Give a formal proof that any sequence of n append or pop operations on an initially empty dynamic array takes O ( n ) time, if using the strategy described in Exercise C-5.16.   Consider a variant of...

Give a formal proof that any sequence of
n
append or pop operations on

an initially empty dynamic array takes
O(n) time, if using the strategy

described in Exercise C-5.16.

Consider a variant of Exercise C-5.16, in which an array of capacity
N
is

resized to capacity precisely that of the number of elements, any time the

number of elements in the array goes strictly below
N/4. Give a formal

proof that any sequence of
n
append or pop operations on an initially

empty dynamic array takes
O(n) time.