关于KMP算法的原理等请参阅这篇文章：Kmp算法浅析（C++实现）

       本篇文章只是对Kmp用Python进行了实现。

        1.时间复杂度分析

        BF算法的时间复杂度：在最坏的情况下，BF算法要将目标串的每一个字符同模式串进行比较一遍，假定目标串长度为m，模式串长度为n，总的时间复杂度为O（m*n）。而对于KMP算法，进行比较的时间复杂度为O（m+n），求next数组的时间复杂度为n，总体时间复杂度为O（m+2n）。

        2.源代码

        源代码介绍：BF_Match为常规的模式匹配算法，KMP_Match_1和KMP_Match_2为KMP算法，二者是一样的，不同之处在于二者调用了不同的求Next数组的函数。求Next数组有两种方法：一种是递推法getNext_1()，一种是直接求取的方法getNext_2()。详情请参阅下面的源代码：

import random
import datetime

def BF_Match(s, t):
    slen = len(s)
    tlen = len(t)
    if slen >= tlen:
        for k in range(slen - tlen + 1):
            i = k
            j = 0
            while i < slen and j < tlen and s[i] == t[j]:
                i = i + 1
                j = j + 1
            if j == tlen:
                return k
            else:
                continue
    return -1

def KMP_Match_1(s, t):
    slen = len(s)
    tlen = len(t)
    if slen >= tlen:
        i = 0
        j = 0
        next_list = [-2 for i in range(len(t))]
        getNext_1(t, next_list)
        #print next_list
        while i < slen:
            if j == -1 or s[i] == t[j]:
                i = i + 1
                j = j + 1
            else:
                j = next_list[j]
            if(j == tlen):
                return i - tlen
    return -1

def KMP_Match_2(s, t):
    slen = len(s)
    tlen = len(t)
    if slen >= tlen:
        i = 0
        j = 0
        next_list = [-2 for i in range(len(t))]
        getNext_2(t, next_list)
        #print next_list
        while i < slen:
            if j == -1 or s[i] == t[j]:
                i = i + 1
                j = j + 1
            else:
                j = next_list[j]
            if j == tlen:
                return i - tlen
    return -1

def getNext_1(t, next_list):
    next_list[0] = -1
    j = 0
    k = -1
    while j < len(t) - 1:
        if k == -1 or t[j] == t[k]:
            j = j + 1
            k = k + 1
            next_list[j] = k
        else:
            k = next_list[k]

def getNext_2(t, next_list):
    next_list[0] = -1
    next_list[1] = 0
    for i in range(2, len(t)):
        tmp = i -1
        for j in range(tmp, 0, -1):
            if equals(t, i, j):
                next_list[i] = j
                break
            next_list[i] = 0

def equals(s, i, j):
    k = 0
    m = i - j
    while k <= j - 1 and m <= i - 1:
        if s[k] == s[m]:
            k = k + 1
            m = m + 1
        else:
            return False
    return True
    

def rand_str(length):
    str_0 = []
    for i in range(length):
        str_0.append(random.choice("abcdefghijklmnopqrstuvwxyz"))
    return str_0

def main():
    x = rand_str(20000)
    y = rand_str(5)

    print "The String X Length is : ", len(x), " String is :",
    for i in range(len(x)):
        print x[i],
    print ""    
    print "The String Y Length is : ", len(y), " String is :",
    for i in range(len(y)):
        print y[i],
    print ""    

    time_1 = datetime.datetime.now()
    pos_1 = BF_Match(x, y)
    time_2 = datetime.datetime.now()
    print "pos_1 = ", pos_1

    time_3 = datetime.datetime.now()
    pos_2 = KMP_Match_1(x, y)
    time_4 = datetime.datetime.now()
    print "pos_2 = ", pos_2

    time_5 = datetime.datetime.now()
    pos_3 = KMP_Match_2(x, y)
    time_6 = datetime.datetime.now()
    print "pos_3 = ", pos_3

    print "Function 1 spend ", time_2 - time_1
    print "Function 2 spend ", time_4 - time_3
    print "Function 3 spend ", time_6 - time_5

main()