Quick Sort (Lomuto)

Choose the last item as a pivot, partition smaller values to its left, then recurse on the two sides.

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 partition(arr, low, high)
	local pivot = arr[high]
	local i = low - 1
	for j = low, high - 1 do
		if arr[j] <= pivot then
			i = i + 1
			arr[i], arr[j] = arr[j], arr[i]
		end
	end
	arr[i + 1], arr[high] = arr[high], arr[i + 1]
	return i + 1
end

local function quick_sort(arr, low, high)
	if low < high then
		local pivot_index = partition(arr, low, high)
		quick_sort(arr, low, pivot_index - 1)
		quick_sort(arr, pivot_index + 1, high)
	end
end

local arr = {4, 1, 5, 2, 3}
quick_sort(arr, 1, #arr)
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^2) worst, O(n log n) average
Space: O(log n) average call stack
Stable: no

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.

pivot The final element is moved to the boundary between smaller and larger values.

partition One scan rearranges the current range before the recursive calls.