Selection Sort - Lua DSA

Repeatedly find the index of the smallest remaining element and swap it into the next "sorted prefix" slot. Unlike bubble sort, only one swap per pass.

Algorithm

Canonical input {5, 1, 4, 2, 8} finishes after four passes, with two real swaps (passes 1 and 2) and two skip-swap passes (min_idx == i). Final array {1, 2, 4, 5, 8}.

running minimum `min_idx` tracks the index of the smallest value seen in `arr[i..n]`.

sorted prefix After each pass, `arr[1..i]` is the final sorted prefix.

Visual walkthrough

The pinned input [5, 1, 4, 2, 8] sorts with two real swaps. The frames keep the running minimum and swap positions visible.

Step 1 - First scan finds 1

In the first pass, min_idx moves from 5 to 1.

Step 2 - Swap 5 and 1

The smallest value moves into the first sorted slot.

Step 3 - Second scan finds 2

In the unsorted suffix, 2 is smaller than 5 and becomes the next minimum.

Step 4 - Sorted after two swaps

Swapping 5 and 2 gives [1, 2, 4, 5, 8]; later passes find no real swap.

Basic Implementation

                            basic.lua
                        

                            local arr = {5, 1, 4, 2, 8}
local n = #arr
local i = 1
while i <= n - 1 do
	local min_idx = i
	local j = i + 1
	while j <= n do
		if arr[j] < arr[min_idx] then
			min_idx = j
		end
		j = j + 1
	end
	if min_idx ~= i then
		local tmp = arr[i]
		arr[i] = arr[min_idx]
		arr[min_idx] = tmp
	end
	i = i + 1
end
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) regardless of input order
Space: O(1)
Stable: no
Swap count: at most n-1

Implementation notes

Lua: same loop shape as Python / Java / JavaScript / C++ / C / Go / Rust / C# / Kotlin / Swift / Scala / Ruby / PHP. The if min_idx ~= i guard is the canonical skip-swap variant from the lesson spec.
min_idx = i keeps the running-minimum invariant visible; the three-line local tmp = arr[i]; arr[i] = arr[min_idx]; arr[min_idx] = tmp swap mirrors the bubble-sort lesson.
The replay highlights the current min_idx distinctly from the scanning index j so the viewer sees the running minimum travel.