Added iterative solution for power calculation

Author: SajeevSenthil

maths/power_using_iteration.py

@@ -0,0 +1,85 @@
+"""
+Iterative solution to calculate the power of a base raised to an exponent.
+
+This implementation uses an iterative approach, unlike the recursive approach
+in `power_using_recursion.py`. The algorithm is based on exponentiation by squaring
+for optimal performance.
+
+Examples:
+    >>> power(2, 3)
+    8
+    >>> power(5, -2)
+    0.04
+    >>> power(10, 0)
+    1
+    >>> Failed example:
+        power(5, -2)
+        Expected:
+            0.04
+        Got:
+            0.04000000000000001
+        1 items had failures:
+        1 of   3 in __main__
+        1 failed in total
+    Raise base to the power of exponent using an optimized approach...
+    Enter the base: 500
+    Enter the exponent: 8
+    500.0 to the power of 8 is 3.90625e+21
+
+Input:
+    base (float): The base number (can be integer or float).
+    exponent (int): The exponent (can be positive, negative, or zero).
+
+Output:
+    float: The result of base raised to the power of exponent.
+
+Note:
+    Results for very large or very small floating-point numbers may have slight precision errors
+    due to the limitations of floating-point arithmetic.
+"""
+
+
+def power(base: float, exponent: int) -> float:
+    """
+    Optimized power function using exponentiation by squaring.
+    It handles both positive and negative exponents efficiently.
+    This function take time complexity O(log n) for exponentiation.
+    space complexity is O(1) as it uses a constant amount of space.
+    """
+    # Handle negative exponents by taking reciprocal of the base
+    if exponent < 0:
+        base = 1 / base
+        exponent = -exponent
+
+    result = 1
+    # Use exponentiation by squaring for efficiency
+    while exponent:
+        if exponent % 2 == 1:  # If the current exponent is odd
+            result *= base
+        base *= base  # Square the base
+        exponent //= 2  # Halve the exponent
+    return result
+
+
+if __name__ == "__main__":
+    import doctest
+
+    doctest.testmod()
+    print("Raise base to the power of exponent using an optimized approach...")
+
+    try:
+        # Input handling and validation
+        base = float(input("Enter the base: ").strip())  # Supports float & int
+        exponent = int(
+            input("Enter the exponent: ").strip()
+        )  # Ensures exponent is an integer
+
+        # Calculate result
+        result = power(base, exponent)
+
+        # Display the result
+        print(f"{base} to the power of {exponent} is {result}")
+
+    except ValueError:
+        # Handle invalid input
+        print("Invalid input! Please enter numeric values for base and exponent.")