1. Complexity of a Bubble Sort
How many comparisons are made on each pass?
n-1 …
n-2
n-3 2 1
How many comparisons are made altogether?
= [(n-1) + 1](n-1) / 2 Sum of an arithmetic series
= [n2 - n] / 2
= n2 /2 - n/2
= O(n2 )
[n2 /2 is the dominant term and the coefficient 1/2 may be ignored - it is just some constant]

2. Suppose n = 10, n2 /2 = 50,000,000
n/2 = ,000
Suppose n = 1,000, n2 /2 = 500,000,000,000
n/2 = ,000
If n = 1,000,000,000 n2 /2 = 500,000,000,000,000,000
n/2 = ,000,000