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].

Basic Implementation

basic.ts 
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));

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.
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.