POJ1961[KMP 失配函数]

最新推荐文章于 2020-11-23 12:33:38 发布

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最新推荐文章于 2020-11-23 12:33:38 发布

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本文介绍了一种用于确定字符串所有前缀周期性的算法。通过分析每个前缀找到其最短重复模式，特别关注如何利用失配部分来快速确定周期。提供了一个C++实现示例。

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Period

Time Limit: 3000MS		Memory Limit: 30000K
Total Submissions: 16776		Accepted: 8077

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

Source

Southeastern Europe 2004

求每个前缀的最短循环节

错位的部分是个循环节

即i%(i-f[i])==0

再次想想从0开始问题

跳到的那个位置之前的所有字符与当前失配字母前的相同数量个字母是相匹配的

#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
const int N=1e6+5;
int n,f[N];
char p[N];
int main(){
    int cas=0;
    while(scanf("%d",&n)!=EOF&&n){
        scanf("%s",p);
        f[0]=f[1]=0;
        for(int i=1;i<n;i++){
            int j=f[i];
            while(j&&p[j]!=p[i]) j=f[j];
            f[i+1]=p[j]==p[i]?j+1:0;
        }
        printf("Test case #%d\n",++cas);
        for(int i=2;i<=n;i++)
            if(f[i]>0&&i%(i-f[i])==0) printf("%d %d\n",i,i/(i-f[i]));
        printf("\n");
    }
}