hdu 1358 Period (KMP求循环节)

最新推荐文章于 2020-03-18 11:50:29 发布

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本文介绍了一种用于检测字符串是否为周期字符串的算法，并通过实例演示了如何使用该算法来找出给定字符串的所有前缀中重复的周期部分及其长度。

Period
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 A K , that is A concatenated K times, for some string A. Of course, we also want to know the period K.
Input
The input file consists of several test cases. Each test case consists of two lines. The first one contains N (2 <= N <= 1 000 000) – the size of the string S. The second line contains the string S. The input file ends with a line, having the number zero on it.
Output
For each test case, output “Test case #” and the consecutive test case number on a single line; then, for each prefix with length i that has a period K > 1, output the prefix size i and the period K separated by a single space; the prefix sizes must be in increasing order. Print a blank line after each test case.
Sample Input
3
aaa
12
aabaabaabaab
0
Sample Output
Test case #1
2 2
3 3

Test case #2
2 2
6 2
9 3
12 4

如果对于next数组中的 i，符合 i % ( i - next[i] ) == 0 && next[i] != 0 , 则说明字符串循环，而且
循环节长度为: i - next[i]
循环次数为: i / ( i - next[i] )

#include <iostream>
#include <cstdio>
#include <cstring>

using namespace std;

const int maxn = 1000000;
int n;
int fail[maxn + 10];
char a[maxn + 10];

void kmp_pre(char x[]) {
    int i, j;
    j = -1;
    fail[0] = -1;
    i = 0;
    while(i < n) {
        while(-1 != j && x[i] != x[j])j = fail[j];
        fail[++i] = ++j;
    }

}

int main() {
    int t = 1;
    while(scanf("%d", &n) != EOF && n) {
        scanf("%s", a);
        kmp_pre(a);
        printf("Test case #%d\n", t++);
        for(int i = 2; a[i - 1]; i++) {
            int p = i - fail[i];//循环节的长度
            if(i % p == 0 && i / p > 1) {
                printf("%d %d\n", i, i / p);//i/p循环的次数
            }
        }
        printf("\n");
    }
}