Can someone please shed some light on how popular languages like Python, Ruby implements hash tables internally for symbol lookup? Do they use the classic "array with linked-list" method, or use a balanced tree?
I need a simple (fewer LOC) and fast method for indexing the symbols in a DSL written in C. Was wondering what others have found most efficient and practical.
The classic "array of hash buckets" you mention is used in every implementation I've seen.
One of the most educative versions is the hash implementation in the Tcl language, in file tcl/generic/tclHash.c. More than half of the lines in the file are comments explaining everything in detail: allocation, search, different hash table types, strategies, etc. Sidenote: the code implementating the Tcl language is really readable.
Perl uses an array with linked lists to hold collisions. It has a simple heuristic to automatically double the size of the array as necessary. There's also code to share keys between hashes to save a little memory. You can read about it in the dated but still relevant Perl Illustrated Guts under "HV". If you're truly adventurous you can dig into hv.c.
The hashing algorithm used to be pretty simple but its probably a lot more complicated now with Unicode. Because the algorithm was predictable there was a DoS attack whereby the attacker generated data which would cause hash collisions. For example, a huge list of keys sent to a web site as POST data. The Perl program would likely split it and dump it into a hash which then shoved it all into one bucket. The resulting hash was O(n) rather than O(1). Throw a whole lot of POST requests at a server and you might clog the CPU. As a result Perl now perturbs the hash function with a bit of random data.
You also might want to look at how Parrot implements basic hashes which is significantly less terrifying than the Perl 5 implementation.
As for "most efficient and practical", use someone else's hash library. For god's sake don't write one yourself for production use. There's a hojillion robust and efficient ones out there already.
Lua tables use an utterly ingenious implemenation which for arbitrary keys behaves like 'array of buckets', but if you use consecutive integers as keys, it has the same representation and space overhead as an array. In the implementation each table has a hash part and an array part.
I think this is way cool :-)
Balanced trees sort of defeat the purpose of hash tables since a hash table can provide lookup in (amortized) constant time, whereas the average lookup on a balanced tree is O(log(n)).
Separate chaining (array with linked list) really works quite well if you have enough buckets, and your linked list implementation uses a pooling allocator rather than malloc()ing each node from the heap individually. I've found it to be just about as performant as any other technique when properly tuned, and it is very easy and quick to write. Try starting with 1/8 as many buckets as source data.
You can also use open addressing with quadratic or polynomial probing, as Python does.
Attractive Chaos have a comparison of Hash Table Libraries and a update. The source code is available and it is in C and C++
If you can read Java, you might want to check out the source code for its various map implementations, in particular HashMap, TreeMap and ConcurrentSkipListMap. The latter two keep the keys ordered.
Java's HashMap uses the standard technique you mention of chaining at each bucket position. It uses fairly weak 32-bit hash codes and stores the keys in the table. The Numerical Recipes authors also give an example (in C) of a hash table essentially structured like Java's but in which (a) you allocate the nodes of the bucket lists from an array, and (b) you use a stronger 64-bit hash code and dispense with storing keys in the table.
What Crashworks mean to say was....
The purpose of Hash tables are constant time lookup, addition and deletion. In terms of Algorithm, the operation for all operation is O(1) amortized. Whereas in case you use tree ...the worst case operation time will be O(log n) for a balanced tree. N is the number of nodes. but, do we really have hash implemented as Tree?
