I'm trying to decide which datastructure to use to store key-value pairs when only features needed are
insertion
lookup
Specifically, I don't need to be able to delete pairs, or iterate through keys/values/pairs.
The keys are integer tuples, the values are pointers (references, whatever). I'm only storing a couple million pairs spread out over (many) objects.
Currently I'm considering using either
a hash table
a kd-tree
a b-tree
I'm leaning toward the hash table (for the O(1) insertion/lookup time), but I wanted to confirm my leanings.
Which structure (of those above or other) would you recommend and why? If you would recommend a hash table, should I create a separate table for each object, or just create a single table and use the object's id as part of the key tuple?
A hashtable will be the best choice here as all the operations that matter to you are O(1) (and as such you shouldn't need to worry about creating multiple hashtables).
I'm a big fan of hash tables, since they are easy and there are implementations available for pretty much every major language out there. The O(1) insertion/lookup is an especially good feature.
You should probably use a single table, to save on memory. Hash tables are notoriously inefficient memory-wise, and using a single table would help to minimize that.
Hash tables would be usefull here and I see no reason to have more than one table.
Most trees have an O(n ln n) lookup time, but hashtables have an O(1) lookup time, so that's the one you want to use. It's also very common, and often the implementation is highly-optimised to boot.
Related
I looked at some existing implementations of adjacency lists online, and most if not all of them have been implemented using dynamic arrays. But wouldn't hashtable based data structures be more suitable? (set and map)
There are very limited scenarios where we would access graph nodes by index. Even if that's the case, if some indices are missing from the graph, there will be wasted space. And if the nodes are not inserted in order, lookups are O(n).
However, if we use a hashtable based data structure, lookups will be O(1) whether the nodes are indexed or otherwise.
So why are maps and sets not the default data structures used when implementing adjacency lists?
The choice of the right container is not quite easy.
I will consider some of the most common:
a list (elements which contain a reference to the next and/or previous)
an array (with consecutive storage)
an associated array
a hash table.
Each of them has advantages and disadvantages.
Concerning a list, insertions and removals can be very fast (worst case O(1) if the insertion point / removal element is known) but a look-up has worst case time complexity of O(N).
The look-up in an array has a complexity of O(1) in worst case if the index is known (but insertion and removal can be slow if the order must be kept).
A hash table has a look-up of O(1) in best case but the worst case might be O(N) (even if it's unlikely to happen often if the hash table isn't completely bad implemented).
An associated array has a time complexity of O(lg N) in worst case.
So the choice always depends on the expected use cases to find the best compromise where the advantages pay off most while the disadvantages doesn't hurt too much.
For the management of node and edge lists in graphs, OP made the observation that arrays seem to be very common.
I recently had a look into the Boost Graph Library (for curiosity and inspiration). Concerning the data structures, it is mentioned:
The adjacency_list class is the general purpose “swiss army knife” of graph classes. It is highly parameterized so that it can be optimized for different situations: the graph is directed or undirected, allow or disallow parallel edges, efficient access to just the out-edges or also to the in-edges, fast vertex insertion and removal at the cost of extra space overhead, etc.
For the configuration (according to a specific use case), there is spent an extra page BGL – adjacency_list.
However, the defaults for vertex (node) list and edge list are in fact vectors (aka. dynamic arrays). Assuming that the average use case is an non-mutable graph (loaded once and never modified) which is explored by algorithms to answer certain user questions, the worst case of O(1) for look-up in arrays is hard to beat and will very probably pay off.
To organize this, the nodes and edges have to be enumerated. If the input data doesn't provide this, it's easy to add this as a kind of internal ID to the in-memory representation of the graph.
In this case, "public" node references have to be mapped into the internal IDs, and answers have to be mapped back. For the mapping of the public node references, the most appropriate container should be used. This might be in fact an associated array or hash table.
Considering that a request like e.g. find the shortest route from A to B has to map A and B once to the corresponding internal IDs but may need many look-up of nodes and edges to compute the answer, the choice of the array for storage of nodes and edges makes very sense.
There are very limited scenarios where we would access graph nodes by index.
This is true, and exactly what you should be thinking about: you want a data structure which can efficiently do whatever operations you actually want to use it for. So the question is, what operations do you want to be efficient?
Suppose you are implementing some kind of standard algorithm which uses an adjacency list, e.g. Dijkstra's algorithm, A* search, depth-first search, breadth-first search, topological sorting, or so on. For almost every algorithm like this, you will find that the only operation you need to use the adjacency list for is: for a given node, iterate over its neighbours.
That operation is more efficient for a dynamic array than for a hashtable, because a hashtable has to be sufficiently sparse to prevent too many collisions. Besides that, dynamic arrays will use less memory than hashtables, for the same reason; and the dynamic arrays are more efficient to build in the first place, because you don't have to compute any hashes.
Now, if you have a different algorithm where you need to be able to test for the existence of an edge in O(1) time, then an adjacency list implemented using hashtables may be a good choice; but you should also consider whether an adjacency matrix is more suitable.
I need to store an array of integers of length about 1000 against an integer ID and string name. The number of such tuples is almost 160000.
I will pick one array and calculate the root mean square deviation (RMSD) elementwise with all others and store an (ID1,ID2,RMSD) tuple in another table.
Could you please suggest the best way to do this? I am currently using MySQL for other datatables in the same project but if necessary I will switch.
One possibility would be to store the arrays in a BINARY or a BLOB type column. Given that the base type of your arrays is an integer, you could step through four bytes at a time to extract values at each index.
If I understand the context correctly, the arrays must all be of the same fixed length, so a BINARY type column would be the most efficient, if it offers sufficient space to hold your arrays. You don't have to worry about database normalisation here, because your array is an atomic unit in this context (again, assuming I'm understanding the problem correctly).
If you did have a requirement to access only part of each array, then this may not be the most practical way to store the data.
The secondary consideration is whether to compute the RMSD value in the database itself, or in some external language on the server. As you've mentioned in your comments, this will be most efficient to do in the database. It sounds like queries are going to be fairly expensive anyway, though, and the execution time may not be a primary concern: simplicity of coding in another language may be more desirable. Also depending on the cost of computing the RMSD value relative to the cost of round-tripping a query to the database, it may not even make that much of a difference?
Alternatively, as you've alluded to in your question, using Postgres could be worth considering, because of its more expressive PL/pgSQL language.
Incidentally, if you want to search around for more information on good approaches, searching for database and time series would probably be fruitful. Your data is not necessarily time series data, but many of the same considerations would apply.
Good day everyone, I'm currently doing research on search algorithm optimization.
As of now, I'm researching on the Database.
In a database w/ SQL Support.
I can write the query for a specific table.
Select Number from Table1 where Name = "Test";
Select * from Table1 where Name = "Test";
1 searches the number from Table1 from where the Name is Test and 2 searches all the column for name Test.
I understand the concept of the function however what I'm interested in learning what is the approach of the search?
Is it just plain linear search where from the first index until the nth index it will grab so long as the condition is true thus having O(n) speed or does it have a unique algorithm that speeds its process?
If there's no indexes, then yes, a linear search is performed.
But, databases typically use a B Tree index when you specify a column(s) as a key. These are special data structure formats that are specifically tuned(high B Tree branching factors) to perform well on magnetic disk hardware, where the most significant time consuming factor is the seek operation(the magnetic head has to move to a diff part of the file).
You can think of the index as a sorted/structured copy of the values in a column. It can be determined quickly if the value being searched for is in the index. If it finds it, then it will also find a pointer that points back to the correct location of the corresponding row in the main data file(so it can go and read the other columns in the row). Sometimes a multi-column index contains all the data requested by the query, and then it doesn't need to skip back to the main file, it can just read what it found and then its done.
There's other types of indexes, but I think you get the idea - duplicate data and arrange it in a way that's fast to search.
On a large database, indexes make the difference between waiting a fraction of a second, vs possibly days for a complex query to complete.
btw- B tree's aren't a simple and easy to understand data structure, and the traversal algorithm is also complex. In addition, the traversal is even uglier than most of the code you will find, because in a database they are constantly loading/unloading chunks of data from disk and managing it in memory, and this significantly uglifies the code. But, if you're familiar with binary search trees, then I think you understand the concept well enough.
Well, it depends on how the data is stored and what are you trying to do.
As already indicated, a common structure for maintaining entries is a B+ tree. The tree is well optimized for disk since the actual data is stored only in leaves - and the keys are stored in the internal nodes. It usually allows a very small number of disk accesses since the top k levels of the tree can be stored in RAM, and only the few bottom levels will be stored on disk and require a disk read for each.
Other alternative is a hash table. You maintain in memory (RAM) an array of "pointers" - these pointers indicate a disk address, which contains a bucket that includes all entries with the corresponding hash value. Using this method, you only need O(1) disk accesses (which is usually the bottleneck when dealing with data bases), so it should be relatively fast.
However, a hash table does not allow efficient range queries (which can be efficiently done in a B+ tree).
The disadvantage of all of the above is that it requires a single key - i.e. if the hash table or B+ tree is built according to the field "id" of the relation, and then you search according to "key" - it becomes useless.
If you want to guarantee fast search for all fields of the relation - you are going to need several structures, each according to a different key - which is not very memory efficient.
Now, there are many optimizations to be considered according to the specific usage. If for example, number of searches is expected to be very small (say smaller loglogN of total ops), maintaining a B+ tree is overall less efficient then just storing the elements as a list and on the rare occasion of a search - just do a linear search.
Very gOod question, but it can have many answers depending on the structure of your table and how is normalized...
Usually to perform a seacrh in a SELECT query the DBMS sorts the table (it uses mergesort because this algorithm is good for I/O in disc, not quicksort) then depending on indexes (if the table has) it just match the numbers, but if the structure is more complex the DBMS can perform a search in a tree, but this is too deep, let me research again in my notes I took.
I recommend activating the query execution plan, here is an example in how to do so in Sql Server 2008. And then execute your SELECT statement with the WHERE clause and you will be able to begin understanding what is going on inside the DBMS.
I have an array of php objects that I want to store into a mysql database table. The only way I can think of is just have a table to represent the object with a unique id and a separate table to store the array (there could be a column array_id and an object_id) but retrieving would require a join I believe which could get expensive. Is there a better way? I don't care much about storage space or insertion time as much as retrieval time.
I don't necessarily need this to work for associative arrays but if the solution could, that would be preferred.
Building a tree structure (read as Array) in mysql can be tricky but it is done all of the time. Almost any forum with nested threads has some mechanism to store a tree structure. As another poster said they do not have to be expensive.
The real question is how you want to use the data. If you need to be able to add/remove data fields from individual nodes in the tree then you can use one of two models
1) Adjacency List Model
2) Modified Preorder Tree Traversal Algorithm
(They sound scary, but it's not that bad I promise.)
The first one listed is probably the more common you will encounter and the second is the one I have begun to use more frequently and has some nice benefits once you wrap your head around it. Take a look at this page--it has an EXCELLENT writeup about both.
http://articles.sitepoint.com/article/hierarchical-data-database
As another poster said though, if you don't need to change the data with queries or search inside the text then use a PHP function to store it in a single field.
$array = array('something'=>'fun', 'nothing'=>'to do')
$storage_array = serialize($array);
//INSERT INTO DB
//DRAW OUT OF DB
$array = unserialize($row['stored_array']);
Presto-changeo, that one is easy.
If you are comfortable with not being able to SQL search through the data within the array, you could add a single column to the table, and serialize the array into it. You would have to deserialize it on retreival.
You could use JSON / PHP serializeation or whatever is more appropriate for the language you're developing in.
Joins don't have to be so expensive - you can define an index.
I have recently run across these terms few times but I am quite confused how they work and when they are usualy implemented?
Well, think of it this way.
If you use an array, a simple index-based data structure, and fill it up with random stuff, finding a particular entry gets to be a more and more expensive operation as you fill it with data, since you basically have to start searching from one end toward the other, until you find the one you want.
If you want to get faster access to data, you typicall resort to sorting the array and using a binary search. This, however, while increasing the speed of looking up an existing value, makes inserting new values slow, as you need to move existing elements around when you need to insert an element in the middle.
A hashtable, on the other hand, has an associated function that takes an entry, and reduces it to a number, a hash-key. This number is then used as an index into the array, and this is where you store the entry.
A hashtable revolves around an array, which initially starts out empty. Empty does not mean zero length, the array starts out with a size, but all the elements in the array contains nothing.
Each element has two properties, data, and a key that identifies the data. For instance, a list of zip-codes of the US would be a zip-code -> name type of association. The function reduces the key, but does not consider the data.
So when you insert something into the hashtable, the function reduces the key to a number, which is used as an index into this (empty) array, and this is where you store the data, both the key, and the associated data.
Then, later, you want to find a particular entry that you know the key for, so you run the key through the same function, get its hash-key, and goes to that particular place in the hashtable and retrieves the data there.
The theory goes that the function that reduces your key to a hash-key, that number, is computationally much cheaper than the linear search.
A typical hashtable does not have an infinite number of elements available for storage, so the number is typically reduced further down to an index which fits into the size of the array. One way to do this is to simply take the modulus of the index compared to the size of the array. For an array with a size of 10, index 0-9 will map directly to an index, and index 10-19 will map down to 0-9 again, and so on.
Some keys will be reduced to the same index as an existing entry in the hashtable. At this point the actual keys are compared directly, with all the rules associated with comparing the data types of the key (ie. normal string comparison for instance). If there is a complete match, you either disregard the new data (it already exists) or you overwrite (you replace the old data for that key), or you add it (multi-valued hashtable). If there is no match, which means that though the hash keys was identical, the actual keys were not, you typically find a new location to store that key+data in.
Collision resolution has many implementations, and the simplest one is to just go to the next empty element in the array. This simple solution has other problems though, so finding the right resolution algorithm is also a good excercise for hashtables.
Hashtables can also grow, if they fill up completely (or close to), and this is usually done by creating a new array of the new size, and calculating all the indexes once more, and placing the items into the new array in their new locations.
The function that reduces the key to a number does not produce a linear value, ie. "AAA" becomes 1, then "AAB" becomes 2, so the hashtable is not sorted by any typical value.
There is a good wikipedia article available on the subject as well, here.
lassevk's answer is very good, but might contain a little too much detail. Here is the executive summary. I am intentionally omitting certain relevant information which you can safely ignore 99% of the time.
There is no important difference between hash tables and hash maps 99% of the time.
Hash tables are magic
Seriously. Its a magic data structure which all but guarantees three things. (There are exceptions. You can largely ignore them, although learning them someday might be useful for you.)
1) Everything in the hash table is part of a pair -- there is a key and a value. You put in and get out data by specifying the key you are operating on.
2) If you are doing anything by a single key on a hash table, it is blazingly fast. This implies that put(key,value), get(key), contains(key), and remove(key) are all really fast.
3) Generic hash tables fail at doing anything not listed in #2! (By "fail", we mean they are blazingly slow.)
When do we use hash tables?
We use hash tables when their magic fits our problem.
For example, caching frequently ends up using a hash table -- for example, let's say we have 45,000 students in a university and some process needs to hold on to records for all of them. If you routinely refer to student by ID number, then a ID => student cache makes excellent sense. The operation you are optimizing for this cache is fast lookup.
Hashes are also extraordinarily useful for storing relationships between data when you don't want to go whole hog and alter the objects themselves. For example, during course registration, it might be a good idea to be able to relate students to the classes they are taking. However, for whatever reason you might not want the Student object itself to know about that. Use a studentToClassRegistration hash and keep it around while you do whatever it is you need to do.
They also make a fairly good first choice for a data structure except when you need to do one of the following:
When Not To Use Hash Tables
Iterate over the elements. Hash tables typically do not do iteration very well. (Generic ones, that is. Particular implementations sometimes contain linked lists which are used to make iterating over them suck less. For example, in Java, LinkedHashMap lets you iterate over keys or values quickly.)
Sorting. If you can't iterate, sorting is a royal pain, too.
Going from value to key. Use two hash tables. Trust me, I just saved you a lot of pain.
if you are talking in terms of Java, both are collections which allow objects addition, deletion and updation and use Hasing algorithms internally.
The significant difference however, if we talk in reference to Java, is that hashtables are inherently synchronized and hence are thread safe while the hash maps are not thread safe collection.
Apart from the synchronization, the internal mechanism to store and retrieve objects is hashing in both the cases.
If you need to see how Hashing works, I would recommend a bit of googling on Data Structers and hashing techniques.
Hashtables/hashmaps associate a value (called 'key' for disambiguation purposes) with another value. You can think them as kind of a dictionary (word: definition) or a database record (key: data).