prompt: You will be provided with a partial code base and an issue statement explaining a problem to resolve.
  <issue>
  Concatenate/consolidate all algorithms with different implementations
  ### Feature description
  
  There are lots of algorithms with the same concept but different implementations/methods in different files. All these should be moved into one file
  
  </issue>
  <code>
  [start of backtracking/minmax.py]
  1 """
  2 Minimax helps to achieve maximum score in a game by checking all possible moves.
  3 
  4 """
  5 from __future__ import annotations
  6 
  7 import math
  8 
  9 
  10 def minimax(
  11     depth: int, node_index: int, is_max: bool, scores: list[int], height: float
  12 ) -> int:
  13     """
  14     depth is current depth in game tree.
  15     node_index is index of current node in scores[].
  16     scores[] contains the leaves of game tree.
  17     height is maximum height of game tree.
  18 
  19     >>> scores = [90, 23, 6, 33, 21, 65, 123, 34423]
  20     >>> height = math.log(len(scores), 2)
  21     >>> minimax(0, 0, True, scores, height)
  22     65
  23     >>> minimax(-1, 0, True, scores, height)
  24     Traceback (most recent call last):
  25         ...
  26     ValueError: Depth cannot be less than 0
  27     >>> minimax(0, 0, True, [], 2)
  28     Traceback (most recent call last):
  29         ...
  30     ValueError: Scores cannot be empty
  31     >>> scores = [3, 5, 2, 9, 12, 5, 23, 23]
  32     >>> height = math.log(len(scores), 2)
  33     >>> minimax(0, 0, True, scores, height)
  34     12
  35     """
  36 
  37     if depth < 0:
  38         raise ValueError("Depth cannot be less than 0")
  39 
  40     if not scores:
  41         raise ValueError("Scores cannot be empty")
  42 
  43     if depth == height:
  44         return scores[node_index]
  45 
  46     return (
  47         max(
  48             minimax(depth + 1, node_index * 2, False, scores, height),
  49             minimax(depth + 1, node_index * 2 + 1, False, scores, height),
  50         )
  51         if is_max
  52         else min(
  53             minimax(depth + 1, node_index * 2, True, scores, height),
  54             minimax(depth + 1, node_index * 2 + 1, True, scores, height),
  55         )
  56     )
  57 
  58 
  59 def main() -> None:
  60     scores = [90, 23, 6, 33, 21, 65, 123, 34423]
  61     height = math.log(len(scores), 2)
  62     print(f"Optimal value : {minimax(0, 0, True, scores, height)}")
  63 
  64 
  65 if __name__ == "__main__":
  66     import doctest
  67 
  68     doctest.testmod()
  69     main()
  70
  [end of backtracking/minmax.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/backtracking/minmax.py b/backtracking/minmax.py
  deleted file mode 100644
  --- a/backtracking/minmax.py
  +++ /dev/null
  @@ -1,69 +0,0 @@
  -"""
  -Minimax helps to achieve maximum score in a game by checking all possible moves.
  -
  -"""
  -from __future__ import annotations
  -
  -import math
  -
  -
  -def minimax(
  -    depth: int, node_index: int, is_max: bool, scores: list[int], height: float
  -) -> int:
  -    """
  -    depth is current depth in game tree.
  -    node_index is index of current node in scores[].
  -    scores[] contains the leaves of game tree.
  -    height is maximum height of game tree.
  -
  -    >>> scores = [90, 23, 6, 33, 21, 65, 123, 34423]
  -    >>> height = math.log(len(scores), 2)
  -    >>> minimax(0, 0, True, scores, height)
  -    65
  -    >>> minimax(-1, 0, True, scores, height)
  -    Traceback (most recent call last):
  -        ...
  -    ValueError: Depth cannot be less than 0
  -    >>> minimax(0, 0, True, [], 2)
  -    Traceback (most recent call last):
  -        ...
  -    ValueError: Scores cannot be empty
  -    >>> scores = [3, 5, 2, 9, 12, 5, 23, 23]
  -    >>> height = math.log(len(scores), 2)
  -    >>> minimax(0, 0, True, scores, height)
  -    12
  -    """
  -
  -    if depth < 0:
  -        raise ValueError("Depth cannot be less than 0")
  -
  -    if not scores:
  -        raise ValueError("Scores cannot be empty")
  -
  -    if depth == height:
  -        return scores[node_index]
  -
  -    return (
  -        max(
  -            minimax(depth + 1, node_index * 2, False, scores, height),
  -            minimax(depth + 1, node_index * 2 + 1, False, scores, height),
  -        )
  -        if is_max
  -        else min(
  -            minimax(depth + 1, node_index * 2, True, scores, height),
  -            minimax(depth + 1, node_index * 2 + 1, True, scores, height),
  -        )
  -    )
  -
  -
  -def main() -> None:
  -    scores = [90, 23, 6, 33, 21, 65, 123, 34423]
  -    height = math.log(len(scores), 2)
  -    print(f"Optimal value : {minimax(0, 0, True, scores, height)}")
  -
  -
  -if __name__ == "__main__":
  -    import doctest
  -
  -    doctest.testmod()
  -    main()
  
verification_info: {"golden_diff": "diff --git a/backtracking/minmax.py b/backtracking/minmax.py\ndeleted file mode 100644\n--- a/backtracking/minmax.py\n+++ /dev/null\n@@ -1,69 +0,0 @@\n-\"\"\"\n-Minimax helps to achieve maximum score in a game by checking all possible moves.\n-\n-\"\"\"\n-from __future__ import annotations\n-\n-import math\n-\n-\n-def minimax(\n-    depth: int, node_index: int, is_max: bool, scores: list[int], height: float\n-) -> int:\n-    \"\"\"\n-    depth is current depth in game tree.\n-    node_index is index of current node in scores[].\n-    scores[] contains the leaves of game tree.\n-    height is maximum height of game tree.\n-\n-    >>> scores = [90, 23, 6, 33, 21, 65, 123, 34423]\n-    >>> height = math.log(len(scores), 2)\n-    >>> minimax(0, 0, True, scores, height)\n-    65\n-    >>> minimax(-1, 0, True, scores, height)\n-    Traceback (most recent call last):\n-        ...\n-    ValueError: Depth cannot be less than 0\n-    >>> minimax(0, 0, True, [], 2)\n-    Traceback (most recent call last):\n-        ...\n-    ValueError: Scores cannot be empty\n-    >>> scores = [3, 5, 2, 9, 12, 5, 23, 23]\n-    >>> height = math.log(len(scores), 2)\n-    >>> minimax(0, 0, True, scores, height)\n-    12\n-    \"\"\"\n-\n-    if depth < 0:\n-        raise ValueError(\"Depth cannot be less than 0\")\n-\n-    if not scores:\n-        raise ValueError(\"Scores cannot be empty\")\n-\n-    if depth == height:\n-        return scores[node_index]\n-\n-    return (\n-        max(\n-            minimax(depth + 1, node_index * 2, False, scores, height),\n-            minimax(depth + 1, node_index * 2 + 1, False, scores, height),\n-        )\n-        if is_max\n-        else min(\n-            minimax(depth + 1, node_index * 2, True, scores, height),\n-            minimax(depth + 1, node_index * 2 + 1, True, scores, height),\n-        )\n-    )\n-\n-\n-def main() -> None:\n-    scores = [90, 23, 6, 33, 21, 65, 123, 34423]\n-    height = math.log(len(scores), 2)\n-    print(f\"Optimal value : {minimax(0, 0, True, scores, height)}\")\n-\n-\n-if __name__ == \"__main__\":\n-    import doctest\n-\n-    doctest.testmod()\n-    main()\n", "issue": "Concatenate/consolidate all algorithms with different implementations\n### Feature description\n\nThere are lots of algorithms with the same concept but different implementations/methods in different files. All these should be moved into one file\n", "before_files": [{"content": "\"\"\"\nMinimax helps to achieve maximum score in a game by checking all possible moves.\n\n\"\"\"\nfrom __future__ import annotations\n\nimport math\n\n\ndef minimax(\n    depth: int, node_index: int, is_max: bool, scores: list[int], height: float\n) -> int:\n    \"\"\"\n    depth is current depth in game tree.\n    node_index is index of current node in scores[].\n    scores[] contains the leaves of game tree.\n    height is maximum height of game tree.\n\n    >>> scores = [90, 23, 6, 33, 21, 65, 123, 34423]\n    >>> height = math.log(len(scores), 2)\n    >>> minimax(0, 0, True, scores, height)\n    65\n    >>> minimax(-1, 0, True, scores, height)\n    Traceback (most recent call last):\n        ...\n    ValueError: Depth cannot be less than 0\n    >>> minimax(0, 0, True, [], 2)\n    Traceback (most recent call last):\n        ...\n    ValueError: Scores cannot be empty\n    >>> scores = [3, 5, 2, 9, 12, 5, 23, 23]\n    >>> height = math.log(len(scores), 2)\n    >>> minimax(0, 0, True, scores, height)\n    12\n    \"\"\"\n\n    if depth < 0:\n        raise ValueError(\"Depth cannot be less than 0\")\n\n    if not scores:\n        raise ValueError(\"Scores cannot be empty\")\n\n    if depth == height:\n        return scores[node_index]\n\n    return (\n        max(\n            minimax(depth + 1, node_index * 2, False, scores, height),\n            minimax(depth + 1, node_index * 2 + 1, False, scores, height),\n        )\n        if is_max\n        else min(\n            minimax(depth + 1, node_index * 2, True, scores, height),\n            minimax(depth + 1, node_index * 2 + 1, True, scores, height),\n        )\n    )\n\n\ndef main() -> None:\n    scores = [90, 23, 6, 33, 21, 65, 123, 34423]\n    height = math.log(len(scores), 2)\n    print(f\"Optimal value : {minimax(0, 0, True, scores, height)}\")\n\n\nif __name__ == \"__main__\":\n    import doctest\n\n    doctest.testmod()\n    main()\n", "path": "backtracking/minmax.py"}]}