Question

Section 4.1.3 states “the space required by the array-based list implementation is Ω(n), but can be greater.” Explain why this is so.

Answer 1

I see that you too this statement from https://opendsa-server.cs.vt.edu/ODSA/Books/CS3/html/ListAnalysis.html

as it says "Array-based lists have the disadvantage that their size must be predetermined before the array can be allocated. Array-based lists cannot grow beyond their predetermined size. Whenever the list contains only a few elements, a substantial amount of space might be tied up in a largely empty array. This empty space is the overhead required by the array-based list. Linked lists have the advantage that they only need space for the objects actually on the list. There is no limit to the number of elements on a linked list, as long as there is free store memory available. The amount of space required by a linked list is Θ(n)Θ(n), while the space required by the array-based list implementation is Ω(n)Ω(n), but can be greater."

Example you need to create a list, now you have 2 choices 1. Array 2. LinkedList

The very basic difference between these two is that Array is contagious in memory ie. all element will be stored on subsequent memory locations and hence you need to make this memory allocation well before in future in advance. No new memory allocation is done while storing a new element.

Linked list is non-contagious, means memory is allocated on the fly and a pointer from last element ( called node ) to newly created node is made to keep the track of all elements.

So example you want to store 10 element in list.

taking Array you have to have 10 element space reserved in advance, so made that but now you just have 3 element to store. So space for 7 elements is just lying there unused, in this case space complexity is higher than required.

But if this would have been Linked list, space for only 3 elements would have been used, and further space be allocated dynamically.

Hope this made you understand!!