1. CSC 213 Lecture 10: BTrees

2. Announcements You should not need to do more than the lab exercise states  If only says add a CharRange, you should not need to define a CharClass  Use your finite state machine drawings and description of classes

3. Red-Black Tree Follow-up Delete 3, 6, 5, 2, 8, 4, 1, 7 from this tree 4 2 1 6 57 8

4. Lies My Professor Told Me Big-Oh notation does not always correctly model algorithm performance For example, big-Oh Treats all memory accesses as equal:  Register: 1 cycle  Cache: 20 cycles  RAM: 240 cycles  Hard Drive: 200,000 cycles

5. Paging == Bad What happens when heap needs more memory than is in RAM?  Disk accesses dominate total running time  Execution can take 20 times or more longer

6. Paging == Bad

7. Virtual Memory Organization Virtual Memory works by dividing memory into pages  Size of a page is constant throughout system 4096 bytes used in a lot of systems  Operating system then handles each page separately When not being used, will evict pages to disk Must reload page whenever it is accessed

8. Problems with Trees Tree are important and common way to organize information  Provide consistent O(log n) access time, something we all like But nodes contain only 1 - 3 entries and 2 – 4 children  Get spread over entire heap in no real order  Great way to torture computer & make hard drive beg for mercy Good when using roommates machine, not so god for your own

9. BTrees to the Rescue! BTrees are the real-world solution to paging  Apple uses them to track directories and files in their file system  Organizational scheme used within MySQL database (e.g., the most popular database)  It also makes julienne fries

10. What is “the BTree?” BTrees are similar to (2,4) trees  All leaves are at same level  Nodes contain variable number of children and entries  But nodes are much, much bigger Usually discuss a BTree of order m  Internal nodes have m / 2 to m entries  Root node has m of fewer entries

11. BTree Order Select order to minimize paging  Sized so that a full node, including its entries, and references to the children fill a page  Since each node has at least m / 2 entries, each page is at least 50% full How many pages will we access searching for an element?

12. Insertion into a BTree Insertion begins as normal  Search through tree to find location to insert  Add entry into the node it belongs Check for overflow  If the node now has m+1 entries? Split into two nodes of size m / 2 and promote median (middle) entry into parent  Check if this causes the parent to overflow

13. Removal from a BTree Swap entry to be removed with its successor at the bottom level If node at bottom level now has fewer than m / 2 entries  If possible, move entry from sibling to parent and steal entry from parent  Otherwise, combine node with its sibling and steal entry from parent Check if this propagates underflow to parent

14. Choosing a Good m How do we choose a BTree’s order?  Want to minimize number of disk accesses  Want to maximize page usage  Select m so a full node fills a page Smallest node (using m / 2 entries) uses ½ a page What is the maximum number of pages used for any search, insert or remove?

15. Using BTrees One very common place to find BTrees is in databases  Often have too much data to fit in RAM  Needs simple, efficient organization But databases also need data to be stored permanently  Does not interact well with heap objects, since heap is stored in RAM

16. Database BTrees Maintain BTree in memory…  … but keep records on disk  Entries include ID and where in file to find the record  Immediately write changes back to the disk So we know that all updates will be saved  Also means we do not need to keep file in any specific order

17. RandomAccessFile For this scheme to work, we cannot read and write file sequentially  Instead, we must be able to jump around throughout entire file  Also need way to specifying locations in the file Java’s solution: the RandomAccessFile class

18. RandomAccessFile Instances can create new files or work with already existing files RandomAccessFile raf = new RandomAccessFile(“file.txt”, “rw”);  Creates file.txt if it does not already exist  Allows read and write access to the file  Throws an IOException if a problem arises  Can now use variable raf to access/modify the file

19. Reading RandomAccessFile Read from RandomAccessFile using normal file input methods:  boolean readBoolean(), int readInt(), double readDouble() … reads and returns the appropriate value  int read(byte[] b) re ad up to b.length bytes and store in b; return the number of bytes read

20. Writing to RandomAccessFile Write to RandomAccessFile using normal file output methods:  void writeInt(int i), void writeDouble(double d) … write the appropriate value to the file  void write(byte[] b) write the contents of the array b to the file

21. Typical File I/O Ordinarily we read and write files sequentially RandomAccessFile raf = new …; while (c != ‘s’) { c = raf.readChar(); } This is an example file we access raf:

22. Typical File I/O Ordinarily we read and write files sequentially RandomAccessFile raf = new …; while (c != ‘s’) { c = raf.readChar(); raf.writeChar(c); } This is an example file we access

23. Typical File I/O Ordinarily we read and write files sequentially RandomAccessFile raf = new …; while (c != ‘s’) { c = raf.readChar(); raf.writeChar(c); } TTis is an example file we access

24. Typical File I/O Ordinarily we read and write files sequentially RandomAccessFile raf = new …; while (c != ‘s’) { c = raf.readChar(); raf.writeChar(c); } TTii is an example file we access

25. Typical File I/O Ordinarily we read and write files sequentially RandomAccessFile raf = new …; while (c != ‘s’) { c = raf.readChar(); raf.writeChar(c); } TTii s an example file we access

26. Typical File I/O Ordinarily we read and write files sequentially RandomAccessFile raf = new …; while (c != ‘s’) { c = raf.readChar(); raf.writeChar(c); } TTii ssan example file we access

27. RandomAccessFile RandomAccessFile includes ability to position where we next read from/write to anywhere in file  void seek(long pos) moves anywhere in file  Positions are specified by the number of bytes from beginning of file

28. RandomAccessFile I/O Ordinarily we read and write files sequentially RandomAccessFile raf = new …; raf.seek(raf.length()-1); c = raf.readChar(); raf.seek(0); raf.writeChar(c); This is an example file we access

29. RandomAccessFile I/O Ordinarily we read and write files sequentially RandomAccessFile raf = new …; raf.seek(raf.length()-1); c = raf.readChar(); raf.seek(0); raf.writeChar(c); shis is an example file we access

30. So, how do we use this? We use these file positions to simplify our BTrees and entries  Each Entry contains the ID number and position of record within the file We can even use this to simplify building our BTree whenever we start the program  Record contents of BTree at end of file  Store num. elements in BTree at start of file  Can then find and read BTree at startup

31. Daily Quiz Write the Entry class that we would use with a disk-based BTree