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：