CSC 301.01, Class 10: An introduction to trees

Overview

• Preliminaries
  • Notes and news
  • Upcoming work
  • Extra credit
  • Questions
• Hash tables: semi-formal analysis
• Other ways to represent dictionaries
• Trees

News / Etc.

• Note: I expect that you follow GNU style guidelines when you submit C code to me. If you don’t know those guidelines, you can find them on the Interweb.
• Note: You should be using gdb or lldb. I do not want to see code with lots of printfs.
  • Actually, I expect that you would ever use printf for tracing output. Use fprintf (stderr, ...)
• Cough drops

Upcoming work

• Read Skiena Chapter 3 for Monday.
• Assignment 4, due 10:30 p.m. Next Wednesday
  • Implement hash tables in Scheme.
  • Reflect on how to implement sets.

Extra credit (Academic)

• CS Table, Tuesday, Hacktivism
• CS Extras, Thursday, Study abroad

Extra credit (Peer)

• Elephantitus, this weekend. (Grinnell High School and Middle School)
  • High school: West on 8th
  • Middle school: South on East
• CS Picnic! 5pm today, Merrill park West. (11th and Main)
• AppDev intro thingy Sunday at 1pm 3919.

Extra Credit (Misc)

• Brazillian Jiu Jitsu Club, Saturday (2017-09-16) 5 PM to 6:30 PM in the Bear Multipurpose Dance Studio

Other good things

• Take care of yourselves and those around you.

Friday PSA

• Don’t feel pressure. The choices you make can/should be your own.
• Consent is absolutely, positively, necessary.
• Embrace self-gov!

Questions

Hash tables: semi-formal analysis

A hash table is a data structure that implements dictionaries.

• We store key/value pairs in an array.
• To store a key/value pair, we compute a “hash” of the key (a function from the key to a number). The key/value pair goes in that hash % array size.
• To look up a value by key, we compute a “hash” of the key and look in the corresponding index (see previous step)
• Complexity: The pigeonhole principle suggests that multiple things will hash to the same array location, so we need to deal with conflicts
  • Option 1 [“Bucketed”/”Chained”]: Store a linked list of key/value pairs in each array entry
  • Option 2 (probed): Look at nearby cells.

Practice hash: Add up the first three letters in your first name

• a is 0, b is 1, c is 2, d is 3, e is 4
• f is 5, g is 6, h is 7, i is 8, j is 9
• k is 10, l is 11, m is 12, n is 13, o is 14
• p is 15, q is 16, r is 17, s is 18, t is 19
• u is 20, v is 21, w is 22, x is 23, y is 24

Note: When the array gets more than 50% full (# of key/value pairs vs. capacity of array), we expand the array.

We have said informally that hash tables have expected Theta(1) behavior.

In this class, we are attempting more formal analyses. So, how could you predict how long it would take to add a key/value pair?

Hint: Consider what happens when we add an element to a 50% full probed hash table with a relatively good hash function.

• 1/2 look at 1 cell 1/2
• 1/4 look at 2 cells 1/2
• 1/8 look at 3 cells 3/8
• 1/16 look at 4 cells 4/16 = 1/4
• 1/32 look at 5 cells 5/32

We could do some extra analysis to see that the sum is bounded by a constant. I”m too lazy.

Other ways to represent dictionaries

What are other ways you might represent a dictionary? Try to come up with at least two that you’ve seen already (one from CSC 151, one from CSC 207) and one new one.

• In CSC 151, we learned about association lists, lists of key/value pairs.
  • O(n) add, O(n) to find
• In CSC 207, you learned about binary search trees
  • Binary tree with key/value pair at each node
  • Things to the left have smaller keys
  • Things to the right have larger keys
  • O(depth) to add or find
  • O(n) to add or find unless you are sure that the tree is balanced.
• In CSC 207, you learned about balanced binary trees (red/black trees)a
  • O(logn) to add or find
  • Complicated
  • We will cover them in 301
• In CSC 207, we learned about tries, O(keylength)
  • We will consider those in 301
• Vector key/value pairs (Associative Array)
  • add is probably O(n)
  • find is probably O(n)
• Sorted array
  • add is O(n)
  • find is O(logn)