Question

Let's imagine we add support to our dynamic array for a new operation PopBack (which removes the last element). Calling PopBack on an empty dynamic array is an error.

PopBack reallocates the dynamically-allocated array to a new array of half the capacity if the size is \leq≤ the capacity / 4 . So, for example, if, before a PopBack the size were 5 and the capacity were 8, then after the PopBack, the size would be 4 and the capacity would be 8. Only after two more PopBack when the size went down to 2 would the capacity go down to 4.

We want to consider the worst-case sequence of any nn PushBack and PopBack operations, starting with an empty dynamic array.

What potential function would work best to show an amortized O(1)O(1) cost per operation?

Φ(h)=2


\Phi(h) = max(0, 2\times size - capacity)Φ(h)=max(0,2×size−capacity)


\Phi(h) = 2 \times size - capacityΦ(h)=2×size−capacity


\Phi(h) = max(2 \times size - capacity, capacity/2 - size)Φ(h)=max(2×size−capacity,capacity/2−size)

Answer 1

Answer:

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