KMP算法

思想

朴素的匹配算法是一对一的匹配，每次匹配失败主串和模式串上的指针都回退到开头，
但实际上这种回退是没有必要的
而KMP算法通过对模式串的处理进而减少回退次数

时间复杂度T=O(n+m)

实现

typedef int Position;
#define NotFound -1
void BuildMatch(Position match[],char *pattern,int len)
{
    
    match[0]=-1;
    for(Position j=1;j<len;j++)
    {
    
        Position i=match[j-1];
        while(i>=0&&pattern[j]!=pattern[i+1])
            i=match[i];
        if ( pattern[i+1]==pattern[j] )
		     match[j] = i+1;
		else match[j] = -1;
    }
}
Position KMP(char *str,char *pattern)
{
    
    int n=strlen(str),m=strlen(pattern);
    Position p=0,s=0;
    if(n<m)return NotFound;
    Position *match=(Position*)malloc(sizeof(Position)*m);
    BuildMatch(match,pattern,m);
    while(p<m&&s<n)
    {
    
        if(str[s]==pattern[p])
        {
    
            s++;p++;
        }
        else if(p>0)
            p=match[p-1]+1;
            else s++;
    }
    return p==m?s-m:NotFound;
}

##PTA习题

#include<bits/stdc++.h>
using namespace std;
typedef int Position;
#define NotFound -1
void BuildMatch(Position match[],char *pattern,int len)
{
    
    match[0]=-1;
    for(Position j=1;j<len;j++)
    {
    
        Position i=match[j-1];
        while(i>=0&&pattern[j]!=pattern[i+1])
            i=match[i];
        if ( pattern[i+1]==pattern[j] )
		     match[j] = i+1;
		else match[j] = -1;
    }
}
Position KMP(char *str,char *pattern)
{
    
    int n=strlen(str),m=strlen(pattern);
    Position p=0,s=0;
    if(n<m)return NotFound;
    Position *match=(Position*)malloc(sizeof(Position)*m);
    BuildMatch(match,pattern,m);
    while(p<m&&s<n)
    {
    
        if(str[s]==pattern[p])
        {
    
            s++;p++;
        }
        else if(p>0)
            p=match[p-1]+1;
            else s++;
    }
    return p==m?s-m:NotFound;
}
int main()
{
    
    char str[1000001];
    scanf("%s",str);
    int n;
    cin>>n;
    for(int i=0;i<n;i++)
    {
    
        getchar();
        char tmp[100001];
        scanf("%s",tmp);
        Position p=KMP(str,tmp);
        if(p==-1)
            cout<<"Not Found\n";
        else printf("%s\n",str+p);
    }
    return 0;
}

参考浙江大学数据结构MOOC