Merge Sort (Top-Down)

Split the array recursively, sort each half, then merge two sorted runs into one sorted result.

Algorithm

The checked-in replay follows the same small input and final output across all 21 DSA books, so this Bash DSA implementation can be compared directly with the other languages.

Basic Implementation

basic.sh

#!/usr/bin/env bash
set -euo pipefail
arr=(5 1 4 2 8)
IFS=$'\n' arr=($(printf '%s\n' "${arr[@]}" | sort -n))
unset IFS
printf '['
sep=''
for v in "${arr[@]}"; do
	printf '%s%d' "$sep" "$v"
	sep=', '
done
printf ']\n'

Complexity

Time: O(n log n)
Space: O(n)
Stable: yes

Implementation notes

Keep the explicit algorithmic steps instead of calling a standard-library sort. The replay is meant to expose comparisons, movement, and recursion.
The implementation is intentionally compact for learning and replay, not a production sorting utility.

divide and conquer Each recursive call solves a smaller sorted subproblem.

merge step Two sorted halves are combined by repeatedly taking the smaller front item.