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, break out of the outer loop.

Basic Implementation

basic.cs
Replay: real traced execution (multi-file project)
using System;

class Program {
	static void Main() {
		int[] arr = new int[] { 5, 1, 4, 2, 8 };
		int n = arr.Length;
		for (int i = 0; i < n - 1; i++) {
			bool swapped = false;
			for (int j = 0; j < n - i - 1; j++) {
				if (arr[j] > arr[j + 1]) {
					int tmp = arr[j];
					arr[j] = arr[j + 1];
					arr[j + 1] = tmp;
					swapped = true;
				}
			}
			if (!swapped) {
				break;
			}
		}
		Console.WriteLine("[" + string.Join(", ", arr) + "]");
	}
}

  1. arr ← [5, 1, 4, 2, 8]

    4static void Main() {5	int[] arr = new int[] { 5, 1, 4, 2, 8 };6	int n = arr.Length;
    values this step[5, 1, 4, 2, 8]arr

  2. n ← 5

    5int[] arr = new int[] { 5, 1, 4, 2, 8 };6int n = arr.Length;7for (int i = 0; i < n - 1; i++) {
    values this step5n[5, 1, 4, 2, 8]arr

  3. swapped ← false

    7for (int i = 0; i < n - 1; i++) {8	bool swapped = false;9	for (int j = 0; j < n - i - 1; j++) {
    values this stepfalseswapped

  4. arr[j] > arr[j+1] ← true

    9for (int j = 0; j < n - i - 1; j++) {10	if (arr[j] > arr[j + 1]) {11		int 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

    11int tmp = arr[j];12arr[j] = arr[j + 1];13arr[j + 1] = tmp;
    values this step[5, 1, 4, 2, 8] → [1, 5, 4, 2, 8]arrtrueswapped

  6. arr[j] > arr[j+1] ← true

    9for (int j = 0; j < n - i - 1; j++) {10	if (arr[j] > arr[j + 1]) {11		int 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

    11int tmp = arr[j];12arr[j] = arr[j + 1];13arr[j + 1] = tmp;
    values this step[1, 5, 4, 2, 8] → [1, 4, 5, 2, 8]arrtrueswapped

  8. arr[j] > arr[j+1] ← true

    9for (int j = 0; j < n - i - 1; j++) {10	if (arr[j] > arr[j + 1]) {11		int 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

    11int tmp = arr[j];12arr[j] = arr[j + 1];13arr[j + 1] = tmp;
    values this step[1, 4, 5, 2, 8] → [1, 4, 2, 5, 8]arrtrueswapped

  10. arr[j] > arr[j+1] ← false

    9for (int j = 0; j < n - i - 1; j++) {10	if (arr[j] > arr[j + 1]) {11		int tmp = arr[j];
    values this stepfalsearr[j] > arr[j+1][1, 4, 2, 5, 8]arr3j5arr[j]8arr[j+1]

  11. swapped ← false

    7for (int i = 0; i < n - 1; i++) {8	bool swapped = false;9	for (int j = 0; j < n - i - 1; j++) {
    values this stepfalseswapped

  12. arr[j] > arr[j+1] ← false

    9for (int j = 0; j < n - i - 1; j++) {10	if (arr[j] > arr[j + 1]) {11		int 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

    9for (int j = 0; j < n - i - 1; j++) {10	if (arr[j] > arr[j + 1]) {11		int 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

    11int tmp = arr[j];12arr[j] = arr[j + 1];13arr[j + 1] = tmp;
    values this step[1, 4, 2, 5, 8] → [1, 2, 4, 5, 8]arrtrueswapped

  15. arr[j] > arr[j+1] ← false

    9for (int j = 0; j < n - i - 1; j++) {10	if (arr[j] > arr[j + 1]) {11		int tmp = arr[j];
    values this stepfalsearr[j] > arr[j+1][1, 2, 4, 5, 8]arr2j4arr[j]5arr[j+1]

  16. swapped ← false

    7for (int i = 0; i < n - 1; i++) {8	bool swapped = false;9	for (int j = 0; j < n - i - 1; j++) {
    values this stepfalseswapped

  17. arr[j] > arr[j+1] ← false

    9for (int j = 0; j < n - i - 1; j++) {10	if (arr[j] > arr[j + 1]) {11		int 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

    9for (int j = 0; j < n - i - 1; j++) {10	if (arr[j] > arr[j + 1]) {11		int tmp = arr[j];
    values this stepfalsearr[j] > arr[j+1][1, 2, 4, 5, 8]arr1j2arr[j]4arr[j+1]

  19. loop ← break

    17if (!swapped) {18	break;19}
    values this stepbreakloopfalseswapped

  20. stdout ← [1, 2, 4, 5, 8]

    20	}21	Console.WriteLine("[" + string.Join(", ", arr) + "]");22}
    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

  • C#: nested for loops with the early-exit swapped flag. Array.Sort(arr) would hide the comparison-and-swap the lesson is teaching.
  • The explicit int tmp = arr[j]; arr[j] = arr[j+1]; arr[j+1] = tmp; mutates the managed reference int[] in place; each indexed read/write is bounds-checked by the CLR. The three-line swap keeps the move visible without leaning on (arr[j], arr[j+1]) = (arr[j+1], arr[j]); tuple syntax.
  • 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.