EBoard 31: Binary search trees

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Approximate overview

• Administrivia
• About MP8
• Questions
• Binary search trees
• Lab

Administrivia

• FYI: There are only two MPs left; I don’t think we should have work due on Thanksgiving (week 12) or during week 14.
• You can use week 14 and finals week to catch up on MP redos and to LAs.
• Please return cards, boards, and markers to the back of the room when you finish class today.

Upcoming Token activities

Academic

• Tuesday, 2023-11-14, Noon, Day PDR: CS Table
• Wednesday, 2023-11-15, 4pm, HSSC Kernel: Madison Van Oort ’08 speaks Frictions in the Future of Work.
• Thursday, 2023-11-16, 4:15pm, HSSC Kernel: CS Poster Session.

Cultural

• Today, 2023-11-10, Jazz Concert
• Saturday, 2023-11-11, Drag.

Peer

• Saturday, 2023-11-11, Noon, Football vs. Cornell
• Sunday, 2023-11-12, 2-5pm, HSSC N3170 - Inquiry Learning Lab: Smash@Grinnell Friendlies.
• Sunday, 2023-11-12, 5:30-7:30, International Food Bazar
• Monday, 2023-11-13, 4-6pm, 3D Printing Workshop, Stew Makerspace Wellness
• Tuesday, 4-6pm, 3rd floor HSSC, somewhere: Wilson Catalyst

Misc

• Sunday, 2023-11-12, 2-3:30 pm, Sebring-Lewis: Grinnell Singers.
• Monday, 2023-11-13, 4-5:30pm, HSSC N1112: Politics of AI Info Session.

Other good things (no tokens)

Upcoming work

• MP7 post-assessment due Friday
• MP8 pre-assessment due Sunday
• MP8 due next Thursday.
• MP8 post-assessment due next Friday

Friday PSA

• You are awesome, please take care of yourself, people care about you (even if our registratoin process suggests otherwise).
• Consent is essential.

About MP8

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Questions

Registration

Trees

Administrative

Will we have two redo opportunities for each mini-project?

I hope so.

MP8

Binary Search Trees

What do you know about binary search trees?

• They are trees.
• In which each node has 0, 1, or 2 children (“binary”)
• You use them to search
• The connections are from parents to children, but not across siblings.
• In many implementations, we terminate with null values.
• How do we arrange a BST to make searching easier?
  • Bad strategy: No particular arrangement, requires searching both halves.
  • Good strategy: Put smaller elements on the left and larger elements on the right. (We normally don’t permit duplicates.)
• How do you search a BST?
  • Look at the current node. If the element in the node matches the sought value, you’re done
  • Otherwise, if the element in the node is larger than the sought value, search in the left subtree
  • Otherwise, we know the element in the node is smaller than the sought value, so search in the right subtree.
  • When you run off the tree, you know the element is not there.
• Running time to search a tree of $n$ nodes? (Big O.)
  • $O(logn)$, in an ideal (balanced) binary tree.
  • $O(n)$, if we arrange the tree badly
  • $O(depth)$
• BSTs encode binary search in the data structure, which should make it possible to have a structure we can extend while still searching efficiently.
• What makes trees efficient? A balanced/complete tree of $n values has height $logn$, so if we can build such a tree and only need to look at one value per level, we generally get $O(logn)$ algorithms.

Detours

• What are the key ideas in quicksort?
  • There’s a pivot (ideally, the median, but usually some random value)
  • We divide our values into those smaller than the pivot and larger than the pivot.
  • We recursively sort both halves.

Draw a BST for the following strings:

• koala, llama, gnu, hippo, aardvark, monkey, baboon, chinchilla, dingo

Lab

Line 24 of SimpleBST.java should read Comparator<? super K> comparator;