kmp的next数组的运用（求字符串的最小循环节）

hdu3746

Cyclic Nacklace

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

Total Submission(s): 2262    Accepted Submission(s): 1005

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

 

分析：题意就是给出一个字符串，问至少需要增加多少个字符可以是修改后的字符串有至少两个循环节。

通过这题得出了一个很重要的结论，在用kmp算法求出next数组后，len-next[len]的值就是该字符串的最小循环节，如果len恰好是len-next[len]的整数倍并且len不等于len-next[len]，那么需要增加的字符个数是len；

否则需要增加的字符是len-len%（len-next[len]）；

程序：

#include"stdio.h"
#include"string.h"
#define M 100009
int next[M],ans;
void getNext(char *b)
{
    int i,j;
    i=0;
    j=-1;
    next[0]=-1;
    while(b[i]!='\0')
    {
        if(j==-1||b[i]==b[j])
        {
            i++;
            j++;
            next[i]=j;
        }
        else
            j=next[j];
    }
}
int main()
{
    char str[M];
    int n,i;
    scanf("%d",&n);
    while(n--)
    {
        scanf("%s",str);
        getNext(str);
        int m=strlen(str);
        int p=m-next[m];
        if(m%p==0&&m>p)
        printf("0\n");
        else
        printf("%d\n",p-(m%p));
    }
}