KMP

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本文深入解析KMP算法的核心思想及其实现过程，通过具体例子展示如何高效匹配目标串与模式串，同时提供完整的C语言代码实现。文章还介绍了如何通过预处理模式串计算next数组，进一步优化匹配效率。

1. 例子

目标串S：ababcabcacbab

模式串P：abcac

匹配过程：

1 ababcabcacbab

abcacd

~~2 ababcabcacbab~~ //KMP算法没有这一趟，再KMP算法中，目标串的指针是不会回溯的

~~abcacd~~

01s s 89

2 ababcabcacbab

abcabd

j j

0123456s s

3 ababcabcacdab //第3趟并没有再比较红色的ab，因为再第2趟已经比较到了第二个ab

abcabd

01j j //模式串两个ab重复 abcabd，如果目标串与模式串第二个ab匹配来，说明一定与第一个ab匹配，因此就不用再与第一个ab比较了

2.求next[j] = k的算法

next[j] = k中j是模式串指针的当前位置，当模式串的 j(5)位置与目标串s(7)位置的元素不匹配时，j(5)应该回溯到模式串的 k(2)位置（即k表示已经匹配上到元素个数），而目s(7)就地不动（不回溯！）

求数组next[j]的算法如下，它只与模式串有关，与目标串无关

void cal_next(char *p, int *next, int len)
{//important!!  array rangs from 0 to len-1
    int i = -1, j = 0;//i == -1 means back to the first elem of p[];
    next[0] = -1;
    //except first element, next[j]=k means that before j, there are k elem matched, 
    while(j < len)
    {
        if(i == -1 || p[i] == p[j])
        {//if p[j] machted, we know that before j+1, there are i elem matched
            i++;
            j++;
            next[j] = i;
        }
        else
        {//go back;
            i = next[i];
        }
    }
}
//e.g1:   p[]   a b c a b c d e
//    next[j]  -1 0 0 0 1 2 3 0
//e.g2:   p[]   a b a a b c a c
//    next[j]  -1 0 0 1 1 2 0 1

3. KMP算法

int KMP(char* s, char *p, int len)
{   //array starts with 0;
    //p is par_string, s is des_string, len is the length of p[];
	int i = 0, j = 0;//i point to s[], j point to p[]
	while(s[i] != '\0' && j < len)
	{//not meet the end of both arrays
		if(j == -1 || p[j] == s[i])
		{//matched
		    i++;
		    j++;
        }
		else
		{//mismatched
		    j = next[j];
        }
	}
	if(j == len)
	{//all matched!
	    printf("\ni = %d, j = %d, match point = %d\n", i, j, i - j);
		return i - j;
	}
	else
	{//fail to match!
	    printf("no match!\n");
		return -1;
	}
}

4. Test program (C)

#include <stdio.h>
#include <stdlib.h>
#define N 100
int next[N];
void cal_next(char *p, int *next, int len)
{//array rangs from 1 to len-1
    int i = -1, j = 0;//i == 0 is invalid
    next[0] = -1;
    //except first element,
    //next[j]=k means that befor j, there are k-1 elem matched
    while(j < len)
    {
        if(i == -1 || p[i] == p[j])
        {
            i++;
            j++;
            next[j] = i;
        }
        else
        {
            i = next[i];
        }
    }
    //print next[]
    printf(" %s\n", p);
    for(i = 0; i < strlen(p); i++)
    {
        printf("%d", next[i]);
    }
}

int KMP(char* s, char *p, int len)
{   //array starts with 0;
    //p is par_string, s is des_string, len is the length of p[];
	int i = 0, j = 0;//i point to s[], j point to p[]
	while(s[i] != '\0' && j < len)
	{//not meet the end of both arrays
		if(j == -1 || p[j] == s[i])
		{//matched
		    i++;
		    j++;
        }
		else
		{//mismatched
		    j = next[j];
        }
	}
	if(j == len)
	{//all matched!
	    printf("\ni = %d, j = %d, match point = %d\n", i, j, i - j);
		return i - j;
	}
	else
	{//fail to match!
	    printf("\n miss match!\n");
		return -1;
	}
}

int main()
{
    char *p = "abcabcde";//par_string
    char *s = "abcdabceabcabcdefabc";//des_string
    cal_next(p, next, strlen(p));
    KMP(s, p, strlen(p));
    return 0;
}

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