【字符串入门专题1】 I - Number Sequence hdu1711【kmp】

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本文介绍了一种基于KMP算法的解决方案，用于在大型数列中查找特定子数列首次出现的位置。通过构建next数组优化搜索过程，实现高效定位。

Number Sequence

Time Limit: 10000/5000 MS (Java/Others) Memory Limit: 32768/32768 K (Java/Others)
Total Submission(s): 28715 Accepted Submission(s): 12063

Problem Description

Given two sequences of numbers : a[1], a[2], ...... , a[N], and b[1], b[2], ...... , b[M] (1 <= M <= 10000, 1 <= N <= 1000000). Your task is to find a number K which make a[K] = b[1], a[K + 1] = b[2], ...... , a[K + M - 1] = b[M]. If there are more than one K exist, output the smallest one.

Input

The first line of input is a number T which indicate the number of cases. Each case contains three lines. The first line is two numbers N and M (1 <= M <= 10000, 1 <= N <= 1000000). The second line contains N integers which indicate a[1], a[2], ...... , a[N]. The third line contains M integers which indicate b[1], b[2], ...... , b[M]. All integers are in the range of [-1000000, 1000000].

Output

For each test case, you should output one line which only contain K described above. If no such K exists, output -1 instead.

Sample Input

2
13 5
1 2 1 2 3 1 2 3 1 3 2 1 2
1 2 3 1 3
13 5
1 2 1 2 3 1 2 3 1 3 2 1 2
1 2 3 2 1

Sample Output

6
-1

题意：找到s2在s1中第一次出现的位置，没有找到输出-1

思路：kmp稍微变形一下，依然可以用来处理数字字符串，只要找到s1中出现s2就直接返回下标，若在循环内没找到，在循环结束后判断s2是不是s1的后缀就行了


#include<stdio.h>
#define inf 99999999
#define N 1100000
#define M 11000
int a[N],b[M];
int next[M];

int kmp(int a[],int b[],int next[])//找到s2第一次在s1中出现的位置 
{
	int j,k,i;
	j = 0;
	k = -1;
	next[0] = -1;
	while(b[j]!=inf)//建立next数组 
	{
		while(k!=-1&&b[k]!=b[j])
		{
			k = next[k];
		}
			
		j++;
		k++;
		if(b[k]!=b[j])
			next[j] = k;
		else
			next[j] = next[k];
	}
	i = j = 0;
	while(a[i]!=inf)
	{
		if(b[j] == inf)
			return i-j+1;//第一次出现就返回在s1中的下标 
		else
		{
			while(j != -1&&a[i]!=b[j])
				j = next[j];
			i++;
			j++;
		}
	}
	if(b[j] == inf)//判断s2是否为s1数组的后缀 
		return i-j+1;
	return -1;//不存在返回-1 
}

int main()
{
	int t,i,j,n,m;
	scanf("%d",&t);
	while(t --)
	{
		scanf("%d%d",&n,&m);
		for(i = 0; i < n; i ++)
			scanf("%d",&a[i]);
		for(j = 0; j < m; j++)
			scanf("%d",&b[j]);
		a[i] = b[j] = inf;//设置截止符 
		
		printf("%d\n",kmp(a,b,next));
	}
	return 0;
}