Divide and Conquer

maths/find_max_recursion.py

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+# Divide and Conquer algorithm
+def find_max(nums, left, right):
+    """
+    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
+
+    >>> nums = [1, 3, 5, 7, 9, 2, 4, 6, 8, 10]
+    >>> find_max(nums, 0, len(nums) - 1) == max(nums)
+    True
+    """
+    if left == right:
+        return nums[left]
+    mid = (left + right) >> 1  # the middle
+    left_max = find_max(nums, left, mid)  # find max in range[left, mid]
+    right_max = find_max(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__":
+    nums = [1, 3, 5, 7, 9, 2, 4, 6, 8, 10]
+    assert find_max(nums, 0, len(nums) - 1) == 10

maths/find_min_recursion.py

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+# Divide and Conquer algorithm
+def find_min(nums, left, right):
+    """
+    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
+
+    >>> nums = [1, 3, 5, 7, 9, 2, 4, 6, 8, 10]
+    >>> find_min(nums, 0, len(nums) - 1) == min(nums)
+    True
+    """
+    if left == right:
+        return nums[left]
+    mid = (left + right) >> 1  # the middle
+    left_min = find_min(nums, left, mid)  # find min in range[left, mid]
+    right_min = find_min(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__":
+    nums = [1, 3, 5, 7, 9, 2, 4, 6, 8, 10]
+    assert find_min(nums, 0, len(nums) - 1) == 1