sandbox/ods/notes/chapter2.txt

# Chapter 2 (Array-based lists)

These data structures have common advantages and limitations:

* constant-time access

* resizing the array adds potentially non-trivial complexity, both in time and
  storage, as a new array generally must be created and the old array copied
  over.

* arrays aren't dynamic, which means inserting or deleting in the middle of an
  array requires shifting all the following elements.

With some careful management, the additional *amortised* complexity added by
resizing isn't too bad.

## Array stack

* Uses backing array *a*.
* Typically, the array will be larger than necessary, so an element *n* is
  used to track the actual number of elements stored in the stack.
* Add and remove requires shifting all the elements after i (O(n - i)
  complexity), ignoring potential calls to resize
* Resizing is triggered when we run out of room in an add or when a remove
  brings us to the point where the array is more than 3n elements
* Resizing creates a new array of size 2n and copies all the elements over;
  this then has complexity O(n).
* The analysis of add and remove didn't consider cost of resize.
* An amortised analysis is done instead that considers the cost of all calls
  to add and remove, given a sequence of *m* calls to either.
* Lemma: if an empty ArrayStack is created and any sequence of *m* >= 1 calls
  to add and remove are performed, the total time spent in calls to resize is 
  O(m).