prompt: You will be provided with a partial code base and an issue statement explaining a problem to resolve.
  <issue>
  Remove duplicate GCD implementation
  ### Feature description
  
  [`greatest_common_divisor.py`](https://github.com/TheAlgorithms/Python/blob/master/maths/greatest_common_divisor.py) and [`euclidean_gcd.py`](https://github.com/TheAlgorithms/Python/blob/master/maths/euclidean_gcd.py) both have basically the same two implementations of the Euclidean algorithm for calculating the GCD of 2 numbers. Thus, one of them should probably be removed as a duplicate.
  
  </issue>
  <code>
  [start of maths/euclidean_gcd.py]
  1 """ https://en.wikipedia.org/wiki/Euclidean_algorithm """
  2 
  3 
  4 def euclidean_gcd(a: int, b: int) -> int:
  5     """
  6     Examples:
  7     >>> euclidean_gcd(3, 5)
  8     1
  9 
  10     >>> euclidean_gcd(6, 3)
  11     3
  12     """
  13     while b:
  14         a, b = b, a % b
  15     return a
  16 
  17 
  18 def euclidean_gcd_recursive(a: int, b: int) -> int:
  19     """
  20     Recursive method for euclicedan gcd algorithm
  21 
  22     Examples:
  23     >>> euclidean_gcd_recursive(3, 5)
  24     1
  25 
  26     >>> euclidean_gcd_recursive(6, 3)
  27     3
  28     """
  29     return a if b == 0 else euclidean_gcd_recursive(b, a % b)
  30 
  31 
  32 def main():
  33     print(f"euclidean_gcd(3, 5) = {euclidean_gcd(3, 5)}")
  34     print(f"euclidean_gcd(5, 3) = {euclidean_gcd(5, 3)}")
  35     print(f"euclidean_gcd(1, 3) = {euclidean_gcd(1, 3)}")
  36     print(f"euclidean_gcd(3, 6) = {euclidean_gcd(3, 6)}")
  37     print(f"euclidean_gcd(6, 3) = {euclidean_gcd(6, 3)}")
  38 
  39     print(f"euclidean_gcd_recursive(3, 5) = {euclidean_gcd_recursive(3, 5)}")
  40     print(f"euclidean_gcd_recursive(5, 3) = {euclidean_gcd_recursive(5, 3)}")
  41     print(f"euclidean_gcd_recursive(1, 3) = {euclidean_gcd_recursive(1, 3)}")
  42     print(f"euclidean_gcd_recursive(3, 6) = {euclidean_gcd_recursive(3, 6)}")
  43     print(f"euclidean_gcd_recursive(6, 3) = {euclidean_gcd_recursive(6, 3)}")
  44 
  45 
  46 if __name__ == "__main__":
  47     main()
  48
  [end of maths/euclidean_gcd.py]
  </code>
  
  I need you to solve this issue by generating a single patch file that I can apply directly to this repository using git apply. Please respond with a single patch file in the following format.
  <patch>
  diff --git a/file.py b/file.py
  --- a/file.py
  +++ b/file.py
  @@ -1,27 +1,35 @@
   def euclidean(a, b):
  -    while b:
  -        a, b = b, a % b
  -    return a
  +    if b == 0:
  +        return a
  +    return euclidean(b, a % b)
   
   
   def bresenham(x0, y0, x1, y1):
       points = []
       dx = abs(x1 - x0)
       dy = abs(y1 - y0)
  -    sx = 1 if x0 < x1 else -1
  -    sy = 1 if y0 < y1 else -1
  -    err = dx - dy
  +    x, y = x0, y0
  +    sx = -1 if x0 > x1 else 1
  +    sy = -1 if y0 > y1 else 1
   
  -    while True:
  -        points.append((x0, y0))
  -        if x0 == x1 and y0 == y1:
  -            break
  -        e2 = 2 * err
  -        if e2 > -dy:
  -            err -= dy
  -            x0 += sx
  -        if e2 < dx:
  -            err += dx
  -            y0 += sy
  +    if dx > dy:
  +        err = dx / 2.0
  +        while x != x1:
  +            points.append((x, y))
  +            err -= dy
  +            if err < 0:
  +                y += sy
  +                err += dx
  +            x += sx
  +    else:
  +        err = dy / 2.0
  +        while y != y1:
  +            points.append((x, y))
  +            err -= dx
  +            if err < 0:
  +                x += sx
  +                err += dy
  +            y += sy
  +
  +    points.append((x, y))
       return points
  
  </patch>
golden_diff: diff --git a/maths/euclidean_gcd.py b/maths/euclidean_gcd.py
  deleted file mode 100644
  --- a/maths/euclidean_gcd.py
  +++ /dev/null
  @@ -1,47 +0,0 @@
  -""" https://en.wikipedia.org/wiki/Euclidean_algorithm """
  -
  -
  -def euclidean_gcd(a: int, b: int) -> int:
  -    """
  -    Examples:
  -    >>> euclidean_gcd(3, 5)
  -    1
  -
  -    >>> euclidean_gcd(6, 3)
  -    3
  -    """
  -    while b:
  -        a, b = b, a % b
  -    return a
  -
  -
  -def euclidean_gcd_recursive(a: int, b: int) -> int:
  -    """
  -    Recursive method for euclicedan gcd algorithm
  -
  -    Examples:
  -    >>> euclidean_gcd_recursive(3, 5)
  -    1
  -
  -    >>> euclidean_gcd_recursive(6, 3)
  -    3
  -    """
  -    return a if b == 0 else euclidean_gcd_recursive(b, a % b)
  -
  -
  -def main():
  -    print(f"euclidean_gcd(3, 5) = {euclidean_gcd(3, 5)}")
  -    print(f"euclidean_gcd(5, 3) = {euclidean_gcd(5, 3)}")
  -    print(f"euclidean_gcd(1, 3) = {euclidean_gcd(1, 3)}")
  -    print(f"euclidean_gcd(3, 6) = {euclidean_gcd(3, 6)}")
  -    print(f"euclidean_gcd(6, 3) = {euclidean_gcd(6, 3)}")
  -
  -    print(f"euclidean_gcd_recursive(3, 5) = {euclidean_gcd_recursive(3, 5)}")
  -    print(f"euclidean_gcd_recursive(5, 3) = {euclidean_gcd_recursive(5, 3)}")
  -    print(f"euclidean_gcd_recursive(1, 3) = {euclidean_gcd_recursive(1, 3)}")
  -    print(f"euclidean_gcd_recursive(3, 6) = {euclidean_gcd_recursive(3, 6)}")
  -    print(f"euclidean_gcd_recursive(6, 3) = {euclidean_gcd_recursive(6, 3)}")
  -
  -
  -if __name__ == "__main__":
  -    main()
  
verification_info: {"golden_diff": "diff --git a/maths/euclidean_gcd.py b/maths/euclidean_gcd.py\ndeleted file mode 100644\n--- a/maths/euclidean_gcd.py\n+++ /dev/null\n@@ -1,47 +0,0 @@\n-\"\"\" https://en.wikipedia.org/wiki/Euclidean_algorithm \"\"\"\n-\n-\n-def euclidean_gcd(a: int, b: int) -> int:\n-    \"\"\"\n-    Examples:\n-    >>> euclidean_gcd(3, 5)\n-    1\n-\n-    >>> euclidean_gcd(6, 3)\n-    3\n-    \"\"\"\n-    while b:\n-        a, b = b, a % b\n-    return a\n-\n-\n-def euclidean_gcd_recursive(a: int, b: int) -> int:\n-    \"\"\"\n-    Recursive method for euclicedan gcd algorithm\n-\n-    Examples:\n-    >>> euclidean_gcd_recursive(3, 5)\n-    1\n-\n-    >>> euclidean_gcd_recursive(6, 3)\n-    3\n-    \"\"\"\n-    return a if b == 0 else euclidean_gcd_recursive(b, a % b)\n-\n-\n-def main():\n-    print(f\"euclidean_gcd(3, 5) = {euclidean_gcd(3, 5)}\")\n-    print(f\"euclidean_gcd(5, 3) = {euclidean_gcd(5, 3)}\")\n-    print(f\"euclidean_gcd(1, 3) = {euclidean_gcd(1, 3)}\")\n-    print(f\"euclidean_gcd(3, 6) = {euclidean_gcd(3, 6)}\")\n-    print(f\"euclidean_gcd(6, 3) = {euclidean_gcd(6, 3)}\")\n-\n-    print(f\"euclidean_gcd_recursive(3, 5) = {euclidean_gcd_recursive(3, 5)}\")\n-    print(f\"euclidean_gcd_recursive(5, 3) = {euclidean_gcd_recursive(5, 3)}\")\n-    print(f\"euclidean_gcd_recursive(1, 3) = {euclidean_gcd_recursive(1, 3)}\")\n-    print(f\"euclidean_gcd_recursive(3, 6) = {euclidean_gcd_recursive(3, 6)}\")\n-    print(f\"euclidean_gcd_recursive(6, 3) = {euclidean_gcd_recursive(6, 3)}\")\n-\n-\n-if __name__ == \"__main__\":\n-    main()\n", "issue": "Remove duplicate GCD implementation\n### Feature description\n\n[`greatest_common_divisor.py`](https://github.com/TheAlgorithms/Python/blob/master/maths/greatest_common_divisor.py) and [`euclidean_gcd.py`](https://github.com/TheAlgorithms/Python/blob/master/maths/euclidean_gcd.py) both have basically the same two implementations of the Euclidean algorithm for calculating the GCD of 2 numbers. Thus, one of them should probably be removed as a duplicate.\n", "before_files": [{"content": "\"\"\" https://en.wikipedia.org/wiki/Euclidean_algorithm \"\"\"\n\n\ndef euclidean_gcd(a: int, b: int) -> int:\n    \"\"\"\n    Examples:\n    >>> euclidean_gcd(3, 5)\n    1\n\n    >>> euclidean_gcd(6, 3)\n    3\n    \"\"\"\n    while b:\n        a, b = b, a % b\n    return a\n\n\ndef euclidean_gcd_recursive(a: int, b: int) -> int:\n    \"\"\"\n    Recursive method for euclicedan gcd algorithm\n\n    Examples:\n    >>> euclidean_gcd_recursive(3, 5)\n    1\n\n    >>> euclidean_gcd_recursive(6, 3)\n    3\n    \"\"\"\n    return a if b == 0 else euclidean_gcd_recursive(b, a % b)\n\n\ndef main():\n    print(f\"euclidean_gcd(3, 5) = {euclidean_gcd(3, 5)}\")\n    print(f\"euclidean_gcd(5, 3) = {euclidean_gcd(5, 3)}\")\n    print(f\"euclidean_gcd(1, 3) = {euclidean_gcd(1, 3)}\")\n    print(f\"euclidean_gcd(3, 6) = {euclidean_gcd(3, 6)}\")\n    print(f\"euclidean_gcd(6, 3) = {euclidean_gcd(6, 3)}\")\n\n    print(f\"euclidean_gcd_recursive(3, 5) = {euclidean_gcd_recursive(3, 5)}\")\n    print(f\"euclidean_gcd_recursive(5, 3) = {euclidean_gcd_recursive(5, 3)}\")\n    print(f\"euclidean_gcd_recursive(1, 3) = {euclidean_gcd_recursive(1, 3)}\")\n    print(f\"euclidean_gcd_recursive(3, 6) = {euclidean_gcd_recursive(3, 6)}\")\n    print(f\"euclidean_gcd_recursive(6, 3) = {euclidean_gcd_recursive(6, 3)}\")\n\n\nif __name__ == \"__main__\":\n    main()\n", "path": "maths/euclidean_gcd.py"}]}