Question

Amortized Analysis

Suppose that instead of contracting a table by halving its size when its load factor drops below we contract it by multiplying its size by when its load factor drops below Using the potential function φ(T) = 2T. num-T. size! (where T. num is the number of elements in the table and T.size is the size of the table), show that the amortized cost of TABLE-DELETE that uses this strategy is bounded by above by a constant.

Answer 1

Notation» G actual cost of- ањ operation x, = amortized cost 아 İth opera tion num, -No.of Îems โ Tațter Îth oþeration sieSze et T ater th apeation φ(T) atter 9th Operation q, Consider -first the case ohen the laod factor dloes not

=3 Nlouw, consider the case tohen -the load factor cbops belouo5 , i e, Si2e, 3 size 7-I Size = 1-I num 1-1 There tore 2 nume Size,)- (-a num + size ) 3 (num)

1 8 +1+23 - ( num +1+ num. 5 -A morti 2e d cost is a most 2 o and thus bounded above a Cons tant