KMP(fail数组应用) LA 3026 Period

题目传送门

题意：(训练指南P213) 求每个前缀的最短循环节

分析：利用失配函数的性质，如果i % (i - fail[i]) == 0，那么正好错位移动一个循环节长度。

#include <bits/stdc++.h>
using namespace std;

const int N = 1e6 + 5;
char str[N];
int fail[N];
int len;

void get_fail(char *P)  {
    int i = 0, j = -1;  fail[i] = j;
    while (i < len) {
        if (j == -1 || P[j] == P[i])    {
            fail[++i] = ++j;
        }
        else    j = fail[j];
    }
}

int main(void)  {
    int cas = 0;
    while (scanf ("%d", &len) == 1) {
        if (!len)   break;
        scanf ("%s", &str);
        get_fail (str);
        for (int i=0; i<=len; ++i)  {
            printf ("%d ", fail[i]);
        }   puts ("");
        printf ("Test case #%d\n", ++cas);
        for (int i=1; i<=len; ++i)   {
            if (fail[i] >= 0 && i % (i - fail[i]) == 0)  {
                int k = i / (i - fail[i]);
                if (k > 1)  {
                    printf ("%d %d\n", i, k);
                }
            }
        }
        puts ("");
    }

    return 0;
}