HDU 1711 Number Sequence （字符串处理 KMP）

题目链接

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`

题目分析：

字符串匹配的问题，kmp算法的应用。定义主串s和字串t，定位字串t就是要在主串s中找到一个与字串t完全相等的子串，返回第一次找到的位置的下标。

KMP算法

#include <cstdio>
const int maxn = 10000 + 10, maxm = 1000000 + 10;
int n, m;
int p[maxn], t[maxm], next[maxn]; //定义模式串，文本串，next数组
void getNext() //O(m)复杂度求Next数组
{
    int i = 0, j = 0, k = -1;
    next[0] = -1;
    while(j < m)
    {
        if(k == -1 || p[k] == p[j]) next[++j] = ++k;
        else k = next[k];
    }
}
int kmp()
{
    int j = 0; //初始化模式串的前一个位置
    getNext(); //生成next数组
    for(int i = 0; i < n; i++) //遍历文本串
    {
        while(j && p[j] != t[i]) j = next[j];//持续走直到可以匹配
        if(p[j] == t[i]) j++; //匹配成功继续下一个位置（j先加1 此时j的位置所对应的值在i的位置所对应的后面）

        //if(j==m)说明子串已经匹配完了（子串的长度是m，m-1是子串的最后一个字符）
        if(j == m) return i-m+2; //找到后返回第一个匹配的位置,因为返回的是逻辑下标（下标从1开始所以是i-m+2，不信自己在纸上画画 （看下图 ））
    }
    return -1; //找不到返回-1
}
int main()
{
    int T;
    scanf("%d", &T);
    while(T--)
    {
        scanf("%d%d", &n, &m);
        for(int i = 0; i < n; i++) scanf("%d", t+i);
        for(int i = 0; i < m; i++) scanf("%d", p+i);
        printf("%d\n", kmp());
    }
    return 0;
}

解释为什么返回 i-m+2