def generate_pascals_triangle(num_rows):
    triangle = []
    for row in range(num_rows):
        # Initialize the row with 1
        current_row = [1]

        # Calculate the values for the current row
        if row > 0:
            previous_row = triangle[row - 1]
            for i in range(len(previous_row) - 1):
                current_row.append(previous_row[i] + previous_row[i + 1])

        # Append 1 at the end of the row
        current_row.append(1)

        # Add the current row to the triangle
        triangle.append(current_row)

    return triangle


def display_pascals_triangle(triangle):
    for row in triangle:
        for number in row:
            print(number, end=" ")
        print()


# Prompt the user for the number of rows
num_rows = int(input("Enter the number of rows for Pascal's Triangle: "))

# Generate Pascal's Triangle
pascals_triangle = generate_pascals_triangle(num_rows)

# Display Pascal's Triangle
display_pascals_triangle(pascals_triangle)

from math import pi

def rads_to_degrees(rad):
  return (rad * 180.0) / pi

rads_to_degrees(pi / 2) # 90.0

# 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)

# Python program for implementation of Bubble Sort

def bubbleSort(arr):
	n = len(arr)

	# Traverse through all array elements
	for i in range(n-1):
	# range(n) also work but outer loop will repeat one time more than needed.

		# Last i elements are already in place
		for j in range(0, n-i-1):

			# traverse the array from 0 to n-i-1
			# Swap if the element found is greater
			# than the next element
			if arr[j] > arr[j+1] :
				arr[j], arr[j+1] = arr[j+1], arr[j]

# Driver code to test above
arr = [64, 34, 25, 12, 22, 11, 90]

bubbleSort(arr)

print ("Sorted array is:")
for i in range(len(arr)):
	print ("%d" %arr[i]),