Consolidate find_min and find_min recursive and find_max and find_max_recursive (TheAlgorithms#8960)

* updating DIRECTORY.md

* refactor(min-max): Consolidate implementations

* updating DIRECTORY.md

* refactor(min-max): Append _iterative to func name

---------

Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>

Author: CaedenPH

Diff for: DIRECTORY.md

@@ -573,9 +573,7 @@
   * [Fermat Little Theorem](maths/fermat_little_theorem.py)
   * [Fibonacci](maths/fibonacci.py)
   * [Find Max](maths/find_max.py)
-  * [Find Max Recursion](maths/find_max_recursion.py)
   * [Find Min](maths/find_min.py)
-  * [Find Min Recursion](maths/find_min_recursion.py)
   * [Floor](maths/floor.py)
   * [Gamma](maths/gamma.py)
   * [Gamma Recursive](maths/gamma_recursive.py)

Diff for: maths/find_max.py

@@ -1,30 +1,83 @@
 from __future__ import annotations
 
 
-def find_max(nums: list[int | float]) -> int | float:
+def find_max_iterative(nums: list[int | float]) -> int | float:
     """
     >>> for nums in ([3, 2, 1], [-3, -2, -1], [3, -3, 0], [3.0, 3.1, 2.9]):
-    ...     find_max(nums) == max(nums)
+    ...     find_max_iterative(nums) == max(nums)
     True
     True
     True
     True
-    >>> find_max([2, 4, 9, 7, 19, 94, 5])
+    >>> find_max_iterative([2, 4, 9, 7, 19, 94, 5])
     94
-    >>> find_max([])
+    >>> find_max_iterative([])
     Traceback (most recent call last):
         ...
-    ValueError: find_max() arg is an empty sequence
+    ValueError: find_max_iterative() arg is an empty sequence
     """
     if len(nums) == 0:
-        raise ValueError("find_max() arg is an empty sequence")
+        raise ValueError("find_max_iterative() arg is an empty sequence")
     max_num = nums[0]
     for x in nums:
         if x > max_num:
             max_num = x
     return max_num
 
 
+# Divide and Conquer algorithm
+def find_max_recursive(nums: list[int | float], left: int, right: int) -> int | float:
+    """
+    find max value in list
+    :param nums: contains elements
+    :param left: index of first element
+    :param right: index of last element
+    :return: max in nums
+
+    >>> for nums in ([3, 2, 1], [-3, -2, -1], [3, -3, 0], [3.0, 3.1, 2.9]):
+    ...     find_max_recursive(nums, 0, len(nums) - 1) == max(nums)
+    True
+    True
+    True
+    True
+    >>> nums = [1, 3, 5, 7, 9, 2, 4, 6, 8, 10]
+    >>> find_max_recursive(nums, 0, len(nums) - 1) == max(nums)
+    True
+    >>> find_max_recursive([], 0, 0)
+    Traceback (most recent call last):
+        ...
+    ValueError: find_max_recursive() arg is an empty sequence
+    >>> find_max_recursive(nums, 0, len(nums)) == max(nums)
+    Traceback (most recent call last):
+        ...
+    IndexError: list index out of range
+    >>> find_max_recursive(nums, -len(nums), -1) == max(nums)
+    True
+    >>> find_max_recursive(nums, -len(nums) - 1, -1) == max(nums)
+    Traceback (most recent call last):
+        ...
+    IndexError: list index out of range
+    """
+    if len(nums) == 0:
+        raise ValueError("find_max_recursive() arg is an empty sequence")
+    if (
+        left >= len(nums)
+        or left < -len(nums)
+        or right >= len(nums)
+        or right < -len(nums)
+    ):
+        raise IndexError("list index out of range")
+    if left == right:
+        return nums[left]
+    mid = (left + right) >> 1  # the middle
+    left_max = find_max_recursive(nums, left, mid)  # find max in range[left, mid]
+    right_max = find_max_recursive(
+        nums, mid + 1, right
+    )  # find max in range[mid + 1, right]
+
+    return left_max if left_max >= right_max else right_max
+
+
 if __name__ == "__main__":
     import doctest
 

Diff for: maths/find_max_recursion.py

@@ -1,33 +1,86 @@
 from __future__ import annotations
 
 
-def find_min(nums: list[int | float]) -> int | float:
+def find_min_iterative(nums: list[int | float]) -> int | float:
     """
     Find Minimum Number in a List
     :param nums: contains elements
     :return: min number in list
 
     >>> for nums in ([3, 2, 1], [-3, -2, -1], [3, -3, 0], [3.0, 3.1, 2.9]):
-    ...     find_min(nums) == min(nums)
+    ...     find_min_iterative(nums) == min(nums)
     True
     True
     True
     True
-    >>> find_min([0, 1, 2, 3, 4, 5, -3, 24, -56])
+    >>> find_min_iterative([0, 1, 2, 3, 4, 5, -3, 24, -56])
     -56
-    >>> find_min([])
+    >>> find_min_iterative([])
     Traceback (most recent call last):
         ...
-    ValueError: find_min() arg is an empty sequence
+    ValueError: find_min_iterative() arg is an empty sequence
     """
     if len(nums) == 0:
-        raise ValueError("find_min() arg is an empty sequence")
+        raise ValueError("find_min_iterative() arg is an empty sequence")
     min_num = nums[0]
     for num in nums:
         min_num = min(min_num, num)
     return min_num
 
 
+# Divide and Conquer algorithm
+def find_min_recursive(nums: list[int | float], left: int, right: int) -> int | float:
+    """
+    find min value in list
+    :param nums: contains elements
+    :param left: index of first element
+    :param right: index of last element
+    :return: min in nums
+
+    >>> for nums in ([3, 2, 1], [-3, -2, -1], [3, -3, 0], [3.0, 3.1, 2.9]):
+    ...     find_min_recursive(nums, 0, len(nums) - 1) == min(nums)
+    True
+    True
+    True
+    True
+    >>> nums = [1, 3, 5, 7, 9, 2, 4, 6, 8, 10]
+    >>> find_min_recursive(nums, 0, len(nums) - 1) == min(nums)
+    True
+    >>> find_min_recursive([], 0, 0)
+    Traceback (most recent call last):
+        ...
+    ValueError: find_min_recursive() arg is an empty sequence
+    >>> find_min_recursive(nums, 0, len(nums)) == min(nums)
+    Traceback (most recent call last):
+        ...
+    IndexError: list index out of range
+    >>> find_min_recursive(nums, -len(nums), -1) == min(nums)
+    True
+    >>> find_min_recursive(nums, -len(nums) - 1, -1) == min(nums)
+    Traceback (most recent call last):
+        ...
+    IndexError: list index out of range
+    """
+    if len(nums) == 0:
+        raise ValueError("find_min_recursive() arg is an empty sequence")
+    if (
+        left >= len(nums)
+        or left < -len(nums)
+        or right >= len(nums)
+        or right < -len(nums)
+    ):
+        raise IndexError("list index out of range")
+    if left == right:
+        return nums[left]
+    mid = (left + right) >> 1  # the middle
+    left_min = find_min_recursive(nums, left, mid)  # find min in range[left, mid]
+    right_min = find_min_recursive(
+        nums, mid + 1, right
+    )  # find min in range[mid + 1, right]
+
+    return left_min if left_min <= right_min else right_min
+
+
 if __name__ == "__main__":
     import doctest