hdu1358：Period

原创于 2018-08-15 23:42:38 发布 · 220 阅读

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本文介绍了一种算法，用于识别给定字符串的所有前缀是否为周期性字符串，即能否由较短的字符串重复构成。通过KMP算法的next数组，高效地找出每个前缀的最长重复周期及重复次数。

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http://acm.hdu.edu.cn/showproblem.php?pid=1358

Problem 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.

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

aaa

aabaabaabaab

Sample Output

Test case #1

2 2

3 3

Test case #2

2 2

6 2

9 3

12 4

找出字符串的每一个前缀在字符串中循环出现的位置和第几次出现，不包括第一次出现。

第一个样例aaa，第一个前缀a第二次出现在2，输出2 2，第三次出现在3，输出3 3。第二个前缀aa后面没有出现，第三个前缀aaa后面也没有出现，在每个样例的后面输出一个空行。

#include<stdio.h>
#include<string.h>
#define N 1000020
char a[N];
int n,next[N],sum=1;
void getnext()
{
	int i,j;
	i=0;
	j=-1;
	next[0]=-1;
	while(i<n)
	{
		if(j==-1||a[i]==a[j])
		{
			i++;
			j++;
			next[i]=j;
		}
		else
			j=next[j];
	}
}
void kmp()
{
	getnext();
	int i,t;
	printf("Test case #%d\n",sum);
	sum++;
	for(i=1;i<=n;i++)
	{
		t=i-next[i];
		if(i%t==0&&i/t>1)
		    printf("%d %d\n",i,i/t);
	}
}
int main()
{
	while(scanf("%d",&n),n!=0)
	{
		scanf("%s",a);
		kmp();
		printf("\n");
	}
	return 0;
}