Create find_median_sorted_arrays.py

data_structures/arrays/find_median_sorted_arrays.py

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+"""
+https://atharayil.medium.com/median-of-two-sorted-arrays-day-36-python-fcbd2dbbb668
+"""
+
+
+def find_median_sorted_arrays(nums1: list[int], nums2: list[int]) -> float:
+    """
+    Finds the median of two sorted arrays.
+
+    :param nums1: The first sorted array.
+    :param nums2: The second sorted array.
+    :return: The median of the combined sorted arrays.
+    :raises ValueError: If both input arrays are empty.
+
+    >>> find_median_sorted_arrays([1, 3], [2])
+    2.0
+    >>> find_median_sorted_arrays([1, 2], [3, 4])
+    2.5
+    >>> find_median_sorted_arrays([1, 3, 5], [2, 4, 6])
+    3.5
+    >>> find_median_sorted_arrays([1, 2, 3], [4, 5, 6, 7])
+    4.0
+    >>> find_median_sorted_arrays([], [2, 3])
+    2.5
+
+    """
+    # Check if both input arrays are empty
+    if not nums1 and not nums2:
+        raise ValueError("Input arrays are not valid")
+
+    # If one is empty, find the median of the non-empty array
+    if not nums1 or not nums2:
+        combined = nums1 if nums1 else nums2
+        mid = len(combined) // 2
+        if len(combined) % 2 == 0:
+            return (combined[mid - 1] + combined[mid]) / 2.0
+        else:
+            return combined[mid]
+
+    # Make sure nums1 is the smaller array
+    if len(nums1) > len(nums2):
+        nums1, nums2 = nums2, nums1
+
+    m, n = len(nums1), len(nums2)
+    total = m + n
+    half = total // 2
+
+    left, right = 0, m
+    while left <= right:
+        partition1 = (left + right) // 2
+        partition2 = half - partition1
+
+        max_left1 = float("-inf") if partition1 == 0 else nums1[partition1 - 1]
+        min_right1 = float("inf") if partition1 == m else nums1[partition1]
+
+        max_left2 = float("-inf") if partition2 == 0 else nums2[partition2 - 1]
+        min_right2 = float("inf") if partition2 == n else nums2[partition2]
+
+        if max_left1 <= min_right2 and max_left2 <= min_right1:
+            if total % 2 == 0:
+                return float(
+                    (max(max_left1, max_left2) + min(min_right1, min_right2)) / 2
+                )
+            else:
+                return float(min(min_right1, min_right2))
+        elif max_left1 > min_right2:
+            right = partition1 - 1
+        else:
+            left = partition1 + 1
+
+    # If the loop exits without returning, the input arrays are not valid
+    raise ValueError("Input arrays are not valid")
+
+
+# Example
+if __name__ == "__main__":
+    nums1 = [1, 3]
+    nums2 = [2]
+    print("Median of Example 1:", find_median_sorted_arrays(nums1, nums2))
+
+    nums1 = [1, 2]
+    nums2 = [3, 4]
+    print("Median of Example 2:", find_median_sorted_arrays(nums1, nums2))