ch[i-1]){
 32                         return 1;
 33                     }
 34                 }
 35             }
 36             else{
 37                 if(ch[i]=='S'){
 38                     if(ch[i+1]==ch[i-1]){
 39                         return 1;
 40                     }
 41                 }
 42                 else{
 43                     if(ch[i+1]!=ch[i-1]) {
 44                         return 1;
 45                     }
 46                 }
 47             }
 48         }
 49         else if(i==n-1){
 50             if(str[i]=='x'){
 51                 if(ch[i]=='S') {
 52                     if(ch[n-2]==ch[0]) return 1;
 53                 }
 54                 else{
 55                     if(ch[n-2]!=ch[0]) return 1;
 56                 }
 57             }
 58             else{
 59                 if(ch[i]=='S'){
 60                     if(ch[n-2]!=ch[0]) return 1;
 61                 }
 62                 else{
 63                     if(ch[n-2]==ch[0]) return 1;
 64                 }
 65             }
 66         }
 67     }
 68     return 0;
 69 }
 70 int main() {
 71     char str[N];
 72     char ch[N];
 73     int n;
 74     int flag=0;
 75     scanf("%d",&n);
 76     scanf("%s",str);
 77     ch[0]='S';
 78     if(str[0]=='o') {
 79         memset(ch,0,sizeof(ch));
 80         ch[0]='S';
 81         ch[1]='S';
 82         ch[n-1]='S';
 83         flag=gh(str,ch,n);
 84         if(flag==0) {
 85             for(int i=0; i<n; i++) printf("%c",ch[i]);
 86             puts("");
 87             return 0;
 88         } else {
 89             memset(ch,0,sizeof(ch));
 90             ch[0]='S';
 91             ch[1]='W';
 92             ch[n-1]='W';
 93             flag=gh(str,ch,n);
 94             if(flag==0){
 95                 for(int i=0;i<n;i++) printf("%c",ch[i]);
 96                 puts("");
 97                 return 0;
 98             }
 99         }
100     }
101     else{
102         memset(ch,0,sizeof(ch));
103         ch[0]='S';
104         ch[1]='S';
105         ch[n-1]='W';
106         flag=gh(str,ch,n);
107         if(flag==0){
108             for(int i=0;i<n;i++) printf("%c",ch[i]);
109             puts("");
110             return 0;
111         }
112         else{
113             memset(ch,0,sizeof(ch));
114             ch[0]='S';
115             ch[1]='W';
116             ch[n-1]='S';
117             flag=gh(str,ch,n);
118             if(flag==0){
119                 for(int i=0;i<n;i++) printf("%c",ch[i]);
120                 puts("");
121                 return 0;
122             }
123         }
124     }
125     ch[0]='W';
126     if(str[0]=='o'){
127         memset(ch,0,sizeof(ch));
128         ch[0]='W';
129         ch[1]='S';
130         ch[n-1]='W';
131         flag=gh(str,ch,n);
132         if(flag==0){
133             for(int i=0;i<n;i++) printf("%c",ch[i]);
134             puts("");
135             return 0;
136         }
137         else{
138             ch[0]='W';
139             ch[1]='W';
140             ch[n-1]='S';
141             flag=gh(str,ch,n);
142             if(flag==0){
143                 for(int i=0;i<n;i++) printf("%c",ch[i]);
144                 puts("");
145                 return 0;
146             }
147         }
148     }
149     else{
150         memset(ch,0,sizeof(ch));
151         ch[0]='W';
152         ch[1]='S';
153         ch[n-1]='S';
154         flag=gh(str,ch,n);
155         if(flag==0){
156             for(int i=0;i<n;i++) printf("%c",ch[i]);
157             puts("");
158         }
159         else{
160             ch[0]='W';
161             ch[1]='W';
162             ch[n-1]='W';
163             flag=gh(str,ch,n);
164             if(flag==0){
165                 for(int i=0;i<n;i++) printf("%c",ch[i]);
166                 puts("");
167                 return 0;
168             }
169         }
170     }
171     puts("-1");
172     return 0;
173 }