Period 和字符串周期

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最新推荐文章于 2025-02-28 17:41:50 发布

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分类专栏： KMP 字符串文章标签：字符串 KMP

本文链接：https://blog.youkuaiyun.com/wuhuajunbao/article/details/22990793

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本文探讨了如何判断一个给定字符串的前缀是否具有周期性，并详细介绍了使用KMP算法来查找最小周期的过程。通过实例展示了算法的应用，包括输入样例、输出样例以及代码实现。

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Period

Time Limit : 6000/3000ms (Java/Other) Memory Limit : 60000/30000K (Java/Other)

Total Submission(s) : 16 Accepted Submission(s) : 3

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 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

求出next[]发现:

前缀为i个字符的串的周期=i-next[i] 循环次数=i/周期, (i % 周期 != 0,不存在周期)。

代码如下：

#include <iostream>
#include <cstring>
#include <cstdio>
using namespace std;
int next[1000005];
char s[1000005];
int n , m ;
void get_next()
{
	int j ;
	next[1]=next[0]= 0;
	for(int i = 1; i < m; i ++)
	{
		j = next[i];
		while(j && s[i] != s[j]) j = next[j];
		next[i + 1] = s[i] == s[j] ? j + 1 : 0;
	}
	printf("Test case #%d\n",n++);
	for(int i = 1; i <= m; i ++)
	{
		if(next[i] > 0 && i % (i - next[i])== 0)
		     printf("%d %d\n",i,i/(i - next[i]));
	}
	printf("\n");
}
int main()
{
	n = 1;
	while(scanf("%d",&m),m)
	{
		scanf("%s",s);
		get_next();
	}
	return 0;
}

与上面的对比：

example:

如果一个字符串可以由某个长度为k的字符串重复多次得到，我们说这个串以k 为周期。如，abcabcabcabc以3为周期（注意，它也以6，12 为周期）。输人一个长度不超过80的串，输出它的最小周期。

代码如下：

#include <iostream>
#include <cstring>
#include <cstdio>
using namespace std;
char str[100];
int next[105];
int m ;
void kmp()
{
    int j = 0;
    next[0] = next[1] = 0;
    for(int i = 1; i < m; i ++)
    {
        j = next[i];
        while(j && str[j]!=str[i]) j = next[j];
        next[i+1] = str[j] == str[i] ? j+1:0;
    }
}
int main()
{
    while(cin >> str)
    {
        m  = strlen(str);
        kmp();
        for(int i = 0; i <= m; i ++)
            cout << next[i] << " ";
        cout << endl;
        if(next[m] != 0 && m %(m-next[m]) == 0) printf("%d\n",m-next[m]);
        else
            printf("%d\n",m);
    }
    return 0;
}