Bubble Sort Explained

On each pass, Bubble Sort walks from the start of the array to the end, comparing each pair of neighbours. If the left element is bigger than the right, they swap. After the first pass the largest element is guaranteed to be at the end. After the second pass the two largest are in place, and so on, until the whole array is sorted.

for i from 0 to n-1:
  swapped = false
  for j from 0 to n-2-i:
    if a[j] > a[j+1]:
      swap(a[j], a[j+1])
      swapped = true
  if not swapped:
    break  // already sorted

The swapped flag is the key optimization: if a full pass makes no swaps, the array is sorted and we stop early.

Bubble Sort is O(n²) on average and worst case because of its nested loops. But with the early-exit flag it reaches O(n) on already-sorted data, making it adaptive. Space is O(1) and it is stable. Watch it run in the visualizer to see the largest values rise to the end pass by pass.

In production, almost never — Insertion Sort beats it for small arrays and built-in sorts beat both. But Bubble Sort's value is pedagogical: it makes comparison and swapping crystal clear, which is why it remains the 'Hello World' of sorting. See how it compares in our Bubble vs Insertion Sort guide.