The little cat is so famous, that many couples tramp over hill and dale to Byteland, and asked the little cat to give names to their newly-born babies. They seek the name, and at the same time seek the fame. In order to escape from such boring job, the innovative little cat works out an easy but fantastic algorithm:
Step1. Connect the father's name and the mother's name, to a new string S.
Step2. Find a proper prefix-suffix string of S (which is not only the prefix, but also the suffix of S).
Example: Father='ala', Mother='la', we have S = 'ala'+'la' = 'alala'. Potential prefix-suffix strings of S are {'a', 'ala', 'alala'}. Given the string S, could you help the little cat to write a program to calculate the length of possible prefix-suffix strings of S? (He might thank you by giving your baby a name:)
Input
The input contains a number of test cases. Each test case occupies a single line that contains the string S described above.
Restrictions: Only lowercase letters may appear in the input. 1 <= Length of S <= 400000.
Output
For each test case, output a single line with integer numbers in increasing order, denoting the possible length of the new baby's name.
Sample Input
ababcababababcabab aaaaa
Sample Output
2 4 9 18 1 2 3 4 5
本题非常的巧妙
我们先利用nxt[n]就是最长的那个 然后不断查找nxt[nxt[n]]
直到为0我们就可以将所有的前后缀全部求出
然后倒序输出即可
#include<cstdio>
#include<string.h>
using namespace std;
char s[400005];
int nxt[400005];
int n;
void get_nxt()
{
int i=0;
int k=-1;
nxt[0]=-1;
while(i<n)
{
if(k==-1||s[i]==s[k])
{
i++;
k++;
nxt[i]=k;
}
else
{
k=nxt[k];
}
}
return;
}
int ans[400005];
int main()
{
while(~scanf("%s",s))
{
n=strlen(s);
get_nxt();
int cnt=0;
ans[++cnt]=n;
int x=n;
while(x)
{
x=nxt[x];
if(x!=0)
{
ans[++cnt]=x;
}
}
for(int i=cnt;i>=1;i--)
{
printf("%d%s",ans[i],i==1?"\n":" ");
}
}
return 0;
}
