E - Period(KMP求循环节的位置以及出现的次数)

最新推荐文章于 2019-09-08 15:32:19 发布

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本文介绍了一种用于检测字符串前缀是否为周期性字符串的方法。该算法通过计算字符串的KMP next数组来找出所有可能的周期，并展示了如何通过输入文件进行测试案例分析，最后输出每个具有周期性的前缀长度及其周期。

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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

#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
using namespace std;
const int maxn = 1000009;
char pattern[maxn];
int nnext[maxn];
void pre()
{
   int patternLen = strlen(pattern);
   int i = 0, j = -1;
   nnext[0] = -1;
   while(i!=patternLen)
   {
      if(j==-1||pattern[i]==pattern[j])
      nnext[++i] = ++j;
      else
      j = nnext[j];
   }
}
int main()
{
  int n;
  int T = 1;
  while(~scanf("%d", &n)&&n)
  {
    scanf("%s", pattern);
    printf("Test case #%d\n", T++);
    pre();
    for(int i=2;pattern[i-1];i++)
    {
      int t = i - nnext[i];//循环的长度
      if(i%t==0&&i/t>1)
      printf("%d %d\n", i, i/t);//循环到的位置，出现的次数
    }
    printf("\n");
  }
  return 0;
}