HDU 3746 - Cyclic Nacklace & HDU 1358 - Period - [KMP求最小循环节]

题目链接：http://acm.hdu.edu.cn/showproblem.php?pid=3746

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)

Problem Description

CC always becomes very depressed at the end of this month, he has checked his credit card yesterday, without any surprise, there are only 99.9 yuan left. he is too distressed and thinking about how to tide over the last days. Being inspired by the entrepreneurial spirit of "HDU CakeMan", he wants to sell some little things to make money. Of course, this is not an easy task.

As Christmas is around the corner, Boys are busy in choosing christmas presents to send to their girlfriends. It is believed that chain bracelet is a good choice. However, Things are not always so simple, as is known to everyone, girl's fond of the colorful decoration to make bracelet appears vivid and lively, meanwhile they want to display their mature side as college students. after CC understands the girls demands, he intends to sell the chain bracelet called CharmBracelet. The CharmBracelet is made up with colorful pearls to show girls' lively, and the most important thing is that it must be connected by a cyclic chain which means the color of pearls are cyclic connected from the left to right. And the cyclic count must be more than one. If you connect the leftmost pearl and the rightmost pearl of such chain, you can make a CharmBracelet. Just like the pictrue below, this CharmBracelet's cycle is 9 and its cyclic count is 2:

Now CC has brought in some ordinary bracelet chains, he wants to buy minimum number of pearls to make CharmBracelets so that he can save more money. but when remaking the bracelet, he can only add color pearls to the left end and right end of the chain, that is to say, adding to the middle is forbidden.
CC is satisfied with his ideas and ask you for help.

 

Input

The first line of the input is a single integer T ( 0 < T <= 100 ) which means the number of test cases.
Each test case contains only one line describe the original ordinary chain to be remade. Each character in the string stands for one pearl and there are 26 kinds of pearls being described by 'a' ~'z' characters. The length of the string Len: ( 3 <= Len <= 100000 ).

 

Output

For each case, you are required to output the minimum count of pearls added to make a CharmBracelet.

 

Sample Input

3

aaa

abca

abcde

 

Sample Output

0

2

5

 

题目大意：

在字符串的左边或者右边添加最少的字符，使得字符串拥有循环节；

 

 

解题思路：

根据直觉，不难发现好像和Next[len]有一定关系，一开始我看了样例，单纯的以为答案就是len-2*Next[len]，十分天真；

后来才发现，len-Next[len]就是最小循环节：

　　

求出循环节之后，再做一点简单的数学计算就可以得到答案了。

（有一点是，如果循环节的组成是C[1…k]+C[1…m]，那是不是就要在左边加字符，或者要做一些特殊处理呢？显然不是，至于为什么，例如abcdabcdab和badcbadcba）

 

AC代码：

#include<cstdio>
#include<cstring>
#define MAX 100000+5
using namespace std;
int Next[MAX];
char pat[MAX];
int len,cycle;
void getnext()
{
    int i=0, j=-1;
    len=strlen(pat);
    Next[0]=-1;
    while(i<len)
    {
        if(j == -1 || pat[i] == pat[j]) Next[++i]=++j;
        else j=Next[j];
    }
}
int main()
{
    int t;
    scanf("%d",&t);
    while(t--)
    {
        scanf("%s",pat);
        getnext();
        cycle=len-Next[len];
        if(len%cycle==0)
        {
            if(len/cycle==1) printf("%d\n",cycle);
            else printf("0\n");
        }
        else printf("%d\n",cycle-(len-len/cycle*cycle));
    }
}

 

                                                                                                                                                                                                                                        

 

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

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 65536/32768 K (Java/Others)

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 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

 

题目大意：

给出一个长度为N的字符串，对其每个前缀串（满足长度≥2，且可以为字符串本身），考察是否存在循环节循环（即存在循环节，且循环节个数≥2）；

若存在，则输出该前缀串的长度，并且输出这个前缀串中循环节循环次数；

例如字符串：“aaa”：

　　前缀串①：“aa”，长度为2，循环节个数为2；

　　前缀串②：“aaa”，长度为3，循环节个数为3；

例如字符串：“aabaabaabaab”：

　　前缀串①：“aa”，长度为2，循环节个数为2；

　　前缀串②：“aabaab”，长度为6，循环节个数为2；

　　前缀串③：“aabaabaab”，长度为9，循环节个数为3；

　　前缀串④：“aabaabaabaab”，长度为12，循环节个数为4；

 

解题思路：

有了上面那题len-Next[len]的铺垫，本题就比较简单了，进行暴力枚举，判断之后输出即可。

 

AC代码：

#include<cstdio>
#include<cstring>
#define MAX 1000000+5
int Next[MAX],len;
char pat[MAX];
void getNext()
{
    int i=0, j=-1;
    Next[0]=-1;
    while(i<len)
    {
        if(j == -1 || pat[i] == pat[j]) Next[++i]=++j;
        else j=Next[j];
    }
}
int main()
{
    int kase=0;
    while(scanf("%d",&len) && len!=0)
    {
        scanf("%s",pat);
        getNext();
        printf("Test case #%d\n",++kase);
        for(int i=2,cycle;i<=len;i++)
        {
            cycle=i-Next[i];
            if(i%cycle == 0 && i/cycle >= 2) printf("%d %d\n",i,i/cycle);
        }
        printf("\n");
    }
}