def insertion_sort(arr):
    # Traverse through 1 to len(arr)
    for i in range(1, len(arr)):
        key = arr[i]
        # Move elements of arr[0..i-1], that are greater than key,
        # to one position ahead of their current position
        j = i - 1
        while j >= 0 and key < arr[j]:
            arr[j + 1] = arr[j]
            j -= 1
        arr[j + 1] = key

# Example usage:
arr = [12, 11, 13, 5, 6, 7, 8, 10]
insertion_sort(arr)
print("Sorted array is:", arr)

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

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

#question1.py
def rose(n) :
  if n==0 : 
    yield []
  else :
    for k in range(0,n) :    
      for l in rose(k) :
        for r in rose(n-1-k) :      
            yield [l]+[r]+[r]
            
def start(n) :
  for x in rose(n) : 
      print(x) #basically I am printing x for each rose(n) file


print("starting program: \n")
start(2) # here is where I call the start function

# 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)

prime_lists=[] # a list to store the prime numbers

def prime(n): # define prime numbers
    if n <= 1:
        return False
    # divide n by 2... up to n-1
    for i in range(2, n):
        if n % i == 0:  # the remainder should'nt be a 0
            return False
    else:
        prime_lists.append(n)
        return True



for n in range(30,1000):  # calling function and passing starting point =30 coz we need primes >30
    prime(n)

check=0 # a var to limit the output  to 10 only
for n in prime_lists:
    for x in prime_lists:
        val=  n *x
        if (val > 1000 ):
            check=check +1
        if (check <10) :
            print("the num is:", val , "=",n , "* ", x )
        break

def counting_sort(arr, exp):
    n = len(arr)
    output = [0] * n
    count = [0] * 10

    for i in range(n):
        index = (arr[i] // exp) % 10
        count[index] += 1

    for i in range(1, 10):
        count[i] += count[i-1]

    i = n - 1
    while i >= 0:
        index = (arr[i] // exp) % 10
        output[count[index] - 1] = arr[i]
        count[index] -= 1
        i -= 1

    for i in range(n):
        arr[i] = output[i]

def radix_sort(arr):
    max_val = max(arr)
    exp = 1
    while max_val // exp > 0:
        counting_sort(arr, exp)
        exp *= 10

if __name__ == "__main__":
    arr = [170, 45, 75, 90, 802, 24, 2, 66]
    print("Original array:", arr)
    radix_sort(arr)
    print("Sorted array:", arr)