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最新推荐文章于 2019-08-31 11:05:30 发布

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#KMP算法

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本文针对字符串前缀的周期性问题进行深入探讨，通过样例解释如何找出字符串中每个前缀的最大周期及其出现次数，并提供了一种有效的算法实现。

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Period

Time Limit: 3000MS		Memory Limit: 30000K
Total Submissions: 18865		Accepted: 9170

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 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 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

题目大意：

给你一个字符串，求这个字符串到第i个字符为止的循环节的次数。

比如aabaabaabaab，长度为12.到第二个a时，a出现2次，输出2.到第二个b时，aab出现了2次，输出2.到第三个b时，aab出现3次，输出3.到第四个b时，aab出现4次，输出4.

是poj 2406的加强版，此链接是2406

#include <iostream>
#include <cstdio>
#include <cstring>
const int N=1000000;
int Next[N+5];
char str[N+5];
int len;
using namespace std;
void getNext()//next数组，跳转表
{
	Next[0]=-1;
	int i=0,j=-1;
	while(i<len)
	{
		if(j==-1||str[i]==str[j])
		{
			i++;
			j++;
			Next[i]=j;
		}
		else
			j=Next[j];
	}
}
int main()
{
	int k=1;
	while(scanf("%d",&len),len)
	{
		scanf("%s",str);
		getNext();
		printf("Test case #%d\n",k++);
		for (int i=1;i<=len;i++)
		{
			if(i%(i-Next[i])==0&&i!=i-Next[i])//循环节
				printf("%d %d\n",i,i/(i-Next[i]));
		}
		printf("\n");
	}
	return 0;
}

参考网址

http://blog.youkuaiyun.com/niushuai666/article/details/6967716