Add new algorithm for max-min problem

divide_and_conquer/max_min.py

@@ -0,0 +1,84 @@
+"""
+The Max-Min Problem is finding the maximum and minimum value in an array.
+
+This is a divide and conquer approach to solve the Max-Min Problem.
+
+For more information:
+https://www.tutorialspoint.com/data_structures_algorithms/max_min_problem.htm
+"""
+
+
+class Pair:
+    """
+    Structure to store both maximum and minimum elements
+    """
+
+    def __init__(self):
+        self.max = 0
+        self.min = 0
+
+
+def max_min_divide_conquer(arr: list, low: int, high: int) -> "Pair":
+    """
+    Returns the maximum and minimum elements in the array.
+
+    Args:
+        arr: A list of integers
+        low: An integer representing the start index of the array
+        high: An integer representing the end index of the array
+
+    Returns:
+        A Pair object containing the maximum and minimum elements in the array
+
+    >>> arr = [1, 3, 4, 2, 8, 9, 7, 6, 5]
+    >>> max_min_divide_conquer(arr, 0, len(arr) - 1).max
+    9
+    >>> max_min_divide_conquer(arr, 0, len(arr) - 1).min
+    1
+    >>> arr = [7]
+    >>> max_min_divide_conquer(arr, 0, len(arr) - 1).max
+    7
+    >>> max_min_divide_conquer(arr, 0, len(arr) - 1).min
+    7
+    >>> arr = [7, 1]
+    >>> max_min_divide_conquer(arr, 0, len(arr) - 1).max
+    7
+    >>> max_min_divide_conquer(arr, 0, len(arr) - 1).min
+    1
+    """
+    result = Pair()
+
+    # If only one element in the array
+    if low == high:
+        result.max = arr[low]
+        result.min = arr[low]
+        return result
+
+    # If there are two elements in the array
+    if high == low + 1:
+        if arr[low] < arr[high]:
+            result.min = arr[low]
+            result.max = arr[high]
+        else:
+            result.min = arr[high]
+            result.max = arr[low]
+        return result
+
+    # If there are more than two elements in the array
+    mid = (low + high) // 2
+    left = max_min_divide_conquer(arr, low, mid)
+    right = max_min_divide_conquer(arr, mid + 1, high)
+
+    # Compare and get the maximum of both parts
+    result.max = max(left.max, right.max)
+
+    # Compare and get the minimum of both parts
+    result.min = min(left.min, right.min)
+
+    return result
+
+
+if __name__ == "__main__":
+    from doctest import testmod
+
+    testmod()