1. CSC 213 – Large Scale Programming Lecture 38: BTrees

2. Today’s Goal Look at using advanced Tree structures Examine BTree implementation of ( a, b )-Tree Discuss how to size a BTree Examine how to implement these structures How we can write classes so trees work well Better ways to manipulate these file systems

3. What is “the BTree?” BTree - common implementation of ( a, b ) tree Every BTree has an order Usually talk about “BTree of order m ” Internal nodes then have m / 2 to m children Root node has m or fewer entries Actually exist many variants of BTree Differences here are very minor Sticking to vanilla BTrees for this lecture

4. BTree Order Select order to minimize paging Full node, including entries and references to children, fills a page with no space left over Each node has at least m / 2 entries Each page used is at least 50% full How many pages touched during operation?

5. Removal from BTree Swap entry with successor on bottom level If node has fewer than m / 2 entries When possible, move entry from sibling to parent and steal one from parent Otherwise, merge node with sibling & steal entry from parent But this might propagate underflow to parent node!

6. Where to Find BTrees Databases very common place to find them Both contain far more data than machine’s RAM Perform lots of data accesses, insertions Need simple, efficient organization Databases also store data permanently Do not want to ever lose information RAM contents lost when powered off But files stored on hard drive (s — l — o —w)

7. Database Implementation Maintain BTree in memory… … but keep copy of records on disk Each Entry has unique ID & its location in file Entry changes written to disk immediately So file is always kept up-to-date In case of program crash, just re-read file Ignore virtual memory & instead use file Records in file stored in random order Order of Entrys may change as program runs

8. Better Ways To Access Data BTrees do not read & write file sequentially Instead they must jump around location in file Also need way to specify each of the Entrys that exist within file Java’s solution: RandomAccessFile

9. RandomAccessFile Create new files or work with existing ones RandomAccessFile raf = new RandomAccessFile(“file.txt”, “rw”); Creates (or rewrites) file.txt Throws IOException when problem arises Allows program to read & write to the file Use raf to access/modify the file

10. Reading RandomAccessFile Read from RandomAccessFile instance using: boolean readBoolean(), int readInt(), double readDouble()… Reads and returns the appropriate value int read(byte[] b) Re ads up to b.length bytes & stores back in b Returns number of bytes read

11. Writing to RandomAccessFile Write to RandomAccessFile instance using: void writeInt(int i), void writeDouble(double d)… Writes the value to the next location in the file Extends the file when at the end of the file Otherwise overwrites whatever data had been there void write(byte[] b) Write contents of array b to the file Overwrites/extends file as it is needed

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

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

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

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

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

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

18. Skipping Around The File Can position RandomAccessFile to read from/write to anywhere in file void seek(long pos) moves to position in file Positions specified as bytes from beginning of file

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

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

21. How do we use this? Use positions to simplify everything Entry contains position of record within file Simplify building nodes from start of program Record new nodes at end of file Store nodes’ size & number of Entrys at file start Node records ID & position of each of its children

22. For Next Lecture Review end of graphs, ( a, b )Tree, & BTree Come with any questions you still have Last of these problem days for the year…