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 Lua 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.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

  • merge_sort(values) takes a Lua table and returns a sorted table rather than mutating the original literal in place.
  • The checked input is {5, 1, 4, 2, 8}, assigned through local arr = merge_sort(...).
  • The base case is if #values <= 1 then return values end.
  • local mid = math.floor(#values / 2) splits the dense table length using integer flooring.
  • Halves are built with 1-based loops: 1..mid fills left, and mid + 1..#values fills right.
  • Appends use table[#table + 1] = value, as in left[#left + 1] = values[i] and merged[#merged + 1] = left[i].
  • The merge cursors start at local i, j = 1, 1 and advance while both halves still have values.
  • The comparison left[i] <= right[j] keeps equal left-side values before right-side values.
  • The trace splits [5, 1, 4, 2, 8] into [5, 1] and [4, 2, 8], sorts them into [1, 5] and [2, 4, 8], then merges [1, 2, 4, 5, 8].
  • The final io.write loop prints [1, 2, 4, 5, 8].