How many passes does a Bubble sort algorithm require for sorting a given list of 'n' items?

Concept:

Bubble sort:

It is the simplest sorting algorithm that works by repeatedly swapping the adjacent elements if they are in the wrong order.

Compare the neighbours, if greater, swap.

E.g. Let’s i / p is 70, 20, 35, 90, 15, 11, 24

No. of elements (n) = 7

Pass – 1: 20, 35, 70, 15, 11, 24, } 90 → 6 comparison

Pass – 2: 20, 35, 15, 11, 24, } 70, 90 → 5 comparison

Pass – 3: 20, 15, 11, 24, } 35, 70, 90 → 4 comparison

Pass – 4: 15, 11, 20, } 24, 35, 70, 90 → 3 comparison

Pass – 5: 11, 15, } 20, 24, 35, 70, 90 → 2 comparison

Pass – 6: 11, 15, 20, 24, 35, 70, 90 → 1 comparison

No. of passes = 6

Note: Bubble sort with n element required n - 1 passes.

Total comparisons: \(\frac{{\left( {n - 1} \right)n}}{2}\)