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Power Strings
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.
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题意：给一个字符串S长度不超过10^6，求最大的n使得S由n个相同的字符串a连接而成，如："ababab"则由n=3个"ab"连接而成，"aaaa"由n=4个"a"连接而成，"abcd"则由n=1个"abcd"连接而成。
定理：假设S的长度为len，则S存在循环子串，当且仅当，len可以被len - next[len]整除，最短循环子串为S[len - next[len]]
思路：利用KMP算法，求字符串的特征向量next，若len可以被len - next[len]整除，则最大循环次数n为len/(len - next[len])，否则为1。
代码：
1 #include <iostream> 2 #include <cstdio> 3 #include <cstring> 4 #include <algorithm> 5 #include <cmath> 6 #include <string> 7 #include <map> 8 #include <stack> 9 #include <vector> 10 #include <set> 11 #include <queue> 12 #pragma comment (linker,"/STACK:102400000,102400000") 13 #define maxn 1005 14 #define MAXN 2005 15 #define mod 1000000009 16 #define INF 0x3f3f3f3f 17 #define pi acos(-1.0) 18 #define eps 1e-6 19 typedef long long ll; 20 using namespace std; 21 22 int N; 23 int nextval[1000010]; 24 char str[1000010]; 25 26 int get_nextval() 27 { 28 int i=0; 29 int len=strlen(str); 30 int j=-1; 31 nextval[i]=-1; 32 while (i<len) 33 { 34 if (j==-1||str[i]==str[j]) 35 { 36 i++; 37 j++; 38 nextval[i]=j; 39 } 40 else 41 j=nextval[j]; 42 } 43 if ((len)%(len-nextval[len])==0) 44 return len/(len-nextval[len]); 45 else 46 return 1; 47 } 48 49 int main() 50 { 51 while (scanf("%s",str)) 52 { 53 if (str[0]==‘.‘) 54 return 0; 55 printf("%d\n",get_nextval()); 56 } 57 return 0; 58 }
标签：des style blog http color io os ar for
原文地址：http://www.cnblogs.com/i8888/p/4046670.html
