From a0d78275d65ea384e887faed07b3ed3ad0422c59 Mon Sep 17 00:00:00 2001
From: Francesco Franco <130352141+Francesco601@users.noreply.github.com>
Date: Sun, 7 May 2023 16:29:12 +0200
Subject: [PATCH] added Z algoritm to PR

Time and space complexity and other details in comments...
---
 z_algoritm.py | 81 +++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 81 insertions(+)
 create mode 100644 z_algoritm.py

diff --git a/z_algoritm.py b/z_algoritm.py
new file mode 100644
index 00000000..53191aa7
--- /dev/null
+++ b/z_algoritm.py
@@ -0,0 +1,81 @@
+# 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)
+
+