Created harshad_numbers.py

maths/harshad_numbers.py

@@ -1,15 +1,19 @@
 """
-A Harshad number is divisible by the sum of its digits in any base n.
+A harshad number (or more specifically an n-harshad number) is a number that's
+divisible by the sum of its digits in some given base n.
 Reference: https://en.wikipedia.org/wiki/Harshad_number
 """
 
 
-def int_to_base(number: int, base_of_interest: int) -> str:
+def int_to_base(number: int, base: int) -> str:
     digits = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ"
     result = ""
 
+    if number < 0:
+        raise ValueError("number must be a positive integer")
+
     while number > 0:
-        number, remainder = divmod(number, base_of_interest)
+        number, remainder = divmod(number, base)
         result = digits[remainder] + result
 
     if result == "":
@@ -18,11 +22,11 @@ def int_to_base(number: int, base_of_interest: int) -> str:
     return result
 
 
-def sum_of_digits(num: int, base_of_interest: int) -> str:
+def sum_of_digits(num: int, base: int) -> str:
     """
     Calculate the sum of digit values in a positive integer
-    converted to the given 'base_of_interest'.
-    Where 'base_of_interest' ranges from 2 to 36.
+    converted to the given 'base'.
+    Where 'base' ranges from 2 to 36.
 
     Examples:
     >>> sum_of_digits(103, 12)
@@ -35,95 +39,92 @@ def sum_of_digits(num: int, base_of_interest: int) -> str:
     >>> sum_of_digits(543, 1)
     Traceback (most recent call last):
         ...
-    ValueError: 'base_of_interest' must be between 36 and 2 inclusive
+    ValueError: 'base' must be between 36 and 2 inclusive
     >>> sum_of_digits(543, 37)
     Traceback (most recent call last):
         ...
-    ValueError: 'base_of_interest' must be between 36 and 2 inclusive
+    ValueError: 'base' must be between 36 and 2 inclusive
     """
 
-    if (base_of_interest > 36) or (base_of_interest < 2):
-        raise ValueError("'base_of_interest' must be between 36 and 2 inclusive")
+    if (base > 36) or (base < 2):
+        raise ValueError("'base' must be between 36 and 2 inclusive")
 
-    num_str = int_to_base(num, base_of_interest)
+    num_str = int_to_base(num, base)
     res = 0
     for char in num_str:
-        res += int(char, base_of_interest)
-    res_str = int_to_base(res, base_of_interest)
+        res += int(char, base)
+    res_str = int_to_base(res, base)
     return res_str
 
 
-def all_harshad_numbers(num: int, base_of_interest: int) -> tuple[int, list[str]]:
+def harshad_numbers_in_base(limit: int, base: int) -> list[str]:
     """
-    Finds all Harshad numbers smaller than num in base 'base_of_interest'.
-    Where 'base_of_interest' ranges from 2 to 36.
+    Finds all Harshad numbers smaller than num in base 'base'.
+    Where 'base' ranges from 2 to 36.
 
     Examples:
-    >>> all_harshad_numbers(15, 2)
-    (7, ['1', '10', '100', '110', '1000', '1010', '1100'])
-    >>> all_harshad_numbers(12, 34)
-    (11, ['1', '2', '3', '4', '5', '6', '7', '8', '9', 'A', 'B'])
-    >>> all_harshad_numbers(12, 4)
-    (7, ['1', '2', '3', '10', '12', '20', '21'])
+    >>> harshad_numbers_in_base(15, 2)
+    ['1', '10', '100', '110', '1000', '1010', '1100']
+    >>> harshad_numbers_in_base(12, 34)
+    ['1', '2', '3', '4', '5', '6', '7', '8', '9', 'A', 'B']
+    >>> harshad_numbers_in_base(12, 4)
+    ['1', '2', '3', '10', '12', '20', '21']
     >>> # bases beyond 36 and below 2 will error
-    >>> all_harshad_numbers(234, 37)
+    >>> harshad_numbers_in_base(234, 37)
     Traceback (most recent call last):
         ...
-    ValueError: 'base_of_interest' must be between 36 and 2 inclusive
-    >>> all_harshad_numbers(234, 1)
+    ValueError: 'base' must be between 36 and 2 inclusive
+    >>> harshad_numbers_in_base(234, 1)
     Traceback (most recent call last):
         ...
-    ValueError: 'base_of_interest' must be between 36 and 2 inclusive
+    ValueError: 'base' must be between 36 and 2 inclusive
     """
 
-    if (base_of_interest > 36) or (base_of_interest < 2):
-        raise ValueError("'base_of_interest' must be between 36 and 2 inclusive")
+    if (base > 36) or (base < 2):
+        raise ValueError("'base' must be between 36 and 2 inclusive")
 
-    result = 0
     numbers = []
-    if num >= 0:
-        for i in range(1, num):
-            y = sum_of_digits(i, base_of_interest)
-            if i % int(y, base_of_interest) == 0:
-                result += 1
-                numbers.append(int_to_base(i, base_of_interest))
+    if limit >= 0:
+        for i in range(1, limit):
+            y = sum_of_digits(i, base)
+            if i % int(y, base) == 0:
+                numbers.append(int_to_base(i, base))
 
-    return result, numbers
+    return numbers
 
 
-def is_harshad_number(num: int, base_of_interest: int) -> bool:
+def is_harshad_number_in_base(num: int, base: int) -> bool:
     """
-    Determines whether n in base 'base_of_interest' is a harshad number.
-    Where 'base_of_interest' ranges from 2 to 36.
+    Determines whether n in base 'base' is a harshad number.
+    Where 'base' ranges from 2 to 36.
 
     Examples:
-    >>> is_harshad_number(18, 10)
+    >>> is_harshad_number_in_base(18, 10)
     True
-    >>> is_harshad_number(21, 10)
+    >>> is_harshad_number_in_base(21, 10)
     True
-    >>> is_harshad_number(-21, 5)
+    >>> is_harshad_number_in_base(-21, 5)
     False
     >>> # bases beyond 36 and below 2 will error
-    >>> is_harshad_number(45, 37)
+    >>> is_harshad_number_in_base(45, 37)
     Traceback (most recent call last):
         ...
-    ValueError: 'base_of_interest' must be between 36 and 2 inclusive
-    >>> is_harshad_number(45, 1)
+    ValueError: 'base' must be between 36 and 2 inclusive
+    >>> is_harshad_number_in_base(45, 1)
     Traceback (most recent call last):
         ...
-    ValueError: 'base_of_interest' must be between 36 and 2 inclusive
+    ValueError: 'base' must be between 36 and 2 inclusive
     """
 
-    if (base_of_interest > 36) or (base_of_interest < 2):
-        raise ValueError("'base_of_interest' must be between 36 and 2 inclusive")
+    if (base > 36) or (base < 2):
+        raise ValueError("'base' must be between 36 and 2 inclusive")
 
-    if num >= 0:
-        n = int_to_base(num, base_of_interest)
-        d = sum_of_digits(num, base_of_interest)
-        if int(n, base_of_interest) % int(d, base_of_interest) == 0:
-            return True
+    if num < 0:
+        return False
 
-    return False
+    n = int_to_base(num, base)
+    d = sum_of_digits(num, base)
+    return int(n, base) % int(d, base) == 0
 
 
 if __name__ == "__main__":