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)

# Prompt user for a decimal number
decimal = int(input("Enter a decimal number: "))

# Convert decimal to binary
binary = bin(decimal)

# Convert decimal to hexadecimal
hexadecimal = hex(decimal)

# Display the results
print("Binary:", binary)
print("Hexadecimal:", hexadecimal)

magnitude = lambda bits: 1_000_000_000_000_000_000 % (2 ** bits)
sign = lambda bits: -1 ** (1_000_000_000_000_000_000 // (2 ** bits))

print("64 bit sum:", magnitude(64) * sign(64))
print("32 bit sum:", magnitude(32) * sign(32))
print("16 bit sum:", magnitude(16) * sign(16))

weigh = lambda a,b: sum(b)-sum(a)
FindCoin = lambda A: 0 if (n := len(A)) == 1 else (m := n//3) * (w := 1 + weigh(A[:m], A[2*m:])) + FindCoin(A[m*w:m*(w+1)])
print(FindCoin([1,1,1,1,1,1,1,2,1]))

def Fibonacci(n): 
    if n<0: 
        print("Incorrect input") 
    # First Fibonacci number is 0 
    elif n==1: 
        return 0
    # Second Fibonacci number is 1 
    elif n==2: 
        return 1
    else: 
        return Fibonacci(n-1)+Fibonacci(n-2) 
  
# Driver Program 
  
print(Fibonacci(9))

# 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")