# Python program that implements Z algorithm
# for pattern searching from Cormen et al.
# Time complexity O(n + m) where n is length
# of text and m is length of pattern
# Space complexity O(n + m) as well

# Fills Z array for given string str[]
def getZarr(string, z):
	n = len(string)

	# [L,R] make a window which matches
	# with prefix of s
	l, r, k = 0, 0, 0
	for i in range(1, n):

		# if i>R nothing matches so we will calculate.
		# Z[i] using naive way.
		if i > r:
			l, r = i, i

			# R-L = 0 in starting, so it will start
			# checking from 0'th index. For example,
			# for "ababab" and i = 1, the value of R
			# remains 0 and Z[i] becomes 0. For string
			# "aaaaaa" and i = 1, Z[i] and R become 5
			while r < n and string[r - l] == string[r]:
				r += 1
			z[i] = r - l
			r -= 1
		else:

			# k = i-L so k corresponds to number which
			# matches in [L,R] interval.
			k = i - l

			# if Z[k] is less than remaining interval
			# then Z[i] will be equal to Z[k].
			# For example, str = "ababab", i = 3, R = 5
			# and L = 2
			if z[k] < r - i + 1:
				z[i] = z[k]

			# For example str = "aaaaaa" and i = 2,
			# R is 5, L is 0
			else:

				# else start from R and check manually
				l = i
				while r < n and string[r - l] == string[r]:
					r += 1
				z[i] = r - l
				r -= 1

# prints all occurrences of pattern
# in text using Z algo
def search(text, pattern):

	# Create concatenated string "P$T"
	concat = pattern + "$" + text
	l = len(concat)

	# Construct Z array
	z = [0] * l
	getZarr(concat, z)

	# now looping through Z array for matching condition
	for i in range(l):

		# if Z[i] (matched region) is equal to pattern
		# length we got the pattern
		if z[i] == len(pattern):
			print("Pattern found at index",
					i - len(pattern) - 1)

# Driver Code
if __name__ == "__main__":
	text = "run away from run time errors"
	pattern = "run"
	search(text, pattern)