Question

Explain why building a list in sorted order is an O(n2) operation. You don’t have to derive it with mathematical formality, but at least explain why, mathematically, it’s O(n2).

Answer 1

for building a list of n items in sorted order.

procedure:
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Adding 1st item in sorted order takes 1 operation.
Adding 2nd item in sorted order takes 2 operations(to add before the first item or after the first item)
...
Adding i+1th item in sorted order after (already sorted i items), it takes i operations.
...

so, total number of operations = 1+2+3+...+n = n(n+1)/2 = (n^2+n)/2
we can ignore constant terms and lower order terms.
so, time complexity is O(n^2)