3.1. Input in Sorted Order

In that case, we know the algorithm always uses 0 iterations of the loop:

p_0=1, p_1 = 0, p_2 = 0, \ldots

So the time is

t_(text(loop)) = t_{text{init}} + \sum_{k=0}^{\infty} p_k ( (k+1)*t_{text{condition}} + k*t_{text{body}})

but plugging in the p's simplifies to

t_(text(loop)) = t_{text{init}} + t_{text{condition}} = O(1)

For this input pattern, the entire algorithm has an average-case complexity of O(1).

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