KMP Python

原创于 2015-03-25 04:16:33 发布 · 820 阅读

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本文深入解析KMP算法，一种用于搜索字符串的高级算法，它利用有限状态机实现最优时间复杂度O(n)。通过构建模式表和DFA（确定有限自动机），实现快速匹配。实例代码演示了从构建模式表到实际搜索过程。

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KMP is an advanced algorithm for search an substring in a string.

It mains definite finite states.

The general worst time complexity is O(n), because we need to search the whole string.

code is as follow?

def kmp(pat):
	M = len(pat)
	#R = len(set(pat))
	table = {}
	i = 0
	for char in pat:
		if char not in table:
			table[char] = i
			i += 1
	R = len(table)
	#print table
	dfa = [[0 for j in range(M)] for  i in range(R)]
	dfa[table[pat[0]]][0] = 1
	last = 0
	for j in xrange(1, M):
	 	for c in range(R):
	 		dfa[c][j] = dfa[c][last] ## copy mismatch
	 	dfa[table[pat[j]]][j] = j + 1 ## update new state
	 	last = dfa[table[pat[j]]][last] ## preserve last state
	return dfa, table

def search(txt, pat):
	n = len(txt)
	m = len(pat)
	dfa, table = kmp(pat)
	j = 0
	for i in range(n):
		if txt[i] in table:
			j = dfa[table[txt[i]]][j]
	if j == len(pat):
		return True
	return False



pat = "ABAB"
txt = "ABCAB"
search(txt, pat)