poj2406 Power Strings（kmp失配函数）

　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　Power Strings

Time Limit: 3000MS		Memory Limit: 65536K
Total Submissions: 39291		Accepted: 16315

Description

Given two strings a and b we define a*b to be their concatenation. For example, if a = "abc" and b = "def" then a*b = "abcdef". If we think of concatenation as multiplication, exponentiation by a non-negative integer is defined in the normal way: a^0 = "" (the empty string) and a^(n+1) = a*(a^n).

Input

Each test case is a line of input representing s, a string of printable characters. The length of s will be at least 1 and will not exceed 1 million characters. A line containing a period follows the last test case.

Output

For each s you should print the largest n such that s = a^n for some string a.

Sample Input

abcd

aaaa

ababab

.

Sample Output

1

4

3

Hint

This problem has huge input, use scanf instead of cin to avoid time limit exceed.

Source

Waterloo local 2002.07.01

【思路】

KMP。

应用KMP算法中的失配函数，如果是一个周期串那么错位部分(n-f[n])一定是一个最小循环节（仔细想想f函数的意义），则答案为i/(n-f[n])。否则ans=1。

　　时间复杂度为O(n)。

【代码】

 #include<cstdio>
 #include<cstring>
 #include<iostream>
 #define FOR(a,b,c) for(int a=(b);a<=(c);a++)
 using namespace std;

 const int maxn = +;

 void getFail(char* P,int* f) {
     int m=strlen(P);
     f[]=f[]=;
     for(int i=;i<m;i++) {
         int j=f[i];
         while(j && P[i]!=P[j]) j=f[j];
         f[i+]=P[i]==P[j]?j+:;
     }
 }

 char s[maxn];
 int f[maxn];

 int main() {
     while(scanf("%s",s)== && s[]!='.') {
         getFail(s,f);
         int n=strlen(s);
         if(f[n]> && n%(n-f[n])==) printf("%d\n",n/(n-f[n]));
         else printf("%d\n",);
     }
     return ;
 }