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'''
There are 4 cases to handle
 * Case 1 : Right side palindrome is totally contained under current palindrome. In this case do not consider this as center.
 * Case 2 : Current palindrome is proper suffix of input. Terminate the loop in this case. No better palindrome will be found on right.
 * Case 3 : Right side palindrome is proper suffix and its corresponding left side palindrome is proper prefix of current palindrome. Make largest such point as next center.
 * Case 4 : Right side palindrome is proper suffix but its left corresponding palindrome is be beyond current palindrome. Do not consider this as center because it will not extend at all.
'''

def longest_palindromic_substring(string):
    # preprocess the string to allow for even length palindromes

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def longest_palindromic_substring(string):
    length = len(string)

    # return the string if the string is only one character long
    if length == 1:
        return string

    palindrome = ""
    palindrome_length = 0

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#!/usr/bin/env python3

def sieve_of_eratosthenes(n):
	'''
	Complexity : O(n log log n) + O(n) ~ O(n log log n)
	'''
	prime = [True for i in range(n+1)]
	p = 2

	# if there are no factors of n till sqrt(n) then the number is prime

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#!/usr/bin/env python3


class Node(object):
	"""Class for tree nodes"""

	def __init__(self, key):
		super(Node, self).__init__()
		self.key = key
		self.left = None

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#!/usr/bin/env python3


"""
Sudoku Solver

guesses:
	1-9

grid:

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#!/usr/bin/env python3


def is_safe(x, y, n, maze):
	if 0 <= x <= n-1 and 0 <= y <= n - 1 and maze[y][x] == 1:
		return True
	else:
		return False

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#!/usr/bin/env python3


def is_safe(row, col, size, board):
	# check vertical
	for y in range(row):
		if board[y][col]:
			return False

	# check left diagonal

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#!/usr/bin/env python3


def memoization(function):
	memo = {}

	def helper(x):
		if x not in memo:
			memo[x] = function(x)
		return memo[x]

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import math


class Point(object):
    '''Creates a point on a coordinate plane with values x and y'''

    def __init__(self, x, y):
        '''Defines the x and y coordinates in the variables'''
        self.X = x
        self.Y = y

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#!/usr/bin/env python3


def tower_of_hanoi(number, beginning, auxiliary, ending):
	if number == 1:
		print("{} -> {}".format(beginning, ending))
		return

	else:
		tower_of_hanoi(number-1, beginning, ending, auxiliary)