CSC151, Class 29: Designing a List Type

Overview:
* What is a list?
* Building the list data type in C.
* Implementing key operations.
* List cursors

Notes:
* Read chapter 9 of Gries for tomorrow.  (A nice long chapter.)
* How did Friday's class go?
* Are there remaining questions on the code?  
  I see that plans has a dialog on the readCity problem.
* What causes segmentation faults?
* Questions on exam 1?

Seg Faults: "You idiot, you're using an invalid memory address".
Why?
(1) Accessing part of an array that's not there.
(2) Uninitialized pointer.
(3) Pointing explicitly to invalid locations (usually due to
    a type error).
  int *ip = (int *) 5;
  int i;
  scanf("%d", i);
(4) Dereferencing null.

Questions on exam 1

  Exponentiation discussion
  Can we do it in better than O(log_2(n)) time?

  Idea: Change the base of the numbers?
    Suppose x is represented in base 2 (pretty easy assumption)

  What are some rules related to exponentiation?

   x^a * x^b = x^(a+b)

   Division algorithm
    Let n/2 be q remainder r
    x^n = x^q * x^r
      n/2 is a right shift
      x^r is either x or 1

  (x^n)^m = x^(n*m)

  x^a / x^b = x^(a-b)

  x^2k = (x^2)^k

  What can we do with x?  Can we express x in another way?

    x = e^ln(x)

    x^n = (e^ln(x))^n
   
    x^n = e^(n*ln(x))

If e^v is constant time and ln(w) is constant time, then
this strategy is constant time.

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What is a list?
* Scheme
  + Built-in data type
  + Operations: cons, cdr, car, null?, null
     (car (cons a b)) = a
     (cdr (cons a b)) = b
     (null? null) = true
     (null? (cons a b)) = false
     Everything else is undefined
  + Behind the scenes, cons creates a pair of pointers.
* Java
  + A standard class
  + A list is a collection
  + Collection operations; add, clear, remove, a lot ...
  + Operations: lots more
* How do lists differ from other collections?
  + "Ordered" - Does this mean "Sorted?" no.
    It does mean that "1,3,4,5,8" is different from "1,3,4,8,5"
  + No random access ...?  Whoops, they are in this 
    implementation (but not efficiently).
    constructor

What's a type?
* Something predefined; you can also define your own
* A collection of valid operations
* A way to interpret bits in memory
* A set of values

Our goal: Look at lists first in the Scheme way and then extend
  them to something closer to the Java list interface.
We are building a data structure called "Linked List"