Sorting

Bubble Sort

Repeatedly walk the array comparing adjacent pairs and swapping any that are out of order. After pass k, the k largest elements are in their final positions at the end. Stop early when a full pass makes zero swaps.

Algorithm

Canonical input [5, 1, 4, 2, 8] finishes after three passes: two with swaps, then a clean pass that triggers the early exit. Final array [1, 2, 4, 5, 8].

adjacent-pair compare and swap Inner loop walks `j` from `0` to `n - i - 2` comparing `arr[j]` and `arr[j + 1]`.
early exit A `swapped` flag set false at the start of each pass. If no swap happened, flip a `done` flag and break out of the outer loop.

Basic Implementation

basic.rb
Replay: real traced execution (multi-file project)
arr = [5, 1, 4, 2, 8]
n = arr.length
i = 0
done = false
while i < n - 1 && !done
	swapped = false
	j = 0
	while j < n - i - 1
		if arr[j] > arr[j + 1]
			tmp = arr[j]
			arr[j] = arr[j + 1]
			arr[j + 1] = tmp
			swapped = true
		end
		j = j + 1
	end
	if !swapped
		done = true
	end
	i = i + 1
end
puts arr.inspect

  1. arr ← [5, 1, 4, 2, 8]

    1arr = [5, 1, 4, 2, 8]2n = arr.length
    values this step[5, 1, 4, 2, 8]arr

  2. n ← 5

    1arr = [5, 1, 4, 2, 8]2n = arr.length3i = 0
    values this step5n[5, 1, 4, 2, 8]arr

  3. swapped ← false

    5while i < n - 1 && !done6	swapped = false7	j = 0
    values this stepfalseswapped

  4. arr[j] > arr[j+1] ← true

    8while j < n - i - 19	if arr[j] > arr[j + 1]10		tmp = arr[j]
    values this steptruearr[j] > arr[j+1][5, 1, 4, 2, 8]arr0j5arr[j]1arr[j+1]

  5. arr ← [1, 5, 4, 2, 8], swapped ← true

    10tmp = arr[j]11arr[j] = arr[j + 1]12arr[j + 1] = tmp
    values this step[5, 1, 4, 2, 8] → [1, 5, 4, 2, 8]arrtrueswapped

  6. arr[j] > arr[j+1] ← true

    8while j < n - i - 19	if arr[j] > arr[j + 1]10		tmp = arr[j]
    values this steptruearr[j] > arr[j+1][1, 5, 4, 2, 8]arr1j5arr[j]4arr[j+1]

  7. arr ← [1, 4, 5, 2, 8], swapped ← true

    10tmp = arr[j]11arr[j] = arr[j + 1]12arr[j + 1] = tmp
    values this step[1, 5, 4, 2, 8] → [1, 4, 5, 2, 8]arrtrueswapped

  8. arr[j] > arr[j+1] ← true

    8while j < n - i - 19	if arr[j] > arr[j + 1]10		tmp = arr[j]
    values this steptruearr[j] > arr[j+1][1, 4, 5, 2, 8]arr2j5arr[j]2arr[j+1]

  9. arr ← [1, 4, 2, 5, 8], swapped ← true

    10tmp = arr[j]11arr[j] = arr[j + 1]12arr[j + 1] = tmp
    values this step[1, 4, 5, 2, 8] → [1, 4, 2, 5, 8]arrtrueswapped

  10. arr[j] > arr[j+1] ← false

    8while j < n - i - 19	if arr[j] > arr[j + 1]10		tmp = arr[j]
    values this stepfalsearr[j] > arr[j+1][1, 4, 2, 5, 8]arr3j5arr[j]8arr[j+1]

  11. swapped ← false

    5while i < n - 1 && !done6	swapped = false7	j = 0
    values this stepfalseswapped

  12. arr[j] > arr[j+1] ← false

    8while j < n - i - 19	if arr[j] > arr[j + 1]10		tmp = arr[j]
    values this stepfalsearr[j] > arr[j+1][1, 4, 2, 5, 8]arr0j1arr[j]4arr[j+1]

  13. arr[j] > arr[j+1] ← true

    8while j < n - i - 19	if arr[j] > arr[j + 1]10		tmp = arr[j]
    values this steptruearr[j] > arr[j+1][1, 4, 2, 5, 8]arr1j4arr[j]2arr[j+1]

  14. arr ← [1, 2, 4, 5, 8], swapped ← true

    10tmp = arr[j]11arr[j] = arr[j + 1]12arr[j + 1] = tmp
    values this step[1, 4, 2, 5, 8] → [1, 2, 4, 5, 8]arrtrueswapped

  15. arr[j] > arr[j+1] ← false

    8while j < n - i - 19	if arr[j] > arr[j + 1]10		tmp = arr[j]
    values this stepfalsearr[j] > arr[j+1][1, 2, 4, 5, 8]arr2j4arr[j]5arr[j+1]

  16. swapped ← false

    5while i < n - 1 && !done6	swapped = false7	j = 0
    values this stepfalseswapped

  17. arr[j] > arr[j+1] ← false

    8while j < n - i - 19	if arr[j] > arr[j + 1]10		tmp = arr[j]
    values this stepfalsearr[j] > arr[j+1][1, 2, 4, 5, 8]arr0j1arr[j]2arr[j+1]

  18. arr[j] > arr[j+1] ← false

    8while j < n - i - 19	if arr[j] > arr[j + 1]10		tmp = arr[j]
    values this stepfalsearr[j] > arr[j+1][1, 2, 4, 5, 8]arr1j2arr[j]4arr[j+1]

  19. done ← true

    17if !swapped18	done = true19end
    values this steptruedonefalseswapped

  20. stdout ← [1, 2, 4, 5, 8]

    21end22puts arr.inspect
    values this step[1, 2, 4, 5, 8]stdout[1, 2, 4, 5, 8]arr

Complexity

  • Time: O(n^2) worst and average; O(n) best (already sorted with early exit)
  • Space: O(1)
  • Stable: yes

Implementation notes

  • Ruby: explicit while loops with local i, j, done, and swapped so the early-exit flow stays visible. The stdlib arr.sort (or arr.sort!) would hide the comparison-and-swap the lesson is teaching, and break inside a block would obscure the done flag.
  • The explicit tmp = arr[j]; arr[j] = arr[j+1]; arr[j+1] = tmp three-line swap keeps the move visible without leaning on parallel assignment like arr[j], arr[j+1] = arr[j+1], arr[j].
  • The replay distinguishes compare frames from swap frames so the moving pivot value is visible. The pass number and swapped flag appear in the trace.