# Given a number n, print all primes smaller than or equal to n. It is also given that n is a small number.
# For example, if n is 10, the output should be “2, 3, 5, 7”. If n is 20, the output should be “2, 3, 5, 7, 11, 13, 17, 19”.


# Python program to print all primes smaller than or equal to
# n using Sieve of Eratosthenes

def SieveOfEratosthenes(n):
	
	# Create a boolean array "prime[0..n]" and initialize
	# all entries it as true. A value in prime[i] will
	# finally be false if i is Not a prime, else true.
	prime = [True for i in range(n + 1)]
	p = 2
	while (p * p <= n):
		
		# If prime[p] is not changed, then it is a prime
		if (prime[p] == True):
			
			# Update all multiples of p
			for i in range(p * 2, n + 1, p):
				prime[i] = False
		p += 1
	prime[0]= False
	prime[1]= False
	# Print all prime numbers
	for p in range(n + 1):
		if prime[p]:
			print (p)

# driver program
if __name__=='__main__':
    n = 30
    print("Following are the prime numbers smaller")
    print("than or equal to ", n)
    print("than or equal to ", n)
    SieveOfEratosthenes(n)

def key_of_min(d):
  return min(d, key = d.get)

key_of_min({'a':4, 'b':0, 'c':13}) # b

# Python program to reverse a linked list
# Time Complexity : O(n)
# Space Complexity : O(n) as 'next'
#variable is getting created in each loop.

# Node class


class Node:

	# Constructor to initialize the node object
	def __init__(self, data):
		self.data = data
		self.next = None


class LinkedList:

	# Function to initialize head
	def __init__(self):
		self.head = None

	# Function to reverse the linked list
	def reverse(self):
		prev = None
		current = self.head
		while(current is not None):
			next = current.next
			current.next = prev
			prev = current
			current = next
		self.head = prev

	# Function to insert a new node at the beginning
	def push(self, new_data):
		new_node = Node(new_data)
		new_node.next = self.head
		self.head = new_node

	# Utility function to print the linked LinkedList
	def printList(self):
		temp = self.head
		while(temp):
			print temp.data,
			temp = temp.next


# Driver program to test above functions
llist = LinkedList()
llist.push(20)
llist.push(4)
llist.push(15)
llist.push(85)

print "Given Linked List"
llist.printList()
llist.reverse()
print "\nReversed Linked List"
llist.printList()

# Python program for Plotting Fibonacci 
# spiral fractal using Turtle 
import turtle 
import math 
  
def fiboPlot(n): 
    a = 0
    b = 1
    square_a = a 
    square_b = b 
  
    # Setting the colour of the plotting pen to blue 
    x.pencolor("blue") 
  
    # Drawing the first square 
    x.forward(b * factor) 
    x.left(90) 
    x.forward(b * factor) 
    x.left(90) 
    x.forward(b * factor) 
    x.left(90) 
    x.forward(b * factor) 
  
    # Proceeding in the Fibonacci Series 
    temp = square_b 
    square_b = square_b + square_a 
    square_a = temp 
      
    # Drawing the rest of the squares 
    for i in range(1, n): 
        x.backward(square_a * factor) 
        x.right(90) 
        x.forward(square_b * factor) 
        x.left(90) 
        x.forward(square_b * factor) 
        x.left(90) 
        x.forward(square_b * factor) 
  
        # Proceeding in the Fibonacci Series 
        temp = square_b 
        square_b = square_b + square_a 
        square_a = temp 
  
    # Bringing the pen to starting point of the spiral plot 
    x.penup() 
    x.setposition(factor, 0) 
    x.seth(0) 
    x.pendown() 
  
    # Setting the colour of the plotting pen to red 
    x.pencolor("red") 
  
    # Fibonacci Spiral Plot 
    x.left(90) 
    for i in range(n): 
        print(b) 
        fdwd = math.pi * b * factor / 2
        fdwd /= 90
        for j in range(90): 
            x.forward(fdwd) 
            x.left(1) 
        temp = a 
        a = b 
        b = temp + b 
  
  
# Here 'factor' signifies the multiplicative  
# factor which expands or shrinks the scale 
# of the plot by a certain factor. 
factor = 1
  
# Taking Input for the number of  
# Iterations our Algorithm will run 
n = int(input('Enter the number of iterations (must be > 1): ')) 
  
# Plotting the Fibonacci Spiral Fractal  
# and printing the corresponding Fibonacci Number 
if n > 0: 
    print("Fibonacci series for", n, "elements :") 
    x = turtle.Turtle() 
    x.speed(100) 
    fiboPlot(n) 
    turtle.done() 
else: 
    print("Number of iterations must be > 0")

def to_roman_numeral(num):
  lookup = [
    (1000, 'M'),
    (900, 'CM'),
    (500, 'D'),
    (400, 'CD'),
    (100, 'C'),
    (90, 'XC'),
    (50, 'L'),
    (40, 'XL'),
    (10, 'X'),
    (9, 'IX'),
    (5, 'V'),
    (4, 'IV'),
    (1, 'I'),
  ]
  res = ''
  for (n, roman) in lookup:
    (d, num) = divmod(num, n)
    res += roman * d
  return res

to_roman_numeral(3) # 'III'
to_roman_numeral(11) # 'XI'
to_roman_numeral(1998) # 'MCMXCVIII'

def check_prop(fn, prop):
  return lambda obj: fn(obj[prop])
  
check_age = check_prop(lambda x: x >= 18, 'age')
user = {'name': 'Mark', 'age': 18}
check_age(user) # True