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poj 2406 Power Strings（KMP求循环次数）

2024-07-17 07:24:45   220人阅读

题目链接：http://poj.org/problem?id=2406


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

题意：

求最小子串的循环次数；

思路：（转）

KMP，next[]表示模式串如果第i位(设str[0]为第0位)与文本串第j位不匹配则要回到第next[i]位继续与文本串第j位匹配。则模式串第1位到next[n]与模式串第n-next[n]位到n位是匹配的。所以思路和上面一样，如果n%（n-next[n]）==0,则存在重复连续子串，长度为n-next[n]。

例如：a    b    a    b    a    b

next:-1   0    0    1    2    3    4

next[n]==4,代表着，前缀abab与后缀abab相等的最长长度，这说明，ab这两个字母为一个循环节，长度=n-next[n];


代码如下：

#include <cstdio>
#include <cstring>
#include <algorithm>
using namespace std;
#define MAXN 1000017
int next[MAXN];
int len;
void getnext( char s[])
{
    int i = 0, j = -1;
    next[0] = -1;
    while(i < len)
    {
        if(j == -1 || s[i] == s[j])
        {
            i++,j++;
            next[i] = j;
        }
        else
            j = next[j];
    }
}
int main()
{
    char ss[MAXN];
    int length;
    while(~scanf("%s",ss))
    {
        if(ss[0] == '.')
            break;
        len = strlen(ss);
        getnext(ss);
        length = len - next[len];//注意
        if(len%length == 0)
            printf("%d\n",len/length);
        else
            printf("1\n");
    }
    return 0;
}



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