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 Lua DSA implementation can be compared directly with the other languages.

Basic Implementation

basic.lua

local function merge_sort(values)
	if #values <= 1 then return values end
	local mid = math.floor(#values / 2)
	local left, right = {}, {}
	for i = 1, mid do left[#left + 1] = values[i] end
	for i = mid + 1, #values do right[#right + 1] = values[i] end
	left = merge_sort(left)
	right = merge_sort(right)
	local merged = {}
	local i, j = 1, 1
	while i <= #left and j <= #right do
		if left[i] <= right[j] then merged[#merged + 1] = left[i]; i = i + 1
		else merged[#merged + 1] = right[j]; j = j + 1 end
	end
	while i <= #left do merged[#merged + 1] = left[i]; i = i + 1 end
	while j <= #right do merged[#merged + 1] = right[j]; j = j + 1 end
	return merged
end

local arr = merge_sort({5, 1, 4, 2, 8})
io.write("[")
for k = 1, #arr do
	if k > 1 then io.write(", ") end
	io.write(tostring(arr[k]))
end
io.write("]\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.