How to analyse complexity of the given optimized bubble sort? -


this pseudo code of optimized bubble sort algorithm. have tried analyze time complexity, not sure cost of line 4 (if a[i-1] > a[i]). answer (n-1)+(n-2)+........+1 ? cost of lines 5 8?

1.for j = a.length 2 2.    swapped = false 3.    = 2 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 8 single iteration o(1).

the cost of loop @ lines 3-8 o(j-1).

the cost of whole sort in worst case o((n-1) + (n-2) + ... + 2) = o(n^2) (but of course in best case, when array sorted, cost o(n-1)).

by way, implementation of optimized bubble sort contains error: if @ line 9 should inside outer loop, outside inner.


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