Bubble Sort — Repeatedly Swap Adjacent Elements

How it works

Walk through the array comparing adjacent pairs. If left > right, swap them. Each pass pushes the next largest element to its final position. Repeat until no swaps are needed.

Optimization

// Early termination
if no swaps in a pass:
array is sorted, stop early
// Each pass shrinks unsorted region by 1

Interactive Visualization

Comparing

Swapping

Sorted

Array:

Array

Bar Chart

Step 0 of 0

Pass

Comparisons

Swaps

Sorted

Ready. Press Play or Next to start.

✓ Sorted

Speed

C++ — Bubble Sort

void bubbleSort(vector<int>& arr) {
    int n = arr.size();
    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]) {
                swap(arr[j], arr[j + 1]);
                swapped = true;
            }
        }
        if (!swapped) break; // optimized
    }
}

Complexity

Time (Worst/Avg)

O(N²)

Nested loops over array.

Time (Best)

O(N)

Already sorted, one pass with early exit.

Space

O(1)

In-place, only temp variable.

Stable?

Yes

Equal elements keep relative order.

📝 Notes

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