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poj 1961 Period(kmp最短循环节)


题目链接 

Description

For each prefix of a given string S with N characters (each character has an ASCII code between 97 and 126, inclusive), we want to know whether the prefix is a periodic string. That is, for each i (2 <= i <= N) we want to know
the largest K > 1 (if there is one) such that the prefix of S with length i can be written as AK ,that is A concatenated K times, for some string A. Of course, we also want to know the period K.……………………


题意:

     给定一个长度为n的字符串s,求他每个前缀的最短循环节。换句话说,对于每个i(2<=i<=n),求一个最大的整数k(如果k存在),使得s的前i个字符可以组成的前缀是某个字符串重复k次得到的。输出所有存在K的i和对应的k。

    这是刘汝佳《算法竞赛入门经典训练指南》上的原题(p213),用KMP构造状态转移表。

解题代码(完全参照白书):

//poj 1961
#include <stdio.h>
const int maxn = 1000000 + 10;

char p[maxn];
int f[maxn];

int main()
{
    int n, t = 1;
    while (scanf("%d",&n) && n)
    {
        scanf("%s",p);
        f[0] = 0;
        f[1] = 0;
        for (int i = 1; i < n; i++)
        {
            int j = f[i];
            while (p[i] != p[j] && j)
                j = f[j];
            f[i+1] = (p[i] == p[j] ? j+1 : 0);
        }/*这段代码就是KMP里面核心的代码,这里没有文本串,
        我们只需要处理模板即可*/
        printf("Test case #%d\n",t++);
        for (int i = 2; i <= n; i++)
        {
            if (f[i] > 0 && i % (i-f[i]) == 0)
                printf("%d %d\n",i, i / (i-f[i]));
        }
        puts("");
    }
    return 0;
}


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