add a new algo in the number_theory

Author: Sangram03

data_structures/hashing/number_theory/median_of_two_sorted_arrays.py

@@ -0,0 +1,59 @@
+"""
+https://www.enjoyalgorithms.com/blog/median-of-two-sorted-arrays
+"""
+
+def find_median_sorted_arrays(nums1: list[int], nums2: list[int]) -> float:
+    """
+    Find the median of two arrays.
+
+    Args:
+        nums1: The first array.
+        nums2: The second array.
+
+    Returns:
+    The median of the two arrays.
+
+    Examples:
+        >>> find_median_sorted_arrays([1, 3], [2])
+        2.0
+
+        >>> find_median_sorted_arrays([1, 2], [3, 4])
+        2.5
+
+        >>> find_median_sorted_arrays([0, 0], [0, 0])
+        0.0
+
+        >>> find_median_sorted_arrays([], [])
+        Traceback (most recent call last):
+            ...
+        ValueError: Both input arrays are empty.
+
+        >>> find_median_sorted_arrays([], [1])
+        1.0
+
+        >>> find_median_sorted_arrays([-1000], [1000])
+        0.0
+
+        >>> find_median_sorted_arrays([-1.1, -2.2], [-3.3, -4.4])
+        -2.75
+    """
+    if not nums1 and not nums2:
+        raise ValueError("Both input arrays are empty.")
+
+    # Merge the arrays into a single sorted array.
+    merged = sorted(nums1 + nums2)
+    total = len(merged)
+
+    if total % 2 == 1:  # If the total number of elements is odd
+        return float(merged[total // 2])  # then return the middle element
+
+    # If the total number of elements is even, calculate
+    # the average of the two middle elements as the median.
+    middle1 = merged[total // 2 - 1]
+    middle2 = merged[total // 2]
+    return (float(middle1) + float(middle2)) / 2.0
+
+
+if __name__ == "__main__":
+    import doctest
+    doctest.testmod()