数据结构-串KMP算法

简介

KMP的基本介绍大家可以百度。在这会前你要理解字符串的前缀和后缀的概念。KMP算法在模式匹配的过程中的主要有点是：**主串(str)不用回退，只需要模式串(pat)**回退即可。
而且模式串回退是有一定规律的。
每次匹配不成功的时候要怎么回退呢？回退多少呢？

next数组

举个例子。模式串：$aabaac$.

	0	1	2	3	4	5
模式串	a	a	b	a	a	c
next	-1	0	1	0	1	2
nextval	-1	-1	1	-1	-1	2

这我们存储模式串的数组下标是从0开始的，我们next第一个要写成-1。后面的数字，就是从当前的（当前的字符不算）下标开始往前找找到最大长度的后缀等于前缀的情况再加1就是此时next[j]的值。
当我们的模式串下标是从1开始的，我们就next第一个要写成0。后面的数字，就是从当前的（当前的字符不算）下标开始往前找找到最大长度的后缀等于前缀的情况就是此时next[j]的值。
公式：
$$\begin{array}{r}next[j]=\{\begin{array}{llc}0，& & j=1\\ max(k|1<k<j{且}^{\prime }{p}_1...p_{k-1}^{\prime }{=}^{\prime }{p}_{j-k+1}...p_{j-1}^{\prime })，& & 此集合不空时\\ 1，& & 其他情况\end{array}\end{array}$$
$nextval[j]=nextvql[next[j]]其中j=1...len(pat)-1$

例题LeetCode28

Implement strStr().

Return the index of the first occurrence of needle in haystack, or -1 if needle is not part of haystack.

Example 1:
Input: haystack = “hello”, needle = “ll”
Output: 2

Example 2:
Input: haystack = “aaaaa”, needle = “bba”
Output: -1

Clarification:
What should we return when needle is an empty string? This is a great question to ask during an interview.

For the purpose of this problem, we will return 0 when needle is an empty string. This is consistent to C’s strstr() and Java’s indexOf().

Constraints:

• haystack and needle consist only of lowercase English characters.

code

def strStr(haystack: str, needle: str) -> int:

	#  get  next
    i, j = 0, -1
    next = [0]*(len(needle)+1)
    next[0] = -1
    while i < len(needle):
        if j == -1 or needle[i] == needle[j]:
            i += 1
            j += 1
            next[i] = j
        else:
            j = next[j]
    print(next)

	#  get  nextval
    i = 1
    while i<len(needle)-1:
        j = next[i]
        if needle[i] == needle[j]:
            next[i] = next[j]
        i += 1
    print(next)

	#  KMP 
    i, j = 0, 0
    while i < len(haystack) and j < len(needle):
        if j == -1 or haystack[i] == needle[j]:
            i += 1
            j += 1
        else:
            j = next[j]

    if j >= len(needle):
        print(i-len(needle))
        return i-len(needle)
    else:
        return -1


haystack = "aabaabaabaac"
needle = "aabaac"
strStr(haystack, needle)