Feb 5

Questions and/or discussion of homework?

data structures

This week: material from chapter 3 in the text.

Be aware that the discussion in this section is full of C jargon. We will use python to talk about the same ideas, but in practice this issues are more about the way computers actually work at a low level (i.e. C) than the abstraction that languages like python supply.

I'll use Skienna's pdf slides to walk through the material from his book, discussing as we go. The week we'll be on lecture4.pdf and lecture5.pdf from http://www.cs.sunysb.edu/~algorith/video-lectures/

First though, two asides.

O() equality

O() notion of "equality" is confusing:

 f(x) = O(g(x))  means   f(x) <= M g(x) for some constant M
 (See e.g. http://en.wikipedia.org/wiki/Big_O_notation )

So really "=" means "<=".

 n = O(n**2)   YES   (less-than)
 n**2 = O(n)   NO    (greater-than)

When in doubt, put some big numbers in.

True or false? (These are all from Skienna lecture4.pdf .)

\[ 2n^2 + 1 = O(n^2) \] \[ \sqrt{n} = O(\log n) \] \[ log n = O(\sqrt{n}) \] \[ n^2 (1 + \sqrt{n}) = O(n^2 \log n) \] \[ 3 n^2 + \sqrt{n} = O(n^2) \] \[ \sqrt{n} \log n = O(n) \] \( \log n = O(n^{-1/2}) \)

(Oh, and if you want to enter formulas in your wiki homework, the square brackets center on a line; parens do inline formulas like \( \sqrt{ \frac{1}{2} } \) ).

pointers and linked lists

The data structures chapter talks about "pointers". What is a pointer look like?

Essentially it's the address of something.

In the C programming language that concept is explicit: all program data is tied to explicitly numbered bytes in memory.

Python uses pointers too, but it doesn't call them that ... and usually we don't think that way.

But consider this

 > a = 5
 > b = a
 > a = 4
 > b              # What is b now?

compared to this

 > a = [2, 3, 4]
 > b = a
 > a[0] = 100
 > b              # What is b now?

So in Python, variables can be "pointers" to lists, dictionaries, and other "object-like" things with internal parts. Python's id() function gives a unique identifier to the data itself, which may have several variables (e.g. (a,b)) that "point" to it.

Skienna gives the following example in C of a linked list structure

 typedef struct node {
   data_type data;
   struct node *next;
 } node;

(I like the words "node" and "data" here rather than "list" and "item", but the idea is the same.)

The details of what this syntax means aren't important.

But the idea is : we can build a list (or trees or graphs) out of elements that contain (1) data, and (2) a reference (i.e. a pointer) or references to other pieces of data.

One way to do a similar thing in python looks like this, along with a "follow along the list and print" function

class Node(object):

  def __init__(self, data=None, next=None):
    self.data = data
    self.next = next

  def print_list(self):
    """Print the list from this node onwards"""
    print "[",
    node = self
    while node != None:
      print str(node.data) + " ",
      node = node.next
    print "]"

a = Node(data = 'Lincoln')
b = Node(data = 'Jefferson')
c = Node(data = 'Clinton')

a.next = b
b.next = c
a.print_list()

Structures like this have a number of interesting properties for implementing algorithms, which are discussed in this chapter.

slides

in class

... we wrote the attached example of a singly linked list in python used to implement a stack.

http://cs.marlboro.edu/ courses/ spring2013/algorithms/ notes/ Feb_5
last modified Tuesday February 5 2013 11:19 am EST

attachments

name last modified size

Algorithms

course

navigation