remove all trailing spaces in algorithms

Author: SatinWukerORIG

maths/aliquot_sum.mojo

@@ -7,24 +7,24 @@
 fn aliquot_sum(input_num: Int) raises -> Int:
     """
     Finds the aliquot sum of an input integer.
-    
+
     The aliquot sum is the sum of all proper divisors of a number (all positive divisors less than the number itself).
     This is a simple O(n) implementation that directly follows the definition.
-    
+
     Parameters:
     - input_num: A positive integer whose aliquot sum is to be found.
     Returns:
     - The aliquot sum of input_num. If input_num is 1, returns 0 since there are no natural numbers less than 1.
     Raises:
     - Error: If input_num is not positive.
-    
+
     Examples:
     - The aliquot sum of 12 is 1 + 2 + 3 + 4 + 6 = 16
     - The aliquot sum of 6 is 1 + 2 + 3 = 6 (perfect number)
     - The aliquot sum of 15 is 1 + 3 + 5 = 9
     - The aliquot sum of 19 is 1 (prime numbers only have 1 as a proper divisor)
     - The aliquot sum of 1 is 0 (there are no natural numbers less than 1)
-    
+
     ```mojo
     from testing import assert_equal, assert_raises
     from aliquot_sum import aliquot_sum, optimized_aliquot_sum
@@ -41,22 +41,22 @@ fn aliquot_sum(input_num: Int) raises -> Int:
     """
     if input_num <= 0:
         raise Error("Input must be positive")
-    
+
     var sum = 0
     for divisor in range(1, input_num // 2 + 1):
         if input_num % divisor == 0:
             sum += divisor
-    
+
     return sum
 
 fn optimized_aliquot_sum(input_num: Int) raises -> Int:
     """
     Optimized implementation of aliquot sum with O(sqrt(n)) time complexity.
-    
+
     This implementation leverages the mathematical property that divisors come in pairs:
     if i is a divisor of n, then n/i is also a divisor. By iterating only up to sqrt(n),
     we can find all divisor pairs and significantly improve performance.
-    
+
     Parameters:
     - input_num: A positive integer whose aliquot sum is to be found.
     Returns:
@@ -66,11 +66,11 @@ fn optimized_aliquot_sum(input_num: Int) raises -> Int:
     """
     if input_num <= 0:
         raise Error("Input must be positive")
-    
+
     var sum = 1  # Start with 1 as it's always a divisor for positive numbers
     if input_num == 1:
         return 0  # Special case: aliquot sum of 1 is 0
-        
+
     # Find all divisor pairs up to sqrt(input_num)
     var i = 2
     while i * i <= input_num:
@@ -80,5 +80,5 @@ fn optimized_aliquot_sum(input_num: Int) raises -> Int:
             if i != input_num // i:
                 sum += input_num // i
         i += 1
-    
+
     return sum

maths/ceil.mojo

@@ -7,13 +7,13 @@
 fn ceil(number: Float64) -> Int:
     """
     Return the ceiling of number as an integer.
-    
+
     Parameters:
     - number: A floating-point number.
 
     Returns:
     - The smallest integer greater than or equal to number.
-    
+
     ```mojo
     from testing import assert_equal
     from ceil import ceil