This is a pseudo code of optimized bubble sort algorithm. I have tried to analyze its time complexity, but i am not sure what is the cost of line 4 (if A[i-1] > A[i]). Is the answer (n-1)+(n-2)+........+1 ? Also what would be the cost of lines 5 to 8?
1.for j = A.length to 2
2. swapped = false
3. for i = 2 to j
4. if A[i-1] > A[i]
5. temp = A[i]
6. A[i-1] = A[i]
7. A[i-1] = temp
8. swapped = true
9. if(!swapped)
10. break
The cost of lines 5 to 8 for a single iteration is O(1).
The cost of loop at lines 3-8 is O(j-1).
The cost of the whole sort in the worst case is O((n-1) + (n-2) + ... + 2) = O(n^2) (but of course in the best case, when the array is already sorted, the cost will be only O(n-1)).
By the way, your implementation of optimized bubble sort contains an error: the if at line 9 should be inside the outer loop, but outside the inner.