prompt: We are currently solving the following issue within our repository. Here is the issue text:
  --- BEGIN ISSUE ---
  maths/number_of_digits.py is naive!
  <code>[maths/number_of_digits.py](https://github.com/TheAlgorithms/Python/blob/master/maths/number_of_digits.py)</code> has a naive method. The suggested method has a time complexity of O(n). We can count number of digits of a number in O(1).
  
  --- END ISSUE ---
  
  Below are some code segments, each from a relevant file. One or more of these files may contain bugs.
  --- BEGIN FILES ---
  Path: `maths/number_of_digits.py`
  Content:
  ```
  1 def num_digits(n: int) -> int:
  2     """
  3     Find the number of digits in a number.
  4 
  5     >>> num_digits(12345)
  6     5
  7     >>> num_digits(123)
  8     3
  9     """
  10     digits = 0
  11     while n > 0:
  12         n = n // 10
  13         digits += 1
  14     return digits
  15 
  16 
  17 if __name__ == "__main__":
  18     print(num_digits(12345))  # ===> 5
  19
  ```
  --- END FILES ---
  
  Please first localize the bug based on the issue statement, and then generate a patch according to the `git diff` format fenced by three backticks.
  
  Here is an example:
  
  ```diff
  diff --git a/examples/server_async.py b/examples/server_async.py
  --- a/examples/server_async.py
  +++ b/examples/server_async.py
  @@ -313,4 +313,4 @@
   
   
   if __name__ == "__main__":
  -    asyncio.run(run_async_server("."), debug=True)
  +    asyncio.run(run_async_server(), debug=True)
  diff --git a/examples/server_sync.py b/examples/server_sync.py
  --- a/examples/server_sync.py
  +++ b/examples/server_sync.py
  @@ -313,5 +313,5 @@
   
   
   if __name__ == "__main__":
  -    server = run_sync_server(".")
  +    server = run_sync_server()
       server.shutdown()
  
  ```
  
golden_diff: diff --git a/maths/number_of_digits.py b/maths/number_of_digits.py
  --- a/maths/number_of_digits.py
  +++ b/maths/number_of_digits.py
  @@ -1,3 +1,7 @@
  +import math
  +from timeit import timeit
  +
  +
   def num_digits(n: int) -> int:
       """
       Find the number of digits in a number.
  @@ -14,5 +18,82 @@
       return digits
   
   
  +def num_digits_fast(n: int) -> int:
  +    """
  +    Find the number of digits in a number.
  +    abs() is used as logarithm for negative numbers is not defined.
  +
  +    >>> num_digits_fast(12345)
  +    5
  +    >>> num_digits_fast(123)
  +    3
  +    """
  +    return (math.floor(math.log(abs(n), 10) + 1))
  +
  +
  +def num_digits_faster(n: int) -> int:
  +    """
  +    Find the number of digits in a number.
  +    abs() is used for negative numbers
  +
  +    >>> num_digits_faster(12345)
  +    5
  +    >>> num_digits_faster(123)
  +    3
  +    """
  +    return (len(str(abs(n))))
  +
  +
  +def benchmark() -> None:
  +    """
  +    Benchmark code for comparing 3 functions,
  +    with 3 different length int values.
  +    """
  +    print('\nFor small_num = ', small_num, ':')
  +    print("> num_digits()",
  +          '\t\tans =', num_digits(small_num),
  +          '\ttime =', timeit("z.num_digits(z.small_num)",
  +                             setup="import __main__ as z"), "seconds")
  +    print("> num_digits_fast()",
  +          '\tans =', num_digits_fast(small_num),
  +          '\ttime =', timeit("z.num_digits_fast(z.small_num)",
  +                             setup="import __main__ as z"), "seconds")
  +    print("> num_digits_faster()",
  +          '\tans =', num_digits_faster(small_num),
  +          '\ttime =', timeit("z.num_digits_faster(z.small_num)",
  +                             setup="import __main__ as z"), "seconds")
  +
  +    print('\nFor medium_num = ', medium_num, ':')
  +    print("> num_digits()",
  +          '\t\tans =', num_digits(medium_num),
  +          '\ttime =', timeit("z.num_digits(z.medium_num)",
  +                             setup="import __main__ as z"), "seconds")
  +    print("> num_digits_fast()",
  +          '\tans =', num_digits_fast(medium_num),
  +          '\ttime =', timeit("z.num_digits_fast(z.medium_num)",
  +                             setup="import __main__ as z"), "seconds")
  +    print("> num_digits_faster()",
  +          '\tans =', num_digits_faster(medium_num),
  +          '\ttime =', timeit("z.num_digits_faster(z.medium_num)",
  +                             setup="import __main__ as z"), "seconds")
  +
  +    print('\nFor large_num = ', large_num, ':')
  +    print("> num_digits()",
  +          '\t\tans =', num_digits(large_num),
  +          '\ttime =', timeit("z.num_digits(z.large_num)",
  +                             setup="import __main__ as z"), "seconds")
  +    print("> num_digits_fast()",
  +          '\tans =', num_digits_fast(large_num),
  +          '\ttime =', timeit("z.num_digits_fast(z.large_num)",
  +                             setup="import __main__ as z"), "seconds")
  +    print("> num_digits_faster()",
  +          '\tans =', num_digits_faster(large_num),
  +          '\ttime =', timeit("z.num_digits_faster(z.large_num)",
  +                             setup="import __main__ as z"), "seconds")
  +
  +
   if __name__ == "__main__":
  -    print(num_digits(12345))  # ===> 5
  +    small_num = 262144
  +    medium_num = 1125899906842624
  +    large_num = 1267650600228229401496703205376
  +    benchmark()
  
verification_info: {"golden_diff": "diff --git a/maths/number_of_digits.py b/maths/number_of_digits.py\n--- a/maths/number_of_digits.py\n+++ b/maths/number_of_digits.py\n@@ -1,3 +1,7 @@\n+import math\n+from timeit import timeit\n+\n+\n def num_digits(n: int) -> int:\n     \"\"\"\n     Find the number of digits in a number.\n@@ -14,5 +18,82 @@\n     return digits\n \n \n+def num_digits_fast(n: int) -> int:\n+    \"\"\"\n+    Find the number of digits in a number.\n+    abs() is used as logarithm for negative numbers is not defined.\n+\n+    >>> num_digits_fast(12345)\n+    5\n+    >>> num_digits_fast(123)\n+    3\n+    \"\"\"\n+    return (math.floor(math.log(abs(n), 10) + 1))\n+\n+\n+def num_digits_faster(n: int) -> int:\n+    \"\"\"\n+    Find the number of digits in a number.\n+    abs() is used for negative numbers\n+\n+    >>> num_digits_faster(12345)\n+    5\n+    >>> num_digits_faster(123)\n+    3\n+    \"\"\"\n+    return (len(str(abs(n))))\n+\n+\n+def benchmark() -> None:\n+    \"\"\"\n+    Benchmark code for comparing 3 functions,\n+    with 3 different length int values.\n+    \"\"\"\n+    print('\\nFor small_num = ', small_num, ':')\n+    print(\"> num_digits()\",\n+          '\\t\\tans =', num_digits(small_num),\n+          '\\ttime =', timeit(\"z.num_digits(z.small_num)\",\n+                             setup=\"import __main__ as z\"), \"seconds\")\n+    print(\"> num_digits_fast()\",\n+          '\\tans =', num_digits_fast(small_num),\n+          '\\ttime =', timeit(\"z.num_digits_fast(z.small_num)\",\n+                             setup=\"import __main__ as z\"), \"seconds\")\n+    print(\"> num_digits_faster()\",\n+          '\\tans =', num_digits_faster(small_num),\n+          '\\ttime =', timeit(\"z.num_digits_faster(z.small_num)\",\n+                             setup=\"import __main__ as z\"), \"seconds\")\n+\n+    print('\\nFor medium_num = ', medium_num, ':')\n+    print(\"> num_digits()\",\n+          '\\t\\tans =', num_digits(medium_num),\n+          '\\ttime =', timeit(\"z.num_digits(z.medium_num)\",\n+                             setup=\"import __main__ as z\"), \"seconds\")\n+    print(\"> num_digits_fast()\",\n+          '\\tans =', num_digits_fast(medium_num),\n+          '\\ttime =', timeit(\"z.num_digits_fast(z.medium_num)\",\n+                             setup=\"import __main__ as z\"), \"seconds\")\n+    print(\"> num_digits_faster()\",\n+          '\\tans =', num_digits_faster(medium_num),\n+          '\\ttime =', timeit(\"z.num_digits_faster(z.medium_num)\",\n+                             setup=\"import __main__ as z\"), \"seconds\")\n+\n+    print('\\nFor large_num = ', large_num, ':')\n+    print(\"> num_digits()\",\n+          '\\t\\tans =', num_digits(large_num),\n+          '\\ttime =', timeit(\"z.num_digits(z.large_num)\",\n+                             setup=\"import __main__ as z\"), \"seconds\")\n+    print(\"> num_digits_fast()\",\n+          '\\tans =', num_digits_fast(large_num),\n+          '\\ttime =', timeit(\"z.num_digits_fast(z.large_num)\",\n+                             setup=\"import __main__ as z\"), \"seconds\")\n+    print(\"> num_digits_faster()\",\n+          '\\tans =', num_digits_faster(large_num),\n+          '\\ttime =', timeit(\"z.num_digits_faster(z.large_num)\",\n+                             setup=\"import __main__ as z\"), \"seconds\")\n+\n+\n if __name__ == \"__main__\":\n-    print(num_digits(12345))  # ===> 5\n+    small_num = 262144\n+    medium_num = 1125899906842624\n+    large_num = 1267650600228229401496703205376\n+    benchmark()\n", "issue": "maths/number_of_digits.py is naive!\n<code>[maths/number_of_digits.py](https://github.com/TheAlgorithms/Python/blob/master/maths/number_of_digits.py)</code> has a naive method. The suggested method has a time complexity of O(n). We can count number of digits of a number in O(1).\n", "before_files": [{"content": "def num_digits(n: int) -> int:\n    \"\"\"\n    Find the number of digits in a number.\n\n    >>> num_digits(12345)\n    5\n    >>> num_digits(123)\n    3\n    \"\"\"\n    digits = 0\n    while n > 0:\n        n = n // 10\n        digits += 1\n    return digits\n\n\nif __name__ == \"__main__\":\n    print(num_digits(12345))  # ===> 5\n", "path": "maths/number_of_digits.py"}], "after_files": [{"content": "import math\nfrom timeit import timeit\n\n\ndef num_digits(n: int) -> int:\n    \"\"\"\n    Find the number of digits in a number.\n\n    >>> num_digits(12345)\n    5\n    >>> num_digits(123)\n    3\n    \"\"\"\n    digits = 0\n    while n > 0:\n        n = n // 10\n        digits += 1\n    return digits\n\n\ndef num_digits_fast(n: int) -> int:\n    \"\"\"\n    Find the number of digits in a number.\n    abs() is used as logarithm for negative numbers is not defined.\n\n    >>> num_digits_fast(12345)\n    5\n    >>> num_digits_fast(123)\n    3\n    \"\"\"\n    return (math.floor(math.log(abs(n), 10) + 1))\n\n\ndef num_digits_faster(n: int) -> int:\n    \"\"\"\n    Find the number of digits in a number.\n    abs() is used for negative numbers\n\n    >>> num_digits_faster(12345)\n    5\n    >>> num_digits_faster(123)\n    3\n    \"\"\"\n    return (len(str(abs(n))))\n\n\ndef benchmark() -> None:\n    \"\"\"\n    Benchmark code for comparing 3 functions,\n    with 3 different length int values.\n    \"\"\"\n    print('\\nFor small_num = ', small_num, ':')\n    print(\"> num_digits()\",\n          '\\t\\tans =', num_digits(small_num),\n          '\\ttime =', timeit(\"z.num_digits(z.small_num)\",\n                             setup=\"import __main__ as z\"), \"seconds\")\n    print(\"> num_digits_fast()\",\n          '\\tans =', num_digits_fast(small_num),\n          '\\ttime =', timeit(\"z.num_digits_fast(z.small_num)\",\n                             setup=\"import __main__ as z\"), \"seconds\")\n    print(\"> num_digits_faster()\",\n          '\\tans =', num_digits_faster(small_num),\n          '\\ttime =', timeit(\"z.num_digits_faster(z.small_num)\",\n                             setup=\"import __main__ as z\"), \"seconds\")\n\n    print('\\nFor medium_num = ', medium_num, ':')\n    print(\"> num_digits()\",\n          '\\t\\tans =', num_digits(medium_num),\n          '\\ttime =', timeit(\"z.num_digits(z.medium_num)\",\n                             setup=\"import __main__ as z\"), \"seconds\")\n    print(\"> num_digits_fast()\",\n          '\\tans =', num_digits_fast(medium_num),\n          '\\ttime =', timeit(\"z.num_digits_fast(z.medium_num)\",\n                             setup=\"import __main__ as z\"), \"seconds\")\n    print(\"> num_digits_faster()\",\n          '\\tans =', num_digits_faster(medium_num),\n          '\\ttime =', timeit(\"z.num_digits_faster(z.medium_num)\",\n                             setup=\"import __main__ as z\"), \"seconds\")\n\n    print('\\nFor large_num = ', large_num, ':')\n    print(\"> num_digits()\",\n          '\\t\\tans =', num_digits(large_num),\n          '\\ttime =', timeit(\"z.num_digits(z.large_num)\",\n                             setup=\"import __main__ as z\"), \"seconds\")\n    print(\"> num_digits_fast()\",\n          '\\tans =', num_digits_fast(large_num),\n          '\\ttime =', timeit(\"z.num_digits_fast(z.large_num)\",\n                             setup=\"import __main__ as z\"), \"seconds\")\n    print(\"> num_digits_faster()\",\n          '\\tans =', num_digits_faster(large_num),\n          '\\ttime =', timeit(\"z.num_digits_faster(z.large_num)\",\n                             setup=\"import __main__ as z\"), \"seconds\")\n\n\nif __name__ == \"__main__\":\n    small_num = 262144\n    medium_num = 1125899906842624\n    large_num = 1267650600228229401496703205376\n    benchmark()\n", "path": "maths/number_of_digits.py"}]}