UVa455 最小周期串问题

最新推荐文章于 2021-09-22 17:40:36 发布

Sinb妃

最新推荐文章于 2021-09-22 17:40:36 发布

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本文链接：https://blog.youkuaiyun.com/weixin_43981315/article/details/94860488

本文介绍了一种用于确定字符字符串最小周期的算法。通过输入一系列非空格字符，该算法能够找出构成字符串的最短重复单元，即其最小周期。示例中详细解释了如何通过比较旋转后的字符串来判断周期性，并提供了完整的C++代码实现。

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A character string is said to have period k if it can be formed by concatenating one or more repetitions
of another string of length k. For example, the string ”abcabcabcabc” has period 3, since it is formed
by 4 repetitions of the string ”abc”. It also has periods 6 (two repetitions of ”abcabc”) and 12 (one
repetition of ”abcabcabcabc”).
Write a program to read a character string and determine its smallest period.
Input
The first line oif the input file will contain a single integer N indicating how many test case that your
program will test followed by a blank line. Each test case will contain a single character string of up
to 80 non-blank characters. Two consecutive input will separated by a blank line.
Output
An integer denoting the smallest period of the input string for each input. Two consecutive output are
separated by a blank line.
Sample Input
1
HoHoHo
Sample Output
2

#include <iostream>
#include<algorithm>
#include<iomanip>
#include<string>
#include<cstring>
using namespace std;
int main()
{
	char a[81];
	int n;
	cin >> n;
	while (n--)
	{
		cin >> a;
		int t = 1;
		while (true)
		{
			int c = 0;
			int len = strlen(a);
			for (int i = 0; i < len; i++)
			{
				if (a[i] == a[(i + t) % len]) c++;
			}
			if (c == len) break;
			++t;
		}
		cout << t << endl;
		if (n != 0) cout << endl;
	}
}

学习笔记：环形串问题可看成一个圆，只要圆转动几次后可回到原位，即最小周期，所以只需要看s[i]==s[(i+t)%len]。