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.ts
Replay: real traced execution (multi-file project)
const arr: number[] = [5, 1, 4, 2, 8];
const n: number = arr.length;
for (let i: number = 0; i < n - 1; i++) {
    let swapped: boolean = false;
    for (let j: number = 0; j < n - i - 1; j++) {
        if (arr[j] > arr[j + 1]) {
            const tmp: number = arr[j];
            arr[j] = arr[j + 1];
            arr[j + 1] = tmp;
            swapped = true;
        }
    }
    if (!swapped) {
        break;
    }
}
console.log(JSON.stringify(arr));

  1. arr ← [5, 1, 4, 2, 8]

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

  2. n ← 5

    1const arr: number[] = [5, 1, 4, 2, 8];2const n: number = arr.length;3for (let i: number = 0; i < n - 1; i++) {
    values this step5n[5, 1, 4, 2, 8]arr

  3. swapped ← false

    3for (let i: number = 0; i < n - 1; i++) {4    let swapped: boolean = false;5    for (let j: number = 0; j < n - i - 1; j++) {
    values this stepfalseswapped

  4. arr[j] > arr[j+1] ← true

    5for (let j: number = 0; j < n - i - 1; j++) {6    if (arr[j] > arr[j + 1]) {7        const tmp: number = 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

    8arr[j] = arr[j + 1];9arr[j + 1] = tmp;10swapped = true;
    values this step[5, 1, 4, 2, 8] → [1, 5, 4, 2, 8]arrtrueswapped

  6. arr[j] > arr[j+1] ← true

    5for (let j: number = 0; j < n - i - 1; j++) {6    if (arr[j] > arr[j + 1]) {7        const tmp: number = 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

    8arr[j] = arr[j + 1];9arr[j + 1] = tmp;10swapped = true;
    values this step[1, 5, 4, 2, 8] → [1, 4, 5, 2, 8]arrtrueswapped

  8. arr[j] > arr[j+1] ← true

    5for (let j: number = 0; j < n - i - 1; j++) {6    if (arr[j] > arr[j + 1]) {7        const tmp: number = 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

    8arr[j] = arr[j + 1];9arr[j + 1] = tmp;10swapped = true;
    values this step[1, 4, 5, 2, 8] → [1, 4, 2, 5, 8]arrtrueswapped

  10. arr[j] > arr[j+1] ← false

    5for (let j: number = 0; j < n - i - 1; j++) {6    if (arr[j] > arr[j + 1]) {7        const tmp: number = arr[j];
    values this stepfalsearr[j] > arr[j+1][1, 4, 2, 5, 8]arr3j5arr[j]8arr[j+1]

  11. swapped ← false

    3for (let i: number = 0; i < n - 1; i++) {4    let swapped: boolean = false;5    for (let j: number = 0; j < n - i - 1; j++) {
    values this stepfalseswapped

  12. arr[j] > arr[j+1] ← false

    5for (let j: number = 0; j < n - i - 1; j++) {6    if (arr[j] > arr[j + 1]) {7        const tmp: number = 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

    5for (let j: number = 0; j < n - i - 1; j++) {6    if (arr[j] > arr[j + 1]) {7        const tmp: number = 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

    8arr[j] = arr[j + 1];9arr[j + 1] = tmp;10swapped = true;
    values this step[1, 4, 2, 5, 8] → [1, 2, 4, 5, 8]arrtrueswapped

  15. arr[j] > arr[j+1] ← false

    5for (let j: number = 0; j < n - i - 1; j++) {6    if (arr[j] > arr[j + 1]) {7        const tmp: number = arr[j];
    values this stepfalsearr[j] > arr[j+1][1, 2, 4, 5, 8]arr2j4arr[j]5arr[j+1]

  16. swapped ← false

    3for (let i: number = 0; i < n - 1; i++) {4    let swapped: boolean = false;5    for (let j: number = 0; j < n - i - 1; j++) {
    values this stepfalseswapped

  17. arr[j] > arr[j+1] ← false

    5for (let j: number = 0; j < n - i - 1; j++) {6    if (arr[j] > arr[j + 1]) {7        const tmp: number = 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

    5for (let j: number = 0; j < n - i - 1; j++) {6    if (arr[j] > arr[j + 1]) {7        const tmp: number = arr[j];
    values this stepfalsearr[j] > arr[j+1][1, 2, 4, 5, 8]arr1j2arr[j]4arr[j+1]

  19. loop ← break

    12}13if (!swapped) {14    break;
    values this stepbreakloopfalseswapped

  20. stdout ← [1, 2, 4, 5, 8]

    16}17console.log(JSON.stringify(arr));
    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

  • TypeScript: nested for loops with the early-exit swapped: boolean flag. Never call arr.sort(); the lesson is teaching the comparison-and-swap.
  • Annotate the boolean explicitly so the early-exit invariant is clear.
  • 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.