# 
# Knuth-Morris-Pratt string matcher (Python)
# 
# Copyright (c) 2020 Project Nayuki. (MIT License)
# https://www.nayuki.io/page/knuth-morris-pratt-string-matching
# 
# Permission is hereby granted, free of charge, to any person obtaining a copy of
# this software and associated documentation files (the "Software"), to deal in
# the Software without restriction, including without limitation the rights to
# use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of
# the Software, and to permit persons to whom the Software is furnished to do so,
# subject to the following conditions:
# - The above copyright notice and this permission notice shall be included in
#   all copies or substantial portions of the Software.
# - The Software is provided "as is", without warranty of any kind, express or
#   implied, including but not limited to the warranties of merchantability,
#   fitness for a particular purpose and noninfringement. In no event shall the
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#   out of or in connection with the Software or the use or other dealings in the
#   Software.
# 

from typing import List, Optional


# Searches for the given pattern string in the given text string using the Knuth-Morris-Pratt string matching algorithm.
# If the pattern is found, this returns the index of the start of the earliest match in 'text'. Otherwise None is returned.
def kmp_search(pattern: str, text: str) -> Optional[int]:
	if pattern == "":
		return 0  # Immediate match
	
	# Compute longest suffix-prefix table
	lsp: List[int] = [0]  # Base case
	for c in pattern[1 : ]:
		j = lsp[-1]  # Start by assuming we're extending the previous LSP
		while j > 0 and c != pattern[j]:
			j = lsp[j - 1]
		if c == pattern[j]:
			j += 1
		lsp.append(j)
	
	# Walk through text string
	j = 0  # Number of chars matched in pattern
	for i in range(len(text)):
		while j > 0 and text[i] != pattern[j]:
			j = lsp[j - 1]  # Fall back in the pattern
		if text[i] == pattern[j]:
			j += 1  # Next char matched, increment position
			if j == len(pattern):
				return i - (j - 1)
	return None  # Not found