kmp算法核心在next函数。就是要计算出一下pattern字符串的位置。
比如：
p r e - a b a b a b c //i = 8
a b a b c //j = 4
当匹配到i=8,j=4时候， 出现了不匹配。需要调整j的位置继续匹配。（就是根据abab这个已经匹配了的子字符串来计算出下一个j的位置），调整后的结果为：
p r e - a b a b a b c //i = 8
a b a b c //j = 2
就是说当j=4时，next j应该是2.
next算法可以通过动态规划算法来实现 。如下：
a b a b c d
0 0 0 0 0 0 0
a 0 1 0 1 0 0 0
b 0 0 2 0 2 0 0
a 0 1 0 3 0 0 0
b 0 0 2 0 4 0 0
c 0 0 0 0 0 5 0
d 0 0 0 0 0 0 6
然后过滤掉无效的数据。生成next数组，就是每列的最大值。
代码如下：
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#include <iostream>
#include <string>
using namespace std;
int *prepro(const char *pattern);
int kmp(const char *pattern, const char *str);
int kmp(const char *pattern, const char *str)
{
//预处理，通过动态规划算法生成next数组
int *next = prepro(pattern);
const int str_len = strlen(str);
const int pattern_len = strlen(pattern);
int i, j;
i = j = 0;
while (i < str_len)
{
bool flag = false;
while (j < pattern_len && pattern[j] == str[i])
{
i++;
j++;
flag = true;
}
//匹配成功
if (j == pattern_len)
{
return i-j;
}
if (flag) //部分匹配，计算next
{
j = next[j];
}
else //不匹配，继续处理
{
i++;
j = 0;
}
}
return -1;
}
int *prepro(const char *pattern)
{
int len = strlen(pattern);
//初始化动态规划数组 arr[len+1][len+1]
int **arr = new int*[len+1];
for (int i=0; i<len+1; i++)
{
arr[i] = new int[len+1];
}
/*
//打印数组
printf("\t\t");
for (int i=0; i printf("\n");
for (int i=0; i {
if (i == 0)
{
printf("\t");
}
else
{
printf("%c\t", pattern[i-1]);
}
for (int j=0; j {
printf("%d\t", arr[i][j]);
}
printf("\n");
}
*/
//生成动态规划数组
for (int i=1; i<len+1; i++)
{
for (int j=1; j<len+1; j++)
{
if (pattern[i-1] == pattern[j-1])
{
arr[i][j] = arr[i-1][j-1] + 1;
}
else
{
arr[i][j] = 0;
}
}
}
cout << "------------------------------" << endl;
printf("\t\t");
for (int i=0; i<len; i++)printf("%c\t", pattern[i]);
printf("\n");
for (int i=0; i<len+1; i++)
{
if (i == 0)
{
printf("\t");
}
else
{
printf("%c\t", pattern[i-1]);
}
for (int j=0; j<len+1; j++)
{
printf("%d\t", arr[i][j]);
}
printf("\n");
}
//生成next数组,首先过滤arr数组，next[j]就是arr[*][j]中的最大值
int *next = new int[len+1];
for (int i=1; i<len+1; i++)
{
for (int j=1; j<len+1; j++)
{
//匹配的长度最多一半
if (2*i > j)
{
arr[i][j] = 0;
}
//必须是从字符串头匹配的才算
if (arr[i][j] != 0 && arr[i][j] != i)
{
arr[i][j] = 0;
}
if (arr[i][j] > next[j])
{
next[j] = arr[i][j];
}
}
}
/*
cout << endl << "------------------------------" << endl;
printf("\t\t");
for (int i=0; i printf("\n");
for (int i=0; i {
if (i == 0)
{
printf("\t");
}
else
{
printf("%c\t", pattern[i-1]);
}
for (int j=0; j {
printf("%d\t", arr[i][j]);
}
printf("\n");
}
*/
//如果子字符串去不相等，更新next
bool *equal = new bool[len+1];
for (int i=0; i<len+1; i++)
{
equal[i] = false;
}
equal[0] = equal[1] = true;
for (int i=2; i<len+1; i++)
{
if (pattern[i-1] == pattern[i-2])
{
equal[i] = true;
}
else
{
break;
}
}
//printf("next=\t");
for (int i=0; i<len+1; i++)
{
//printf("%d\t", next[i]);
if (equal[i] && next[i] > 0)next[i] = i-1;
//printf("%d\t", next[i]);
}
//cout << endl << "---------------------------------------" << endl;
return next;
}
int main(int argc, char **argv)
{
const char *pattern = argv[1];
const char *str = argv[2];
cout << kmp(pattern, str) << endl;
return 0;
}
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直接g++编译ok。
发现next函数不用动态规划算法，大财小用了啊.应该是：
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#include <iostream>
#include <string>
using namespace std;
void fun(const char *str)
{
int len = strlen(str);
int *p = new int[len];
for (int i=0; i<len; i++)
{
if (str[i] == str[0])
{
p[i] = 1;
}
}
if (len < 2)return;
for (int i=2; i<len; i++)
{
if (p[i-1] != 0)
{
if (i+1 >= 2*(p[i-1]+1) && str[i] == str[p[i-1]])
p[i] = p[i-1]+1;
}
}
bool equal = true;
for (int i=1; i<len; i++)
{
if (equal)
{
if (str[i] == str[i-1])
{
p[i] = i;
}
else
{
equal = false;
}
}
else
{
break;
}
}
for (int i=0; i<len; i++)
{
cout << str[i] << " ";
}
cout << endl;
for (int i=0; i<len; i++)
{
cout << p[i] << " ";
}
cout << endl;
return;
}
int main(int argc, char **argv)
{
fun(argv[1]);
return 0;
}
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