import math """ Solving Problems without Loops or Recursion. Discover the power of mathematics in programming with these Python functions that solve common problems without using loops or recursion. From calculating the sum of natural numbers, squares, and cubes, to finding arithmetic and geometric progressions, checking if a number is a power of two, and even swapping two numbers - all achieved purely through mathematical operations. This code demonstrates how a deep understanding of mathematics can lead to efficient and elegant solutions in programming. """ # Sum of Natural Numbers def Sum(n:int)->int: return n*(n+1)/2 # Sum of Squares of Natural Numbers def SumSquare(n:int)->int: return n*(n+1)*(2*n+1)/6 # Sum of Cubes of Natural Numbers def Cubes(n:int)->int: return (n*(n+1)/2)**2 # Arithmetic Progression def ArithmeticProgression(n:int, a:int, d:int)->int: return n/2*(2*a + (n-1)*d) # Geometric Progression def GeometricProgression(n:int, a:int, r:int)->int: return a * (r**n - 1) / (r - 1) # Checking if a Number is a Power of Two def isPowerOfTwo(n:int)->bool: return (n & (n - 1)) == 0 def SuperDigit(n:int)->int: return 1+(n-1)%9 # Swapping Two Numbers def Swap(a:int, b:int)->(int,int): a = a + b b = a - b a = a - b return a,b def ReverseNumber(num): reversed = 0 while (num > 0): last_digit = num % 10 reversed *= 10 reversed += last_digit num //= 10 return reversed def degree_to_radian(degree:float)->float: return degree * (math.pi / 180) def radian_to_degree(radian:float)->float: return radian * (180 / math.pi) n = 12345 rn = ReverseNumber(n) print( # Output 54321 f"Original: {n}\nReversed: {rn}\n") print( # Output: 55 f"{'Sum:':<25}{Sum(10)}\n") print( # Output: 385 f"{'Sum of Squares:':<25}{SumSquare(10)}\n") print( # Output: 3025 f"{'Sum of Cubes:':<25}{Cubes(10)}\n") print( # Output: 100 f"{'Arithmetic Progression:':<25}{ArithmeticProgression(10, 1, 2)}\n") print( # Output: 1023 f"{'Geometric Progression:':<25}{GeometricProgression(10, 1, 2)}\n") print( # Output: True f"{'Is Power Of Two (16):':<25}{isPowerOfTwo(16)}\n") print( # Output: False f"{'Is Power Of Two (18):':<25}{isPowerOfTwo(18)}\n") a, b = Swap(5, 10) print( # Output: 10 5 f"{'Swapped Numbers:':<25}{a}, {b}\n") print( # Output: 2 f"{'Super Digit:':<25}{SuperDigit(9875)}\n") dr = degree_to_radian(45) rd = radian_to_degree(math.pi / 2) print( # Output: math.pi / 4 f"{'Degree to Radian:':<25}{dr}\n") print( # Output: 90 f"{'Radian to Degree:':<25}{rd}")

Math Magic in programming