POJ 3461 Oulipo

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本文介绍了一个基于KMP算法的比赛题目，任务是在一个大型文本中找出特定模式串出现的次数。文章详细解释了如何构建失配数组并使用它来高效地进行模式匹配。

Oulipo

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 42924		Accepted: 17251

Description

The French author Georges Perec (1936–1982) once wrote a book, La disparition, without the letter 'e'. He was a member of the Oulipo group. A quote from the book:

Tout avait Pair normal, mais tout s’affirmait faux. Tout avait Fair normal, d’abord, puis surgissait l’inhumain, l’affolant. Il aurait voulu savoir où s’articulait l’association qui l’unissait au roman : stir son tapis, assaillant à tout instant son imagination, l’intuition d’un tabou, la vision d’un mal obscur, d’un quoi vacant, d’un non-dit : la vision, l’avision d’un oubli commandant tout, où s’abolissait la raison : tout avait l’air normal mais…

Perec would probably have scored high (or rather, low) in the following contest. People are asked to write a perhaps even meaningful text on some subject with as few occurrences of a given “word” as possible. Our task is to provide the jury with a program that counts these occurrences, in order to obtain a ranking of the competitors. These competitors often write very long texts with nonsense meaning; a sequence of 500,000 consecutive 'T's is not unusual. And they never use spaces.

So we want to quickly find out how often a word, i.e., a given string, occurs in a text. More formally: given the alphabet {'A', 'B', 'C', …, 'Z'} and two finite strings over that alphabet, a word W and a text T, count the number of occurrences of W in T. All the consecutive characters of W must exactly match consecutive characters of T. Occurrences may overlap.

Input

The first line of the input file contains a single number: the number of test cases to follow. Each test case has the following format:

One line with the word W, a string over {'A', 'B', 'C', …, 'Z'}, with 1 ≤ |W| ≤ 10,000 (here |W| denotes the length of the string W).
One line with the text T, a string over {'A', 'B', 'C', …, 'Z'}, with |W| ≤ |T| ≤ 1,000,000.

Output

For every test case in the input file, the output should contain a single number, on a single line: the number of occurrences of the word W in the text T.

Sample Input

3
BAPC
BAPC
AZA
AZAZAZA
VERDI
AVERDXIVYERDIAN

Sample Output

1
3
0

题目链接：http://poj.org/problem?id=3461

题意：输入测试组数t，每组测试数据包括两个字符串W和T，求W在T中的出现次数。

解题思路：裸的KMP算法，求出W的失配函数，再利用失配函数fail将W与T匹配。

AC代码：

#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
const int MAXM = 1e4 + 10;//最大的W长度 
const int MAXN = 1e6 + 10;//最大的T长度 
char W[MAXM];
char T[MAXN];
int fail[MAXM];//失配数组 
void get_fail(int m)//获得失配数组 
{
	fail[0]=0;
	fail[1]=0;
	for(int i=1;i<m;i++)
	{
		int j=fail[i];
		while(j && W[i]!=W[j]) j=fail[j];//回溯求fail[i] 
		fail[i+1]=W[i]==W[j]?j+1:0;
	}
}
int find()//查询函数 
{
	int n=strlen(T);
	int m=strlen(W);
	get_fail(m);
	int ans=0;
	int j=0;
	for(int i=0;i<n;i++) 
	{
		while(j && T[i]!=W[j]) j=fail[j];
		if(T[i]==W[j]) j++;
		if(j==m) ans++;//匹配成功将数量加一 
	}
	return ans;//返回答案 
}
int main(void)
{
	int t;//测试组数 
	scanf("%d",&t);
	getchar();
	while(t--)
	{
		gets(W);
		gets(T);
		printf("%d\n",find());
	}
	return 0;
}