KMP算法

KMP 算法公式：

///推导公式
/// f(j)=pattern[1...(k-1)]=pattern[j-(k-1)...(j-1)];j表示pattern中的字符数，K表示前缀字符串中K的最大值，K<J;
/// pattern[j]!=pattern[f(j)];next[j]=f(j);
/// pattern[j]==pattern[f(j)];next[j]=next[f(j)];

先付代码：后做详细分析；

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace KMP
{
class Program
{
static void Main(string[] args)
{
string pattern = "abcabcacab";
string target = "babcbabcabcaabcabcabcacabc";
Program pg = new Program();
int n = pg.KMPMatch(target.ToCharArray(), pattern.ToCharArray());
Console.WriteLine("pattern 在 target 中匹配的次数是:"+n);
Console.Read();
}
///推导公式
/// f(j)=pattern[1...(k-1)]=pattern[j-(k-1)...(j-1)];j表示pattern中的字符数，K表示前缀字符串中K的最大值，K<J;
/// pattern[j]!=pattern[f(j)];next[j]=f(j);
/// pattern[j]==pattern[f(j)];next[j]=next[f(j)];
/// <summary>
/// 建立Next表
/// </summary>
/// <param name="pattern"></param>
/// <returns>next</returns>
protected int[] BuildNext(char[] pattern)
{
int patternLength = pattern.Length;
//设置next
int[] next = new int[patternLength];
int j = 1;//表示模板第几个字符个数。
int k = 0;//默认值为0，表示f(j)中K的最大值;
//初始化next
for (int i = 0; i < patternLength; i++)
{
next[i] = 0;
}
//计算next表
while (j < patternLength)
{
//控制前缀字符串包含，则K++;否则至为0；
while (k > 0 && pattern[j - 1] != pattern[k - 1])
{
k = next[k - 1];//把k设置为0，或者写为k=0;
}
j++;
k++;
//更据推导公式
if (pattern[j - 1] != pattern[k - 1])
{
next[j - 1] = k;
} else
{
next[j - 1] = next[k - 1];
}
}
return next;
}
public int KMPMatch(char[] target, char[] pattern)
{
int n = 0;//表示返回匹配的字符串个数;
int[] matches = new int[target.Length];
int[] next = BuildNext(pattern);//获取next跳转表；
int i = 0;//target字符开始匹配的i;
int j = 1;//pattern 字符匹配，必须设置1；
//target最小长度必须大于pattern的长度;
while(pattern.Length-j<=target.Length-i)
{
if(target[i]==pattern[j-1])
{
i++;
j++;
if(j==pattern.Length)
{
matches[n++] = i + 1 - pattern.Length;//获取匹配成功的位置；
j = next[j - 1];
if(j==0)
{
j++;
}
}
}
else
{
j = next[j - 1];
if(j==0)
{
j++;
i++;
}
}
}
return n;
}
}
}

　　运行结果：