KMP_algoritm.py

# Python implementation of KMP (Knuth Morris Pratt)
# pattern-matching algorithm. Worst case time complexity
# O(n + m) where n is the length of text and m is the length
# of the pattern to be found. Auxiliary space: O(M)
# Worst case is as better than naive search and equal to
# Rabin-Karp algorithm.

def KMPSearch(pat, txt):
	M = len(pat)
	N = len(txt)

	# create lps[] that will hold the longest prefix suffix
	# values for pattern
	lps = [0]*M
	j = 0 # index for pat[]

	# Preprocess the pattern (calculate lps[] array)
	computeLPSArray(pat, M, lps)

	i = 0 # index for txt[]
	while (N - i) >= (M - j):
		if pat[j] == txt[i]:
			i += 1
			j += 1

		if j == M:
			print("Found pattern at index " + str(i-j))
			j = lps[j-1]

		# mismatch after j matches
		elif i < N and pat[j] != txt[i]:
			# Do not match lps[0..lps[j-1]] characters,
			# they will match anyway
			if j != 0:
				j = lps[j-1]
			else:
				i += 1


# Function to compute LPS array
def computeLPSArray(pat, M, lps):
	len = 0 # length of the previous longest prefix suffix

	lps[0] = 0 # lps[0] is always 0
	i = 1

	# the loop calculates lps[i] for i = 1 to M-1
	while i < M:
		if pat[i] == pat[len]:
			len += 1
			lps[i] = len
			i += 1
		else:
			# This is tricky. Consider the example.
			# AAACAAAA and i = 7. The idea is similar
			# to search step.
			if len != 0:
				len = lps[len-1]

				# Also, note that we do not increment i here
			else:
				lps[i] = 0
				i += 1


# Driver code
if __name__ == '__main__':
	txt = "ABABDABACDABABCABAB"
	pat = "ABABCABAB"
	KMPSearch(pat, txt)