Sorting

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.

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.

Visual walkthrough

The pinned input is [5, 1, 4, 2, 8]. The diagrams show the split into recursive halves, the sorted subarrays, and the final merge choices.

Step 1 - Split the input

The first midpoint splits [5, 1, 4, 2, 8] into left [5, 1] and right [4, 2, 8].

Top-down split used by merge_sort.[5,1,4,2,8]mid = 2[5,1]left[4,2,8]right

Step 2 - Sorted halves return

Recursive calls return [1, 5] and [2, 4, 8] before the final merge begins.

Returned subarrays before the final merge.sidebefore sortafter sortleft[5, 1][1, 5]right[4, 2, 8][2, 4, 8]

Step 3 - Merge by taking smaller fronts

Take 1 from left, then 2 and 4 from right, then the remaining 5 and 8.

Final merge produces [1, 2, 4, 5, 8].choiceleft frontright frontmergedtake 112[1]take 252[1, 2]take 454[1, 2, 4]extend58[1, 2, 4, 5, 8]

Basic Implementation

basic.sh 
#!/usr/bin/env bash
set -euo pipefail

merge_sort() {
	local values=("$@")
	local n=${#values[@]}
	if ((n <= 1)); then
		printf '%s\n' "${values[@]}"
		return
	fi

	local mid=$((n / 2))
	local left=("${values[@]:0:mid}")
	local right=("${values[@]:mid}")
	local sorted_left=()
	local sorted_right=()
	mapfile -t sorted_left < <(merge_sort "${left[@]}")
	mapfile -t sorted_right < <(merge_sort "${right[@]}")

	local i=0
	local j=0
	while ((i < ${#sorted_left[@]} && j < ${#sorted_right[@]})); do
		if ((sorted_left[i] <= sorted_right[j])); then
			printf '%s\n' "${sorted_left[i]}"
			i=$((i + 1))
		else
			printf '%s\n' "${sorted_right[j]}"
			j=$((j + 1))
		fi
	done
	while ((i < ${#sorted_left[@]})); do
		printf '%s\n' "${sorted_left[i]}"
		i=$((i + 1))
	done
	while ((j < ${#sorted_right[@]})); do
		printf '%s\n' "${sorted_right[j]}"
		j=$((j + 1))
	done
}

arr=(5 1 4 2 8)
mapfile -t arr < <(merge_sort "${arr[@]}")
printf '['
sep=''
for v in "${arr[@]}"; do
	printf '%s%d' "$sep" "$v"
	sep=', '
done
printf ']\n'

Complexity

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

Implementation notes

  • arr=(5 1 4 2 8) is the pinned Bash indexed array. The script now sorts it with merge_sort, not external sort.
  • merge_sort() copies its arguments into a local array with local values=("$@"), then uses n=${#values[@]} as the base-case size.
  • For more than one value, mid=$((n / 2)) splits local arrays with Bash slice syntax: left=("${values[@]:0:mid}") and right=("${values[@]:mid}").
  • Bash functions cannot return arrays directly. Each recursive call prints one sorted value per line, and mapfile -t sorted_left < <(merge_sort ...) captures that stdout stream back into a local array.
  • That stream shape is intentionally simple for these pinned integers: one number per line, no spaces inside values.
  • The merge loop compares numbers with Bash arithmetic evaluation: ((sorted_left[i] <= sorted_right[j])).
  • The <= branch chooses the left value first on ties, so equal values keep their left-before-right order.
  • Remaining left or right values are printed by the two cleanup while loops.

Replay steps

start: [5, 1, 4, 2, 8]
split: left [5, 1], right [4, 2, 8]
sort:  left [1, 5], right [2, 4, 8]
merge: [1, 2, 4, 5, 8]
  • Final output uses the same formatter as nearby Bash sorting lessons: printf '[', sep='', for v in "${arr[@]}", printf '%s%d' "$sep" "$v", then printf ']\n'.