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Added notes on practical use of different flavors of balanced search trees.

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John Washam 2016-07-11 11:09:29 -07:00
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@ -443,35 +443,77 @@ Then test it out on a computer to make sure it's not buggy from syntax.
- Know least one type of balanced binary tree (and know how it's implemented):
- [x] **AVL trees**
- In practice:
From what I can tell, these aren't used much in practice, but I could see where they would be:
The AVL tree is another structure supporting O(log n) search, insertion, and removal. It is more rigidly
balanced than red–black trees, leading to slower insertion and removal but faster retrieval. This makes it
attractive for data structures that may be built once and loaded without reconstruction, such as language
dictionaries (or program dictionaries, such as the opcodes of an assembler or interpreter).
- [x] MIT AVL Trees / AVL Sort: https://www.youtube.com/watch?v=FNeL18KsWPc&list=PLUl4u3cNGP61Oq3tWYp6V_F-5jb5L2iHb&index=6
- [x] https://www.coursera.org/learn/data-structures/lecture/Qq5E0/avl-trees
- [x] https://www.coursera.org/learn/data-structures/lecture/PKEBC/avl-tree-implementation
- [x] https://www.coursera.org/learn/data-structures/lecture/22BgE/split-and-merge
- [x] **Splay trees**
- In practice:
Splay trees are typically used in the implementation of caches, memory allocators, routers, garbage collectors,
data compression, ropes (replacement of string used for long text strings), in Windows NT (in the virtual memory,
networking, and file system code) etc.
- [x] CS 61B: Splay Trees: https://www.youtube.com/watch?v=Najzh1rYQTo&index=23&list=PL-XXv-cvA_iAlnI-BQr9hjqADPBtujFJd
- [x] MIT Lecture: Splay Trees:
- Gets very mathy, but watch the last 10 minutes for sure.
- https://www.youtube.com/watch?v=QnPl_Y6EqMo
- [x] **2-3-4 Trees**
- [x] CS 61B Lecture 26: Balanced Search Trees: https://www.youtube.com/watch?v=zqrqYXkth6Q&index=26&list=PL4BBB74C7D2A1049C
- [x] **2-3 search trees**
- In practice:
2-3 trees have faster inserts at the expense of slower searches (since height is more compared to AVL trees).
You would use 2-3 tree very rarely because its implementation involves different types of nodes. Instead, people use Red Black trees.
- [ ] 23-Tree Intuition and Definition: https://www.youtube.com/watch?v=C3SsdUqasD4&list=PLA5Lqm4uh9Bbq-E0ZnqTIa8LRaL77ica6&index=2
- [ ] Binary View of 23-Tree: https://www.youtube.com/watch?v=iYvBtGKsqSg&index=3&list=PLA5Lqm4uh9Bbq-E0ZnqTIa8LRaL77ica6
- [x] 2-3 Trees (student recitation): https://www.youtube.com/watch?v=TOb1tuEZ2X4&index=5&list=PLUl4u3cNGP6317WaSNfmCvGym2ucw3oGp
- [x] **2-3-4 Trees (aka 2-4 trees)**
- In practice:
For every 2-4 tree, there are corresponding red–black trees with data elements in the same order. The insertion and deletion
operations on 2-4 trees are also equivalent to color-flipping and rotations in red–black trees. This makes 2-4 trees an
important tool for understanding the logic behind red–black trees, and this is why many introductory algorithm texts introduce
2-4 trees just before red–black trees, even though **2-4 trees are not often used in practice**.
- [x] CS 61B Lecture 26: Balanced Search Trees: https://www.youtube.com/watch?v=zqrqYXkth6Q&index=26&list=PL4BBB74C7D2A1049C
- [ ] Bottom Up 234-Trees: https://www.youtube.com/watch?v=DQdMYevEyE4&index=4&list=PLA5Lqm4uh9Bbq-E0ZnqTIa8LRaL77ica6
- [ ] Top Down 234-Trees: https://www.youtube.com/watch?v=2679VQ26Fp4&list=PLA5Lqm4uh9Bbq-E0ZnqTIa8LRaL77ica6&index=5
- [ ] **Red/black trees**
- In practice:
Red–black trees offer worst-case guarantees for insertion time, deletion time, and search time.
Not only does this make them valuable in time-sensitive applications such as real-time applications,
but it makes them valuable building blocks in other data structures which provide worst-case guarantees;
for example, many data structures used in computational geometry can be based on red–black trees, and
the Completely Fair Scheduler used in current Linux kernels uses red–black trees. In the version 8 of Java,
the Collection HashMap has been modified such that instead of using a LinkedList to store identical elements with poor
hashcodes, a Red-Black tree is used.
- [ ] Aduni - Algorithms - Lecture 4
link jumps to starting point:
https://youtu.be/1W3x0f_RmUo?list=PLFDnELG9dpVxQCxuD-9BSy2E7BWY3t5Sm&t=3871
- [ ] Aduni - Algorithms - Lecture 5: https://www.youtube.com/watch?v=hm2GHwyKF1o&list=PLFDnELG9dpVxQCxuD-9BSy2E7BWY3t5Sm&index=5
- [ ] **B-Trees**
- fun fact: B could stand for Boeing, Balanced, or Bayer (co-inventor)
- fun fact: it's a mystery, but the B could stand for Boeing, Balanced, or Bayer (co-inventor)
- In Practice:
B-Trees are widely used in databases. Most modern filesystems use B-trees (or Variants
[https://en.wikipedia.org/wiki/B-tree]). In addition to its use in databases, the B-tree is also used in
filesystems to allow quick random access to an arbitrary block in a particular file. The basic problem is
turning the file block i address into a disk block(or perhaps to a cylinder-head-sector) address.
- [ ] Binary Search Tree Review: https://www.youtube.com/watch?v=x6At0nzX92o&index=1&list=PLA5Lqm4uh9Bbq-E0ZnqTIa8LRaL77ica6
- [ ] Introduction to B-Trees: https://www.youtube.com/watch?v=I22wEC1tTGo&list=PLA5Lqm4uh9Bbq-E0ZnqTIa8LRaL77ica6&index=6
- [ ] B-Tree Definition and Insertion: https://www.youtube.com/watch?v=s3bCdZGrgpA&index=7&list=PLA5Lqm4uh9Bbq-E0ZnqTIa8LRaL77ica6
- [ ] B-Tree Deletion: https://www.youtube.com/watch?v=svfnVhJOfMc&index=8&list=PLA5Lqm4uh9Bbq-E0ZnqTIa8LRaL77ica6
- [ ] **Skip lists**
- [ ] MIT: Randomization: Skip Lists: https://www.youtube.com/watch?v=2g9OSRKJuzM&index=10&list=PLUl4u3cNGP6317WaSNfmCvGym2ucw3oGp
- [ ] **Memory Model & Trees**
- [ ] MIT 6.851 - Memory Hierarchy Models: https://www.youtube.com/watch?v=V3omVLzI0WE&index=7&list=PLUl4u3cNGP61hsJNdULdudlRL493b-XZf
- [ ] **Treap**
- [ ] ?