Merge sort

Faster sorts · Article 4 of 8 · 4 min read

Split the list, sort each half, then merge: your first divide and conquer algorithm.

The short version

Merge sort splits a list in half, sorts each half the same way, then merges the two sorted halves into one.

Details

Halving takes about log n levels and each level merges n items, so the total is n log n whatever the input. Merging needs extra space for the result.

Try it yourself

def merge_sort(items):
    if len(items) <= 1:
        return items
    middle = len(items) // 2
    left = merge_sort(items[:middle])
    right = merge_sort(items[middle:])
    merged = []
    i = j = 0
    while i < len(left) and j < len(right):
        if left[i] <= right[j]:
            merged.append(left[i])
            i += 1
        else:
            merged.append(right[j])
            j += 1
    return merged + left[i:] + right[j:]

print(merge_sort([5, 2, 9, 1]))

You should see [1, 2, 5, 9].

Explain it to the duck

Why does using <= instead of < when merging keep the sort stable?

Tested with: Python 3.13.