Find Median of Two Sorted Arrays in Python

Merges two sorted arrays with a two-pointer walk and returns the median of the combined sorted sequence.

Easy Python 3.9+ Aug 9, 2026 Algorithms & data structures 16 views 0 copies

median two-pointer merge sorted-arrays algorithms

Python code

24 lines

Python 3.9+

def median_of_two_sorted_arrays(nums1, nums2):
    merged = []
    i = j = 0
    while i < len(nums1) and j < len(nums2):
        if nums1[i] <= nums2[j]:
            merged.append(nums1[i])
            i += 1
        else:
            merged.append(nums2[j])
            j += 1
    merged.extend(nums1[i:])
    merged.extend(nums2[j:])
    n = len(merged)
    if n % 2 == 1:
        return float(merged[n // 2])
    return (merged[n // 2 - 1] + merged[n // 2]) / 2.0

if __name__ == "__main__":
    a = [1, 3, 8]
    b = [2, 4, 5, 6]
    print(median_of_two_sorted_arrays(a, b))
    c = [1, 2]
    d = [3, 4]
    print(median_of_two_sorted_arrays(c, d))

Output

stdout

4.0
2.5

How it works

The algorithm performs a merge walk: it advances two pointers through the arrays, always appending the smaller current element to a merged list. After the merge, the median is found from the merged list — the middle element for odd length, or the average of the two middle elements for even length. This approach is straightforward and runs in O(n + m) time, using O(n + m) extra memory.

Common mistakes

Using floor division on an even-length merged list without averaging the two middle values.
Forgetting to extend the merged list with remaining elements from either array after the main loop.
Assuming the arrays are not empty; the code does not handle empty inputs explicitly.

Variations

Use a binary search approach for an O(log(min(n, m))) solution.
Use `heapq.merge` to combine the arrays before computing the median.

Real-world use cases

Calculating the median performance metric from two sorted log files in a monitoring system.
Computing the median latency from two sorted data streams in real-time analytics pipelines.
Finding a percentile boundary when merging sorted results from two database shards.

Find Median of Two Sorted Arrays in Python

Python code

Output

How it works

Common mistakes

Variations

Real-world use cases

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