How much time does it take one to build the trie - language-agnostic

There is a lot of information in the literature which says that the time to search a trie is O(N) where N is the length of the pattern.
However, building the tree will also take some time. To me, let's say there are X words with a total of Y characters.
So then O(Y) is the time (because we have to insert each character). Is this assessment correct (I am usually not correct)

So then O(Y) is the time (because we have to insert each character)
Sure, you have to process each input character, and either follow an existing branch or insert a new char.
It can't be faster then O(Y), since you have to look at each input char. There's neither sorting nor any other operation which could make it slower.

Wrong. Creating a trie and searching a trie are two different algorithms. One wouldn't build a trie, search it, then throw away the entire data structure.

Related

MySQL: Best way to do a backwords full text search?

I am trying to do basically a reverse full test search but have no clue of the best way to go about doing it.
Basically I have a table of key phrases laid out like this:
id - phrase
1 - "hello world"
2 - "goodbye world"
3 - "this is my world"
I then have a set string, such as "Welcome to the hello world group". I want to find the ID of all rows in my table that has an exact match for phrase. Meaning "o the" would not match because the word is "to the". Also "ello" would not match because the world is "hello".
Using Full Text Search, this can easily be achieved by doing a search of:
AGAINST ('"hello world"' IN BOOLEAN MODE);
Problem is, I don't believe I can use a full text search, since a full text search would find all rows that contains a single phrase. I want all phrases (from a known set of phrases) that match a single set.
I know how to do this using RegEx using the following, however this is way to slow. On a table with 400,000 key phrases it took over 40 seconds:
WHERE "the data I know I want to search goes here" REGEXP CONCAT('[[:<:]]', phrases, '[[:>:]]')
What I need is a more optimized way to do this. How would I possibly go about doing this as a full text search, even if i have to temporarily add it to a table without actually doing a LOOP individually checking each keyword.
I really appreciate the feedback as this is really causing my site to lag on adding new data.
If you are willing to consider a solution that reads the phrases out of the database and constructs a separate data structure used for optimized phrase detection, there are two main techniques that solve the problem. Which one is best for you depends on a number of factors, in particular:
How frequently the phrase list is updated
Whether and how you tokenise the text before running the phrase detection
How long the target strings are
Option 1: Hash-table of the phrases This means you simply insert each of the phrases as key into a hash table (aka dictionary or hash map in many programming languages). The phrase id becomes the value. Updates are fast and easy, but detecting the phrases in a given string can be hard: Firstly you need to tokenise the string and be sure that phrases only occur between token boundaries. Secondly, you need to make a lookup in the hash not only for every token, but also for every pair, triple, quadruple etc. of consecutive tokens. This still works well if the target strings are generally short. You can also maintain a copy of the hash table on disk, e.g. using the Berkeley DB. There are ready-to-use modules in the standard library of most programming languages for this.
Option 2: Search trie (or, slightly more advanced, a minimised search trie or a finite state machine). This can be implemented in very space-efficient ways but is generally larger than a hash table (although 400k entries will not be a problem at all). The big advantage during phrase detection is that you need not cut out tokens (or candidate phrases between token boundaries) before making look-ups. Instead you perform a longest-match look-up at each candidate start position in the text. Storing on disk is possible, although in most programming languages there won't be a standard-library module for this. Updates are quite easy in a trie, but can get difficult (and potentially time-consuming) in a minimised trie or FST.
Both options allow the data structure to be maintained on disk (or a copy of it to be stored on disk, while the actual look-ups happen memory). But you won't get transaction safety or fault-tolerance (which I understand you are not looking for).
You can use search engine. For example solr. You can set specific search filters against text. + search for words only. + It will be blindingly fast.
Or, second idea you can create your own table that stores all words and id of phrase. and search that table maching words only. It will be faster because you can add index on words better then phrases altogether.

implementing a blacklist of usernames

I have a block list of names/words, has about 500,000+ entries. The use of the data is to prevent people from entering these words as their username or name. The table structure is simple: word_id, word, create_date.
When the user clicks submit, I want the system to lookup whether the entered name is an exact match or a word% match.
Is this the only way to implement a block or is there a better way? I don't like the idea of doing lookups of this many rows on a submit as it slows down the submit process.
Consider a few points:
Keep your blacklist (business logic) checking in your application, and perform the comparison in your application. That's where it most belongs, and you'll likely have richer programming languages to implement that logic.
Load your half million records into your application, and store it in a cache of some kind. On each signup, perform your check against the cache. This will avoid hitting your table on each signup. It'll be all in-memory in your application, and will be much more performant.
Ensure myEnteredUserName doesn't have a blacklisted word at the beginning, end, and anywhere in between. Your question specifically had a begins-with check, but ensure that you don't miss out on 123_BadWord999.
Caching bring its own set of new challenges; consider reloading from the database everyday n minutes, or at a certain time or event. This will allow new blacklisted words to be loaded, and old ones to be thrown out.
You can't do where 'loginName' = word%. % can only be used in the literal string, not as part of the column data.
You would need to say where 'logi' = word or 'login' = word or ... where you compare substrings of the login name with the bad words. You'll need to test each substring whose length is between the shortest and longest bad word, inclusive.
Make sure you have an index on the word column of your table, and see what performance is like.
Other ways to do this would be:
Use Lucene, it's good at quickly searching text, espacially if you just need to know whether or not your substring exists. Of course Lucene might not fit technically in your environment -- it's a Java library.
Take a hash of each bad word, and record them in a bitset in memory -- this will be small and fast to look up, and you'll only need to go to the database to make sure that a positive isn't false.

Optimizing binary tree inserts to O(1) with hash map for write heavy trees

First of all I assume I've missed something major when thinking about this, but I still wanted to post about it to see if I really didn't miss anything, on with it...
I have a pretty write heavy binary tree (about 50/50 between writes and reads), and on the way home today I was thinking about ways to optimize this, especially make the writes faster - this is what I came up with.
Considering that the operation add(T, x) to add x to tree T first consists of find(T, x) to see if x already exists, and in that case it doesn't return the parent so we can add it instead of one of the parents empty leaves.
What if we add a hash table as an intermediate cache to the add operation, so when we call add(T, x) what really happens is that x is hashed and inserted into the hash map M. And that's it. The optimization takes place when we somewhere else asks to find(T, x), now when we search the tree we will come to a leaf node, since x isn't inserted the tree yet (it only exists in the hash map M), we hash x and compare it to the keys in M to see if it is supposed to be in the tree. If it's found in M then we add it to the tree and remove it from M.
This would eliminate the find(T, x) operation on add(T, x) and reduce it to add(M, x) which is O(1). And then (ab)-use the find(T, x) operation that is performed when we look up the node the first time to insert it.
Why not use a hashtable for everything and omit the binary tree entirely?
It all depends why you were using binary trees in the first place. If you chose binary trees to enhance sharing, you lose with the hashtable caches because hashtables are not shared.
The caches do not make comparing two maps any easier either.
EDIT:
If the operations that take advantage of the specificities of trees are rare (you mention taking advantage of the fact that RB trees are sorted) and if, on the other hand, you often look up a key that has recently been added, or replace the value of a key that has recently been added, a small-size cache implemented with another structure may make sense. You can also consider using a hashtable representation with the occasional conversion to a tree.
The additional complexity of this cache layer may mean that you do not gain any time in practice though, or not enough to repay the technical debt of having an ad-hoc data structure like this.
If your need is to have a structure that has O(1) inserts, and approximately O(n) amortized ordered iteration, I had the same problem:
Key-ordered dict in Python
The answer (keeping a hash and a partially sorted list, and using a partially-sorted-structure-friendly sort like TimSort) worked very well in practice in my case.

How to correct the user input (Kind of google "did you mean?")

I have the following requirement: -
I have many (say 1 million) values (names).
The user will type a search string.
I don't expect the user to spell the names correctly.
So, I want to make kind of Google "Did you mean". This will list all the possible values from my datastore. There is a similar but not same question here. This did not answer my question.
My question: -
1) I think it is not advisable to store those data in RDBMS. Because then I won't have filter on the SQL queries. And I have to do full table scan. So, in this situation how the data should be stored?
2) The second question is the same as this. But, just for the completeness of my question: how do I search through the large data set?
Suppose, there is a name Franky in the dataset.
If a user types as Phranky, how do I match the Franky? Do I have to loop through all the names?
I came across Levenshtein Distance, which will be a good technique to find the possible strings. But again, my question is do I have to operate on all 1 million values from my data store?
3) I know, Google does it by watching users behavior. But I want to do it without watching user behavior, i.e. by using, I don't know yet, say distance algorithms. Because the former method will require large volume of searches to start with!
4) As Kirk Broadhurst pointed out in an answer below, there are two possible scenarios: -
Users mistyping a word (an edit
distance algorithm)
Users not knowing a word and guessing
(a phonetic match algorithm)
I am interested in both of these. They are really two separate things; e.g. Sean and Shawn sound the same but have an edit distance of 3 - too high to be considered a typo.
The Soundex algorithm may help you out with this.
http://en.wikipedia.org/wiki/Soundex
You could pre-generate the soundex values for each name and store it in the database, then index that to avoid having to scan the table.
the Bitap Algorithm is designed to find an approximate match in a body of text. Maybe you could use that to calculate probable matches. (it's based on the Levenshtein Distance)
(Update: after having read Ben S answer (use an existing solution, possibly aspell) is the way to go)
As others said, Google does auto correction by watching users correct themselves. If I search for "someting" (sic) and then immediately for "something" it is very likely that the first query was incorrect. A possible heuristic to detect this would be:
If a user has done two searches in a short time window, and
the first query did not yield any results (or the user did not click on anything)
the second query did yield useful results
the two queries are similar (have a small Levenshtein distance)
then the second query is a possible refinement of the first query which you can store and present to other users.
Note that you probably need a lot of queries to gather enough data for these suggestions to be useful.
I would consider using a pre-existing solution for this.
Aspell with a custom dictionary of the names might be well suited for this. Generating the dictionary file will pre-compute all the information required to quickly give suggestions.
This is an old problem, DWIM (Do What I Mean), famously implemented on the Xerox Alto by Warren Teitelman. If your problem is based on pronunciation, here is a survey paper that might help:
J. Zobel and P. Dart, "Phonetic String Matching: Lessons from Information Retieval," Proc. 19th Annual Inter. ACM SIGIR Conf. on Research and Development in Information Retrieval (SIGIR'96), Aug. 1996, pp. 166-172.
I'm told by my friends who work in information retrieval that Soundex as described by Knuth is now considered very outdated.
Just use Solr or a similar search server, and then you won't have to be an expert in the subject. With the list of spelling suggestions, run a search with each suggested result, and if there are more results than the current search query, add that as a "did you mean" result. (This prevents bogus spelling suggestions that don't actually return more relevant hits.) This way, you don't require a lot of data to be collected to make an initial "did you mean" offering, though Solr has mechanisms by which you can hand-tune the results of certain queries.
Generally, you wouldn't be using an RDBMS for this type of searching, instead depending on read-only, slightly stale databases intended for this purpose. (Solr adds a friendly programming interface and configuration to an underlying Lucene engine and database.) On the Web site for the company that I work for, a nightly service selects altered records from the RDBMS and pushes them as a documents into Solr. With very little effort, we have a system where the search box can search products, customer reviews, Web site pages, and blog entries very efficiently and offer spelling suggestions in the search results, as well as faceted browsing such as you see at NewEgg, Netflix, or Home Depot, with very little added strain on the server (particularly the RDBMS). (I believe both Zappo's [the new site] and Netflix use Solr internally, but don't quote me on that.)
In your scenario, you'd be populating the Solr index with the list of names, and select an appropriate matching algorithm in the configuration file.
Just as in one of the answers to the question you reference, Peter Norvig's great solution would work for this, complete with Python code. Google probably does query suggestion a number of ways, but the thing they have going for them is lots of data. Sure they can go model user behavior with huge query logs, but they can also just use text data to find the most likely correct spelling for a word by looking at which correction is more common. The word someting does not appear in a dictionary and even though it is a common misspelling, the correct spelling is far more common. When you find similar words you want the word that is both the closest to the misspelling and the most probable in the given context.
Norvig's solution is to take a corpus of several books from Project Gutenberg and count the words that occur. From those words he creates a dictionary where you can also estimate the probability of a word (COUNT(word) / COUNT(all words)). If you store this all as a straight hash, access is fast, but storage might become a problem, so you can also use things like suffix tries. The access time is still the same (if you implement it based on a hash), but storage requirements can be much less.
Next, he generates simple edits for the misspelt word (by deleting, adding, or substituting a letter) and then constrains the list of possibilities using the dictionary from the corpus. This is based on the idea of edit distance (such as Levenshtein distance), with the simple heuristic that most spelling errors take place with an edit distance of 2 or less. You can widen this as your needs and computational power dictate.
Once he has the possible words, he finds the most probable word from the corpus and that is your suggestion. There are many things you can add to improve the model. For example, you can also adjust the probability by considering the keyboard distance of the letters in the misspelling. Of course, that assumes the user is using a QWERTY keyboard in English. For example, transposing an e and a q is more likely than transposing an e and an l.
For people who are recommending Soundex, it is very out of date. Metaphone (simpler) or Double Metaphone (complex) are much better. If it really is name data, it should work fine, if the names are European-ish in origin, or at least phonetic.
As for the search, if you care to roll your own, rather than use Aspell or some other smart data structure... pre-calculating possible matches is O(n^2), in the naive case, but we know in order to be matching at all, they have to have a "phoneme" overlap, or may even two. This pre-indexing step (which has a low false positive rate) can take down the complexity a lot (to in the practical case, something like O(30^2 * k^2), where k is << n).
You have two possible issues that you need to address (or not address if you so choose)
Users mistyping a word (an edit distance algorithm)
Users not knowing a word and guessing (a phonetic match algorithm)
Are you interested in both of these, or just one or the other? They are really two separate things; e.g. Sean and Shawn sound the same but have an edit distance of 3 - too high to be considered a typo.
You should pre-index the count of words to ensure you are only suggesting relevant answers (similar to ealdent's suggestion). For example, if I entered sith I might expect to be asked if I meant smith, however if I typed smith it would not make sense to suggest sith. Determine an algorithm which measures the relative likelihood a word and only suggest words that are more likely.
My experience in loose matching reinforced a simple but important learning - perform as many indexing/sieve layers as you need and don't be scared of including more than 2 or 3. Cull out anything that doesn't start with the correct letter, for instance, then cull everything that doesn't end in the correct letter, and so on. You really only want to perform edit distance calculation on the smallest possible dataset as it is a very intensive operation.
So if you have an O(n), an O(nlogn), and an O(n^2) algorithm - perform all three, in that order, to ensure you are only putting your 'good prospects' through to your heavy algorithm.

1-1 mappings for id obfuscation

I'm using sequential ids as primary keys and there are cases where I don't want those ids to be visible to users, for example I might want to avoid urls like ?invoice_id=1234 that allow users to guess how many invoices the system as a whole is issuing.
I could add a database field with a GUID or something conjured up from hash functions, random strings and/or numeric base conversions, but schemes of that kind have three issues that I find annoying:
Having to allocate the extra database field. I know I could use the GUID as my primary key, but my auto-increment integer PK's are the right thing for most purposes, and I don't want to change that.
Having to think about the possibility of hash/GUID collisions. I give my full assent to all the arguments about GUID collisions being as likely as spontaneous combustion or whatever, but disregarding exceptional cases because they're exceptional goes against everything else I've been taught, and it continues to bother me even when I know I should be more bothered about other things.
I don't know how to safely trim hash-based identifiers, so even if my private ids are 16 or 32 bits, I'm stuck with 128 bit generated identifiers that are a nuisance in urls.
I'm interested in 1-1 mappings of an id range, stretchable or shrinkable so that for example 16-bit ids are mapped to 16 bit ids, 32 bit ids mapped to 32 bit ids, etc, and that would stop somebody from trying to guess the total number of ids allocated or the rate of id allocation over a period.
For example, if my user ids are 16 bit integers (0..65535), then an example of a transformation that somewhat obfuscates the id allocation is the function f(x) = (x mult 1001) mod 65536. The internal id sequence of 1, 2, 3 becomes the public id sequence of 1001, 2002, 3003. With a further layer of obfuscation from base conversion, for example to base 36, the sequence becomes 'rt', '1jm', '2bf'. When the system gets a request to the url ?userid=2bf, it converts from base 36 to get 3003 and it applies the inverse transformation g(x) = (x mult 1113) mod 65536 to get back to the internal id=3.
A scheme of that kind is enough to stop casual observation by casual users, but it's easily solvable by someone who's interested enough to try to puzzle it through. Can anyone suggest something that's a bit stronger, but is easily implementable in say PHP without special libraries? This is getting close to a roll-your-own encryption scheme, so maybe there is a proper encryption algorithm that's widely available and has the stretchability property mentioned above?
EDIT: Stepping back a little bit, some discussion at codinghorror about choosing from three kinds of keys - surrogate (guid-based), surrogate (integer-based), natural. In those terms, I'm trying to hide an integer surrogate key from users but I'm looking for something shrinkable that makes urls that aren't too long, which I don't know how to do with the standard 128-bit GUID. Sometimes, as commenter Princess suggests below, the issue can be sidestepped with a natural key.
EDIT 2/SUMMARY:
Given the constraints of the question I asked (stretchability, reversibility, ease of implementation), the most suitable solution so far seems to be the XOR-based obfuscation suggested by Someone and Breton.
It would be irresponsible of me to assume that I can achieve anything more than obfuscation/security by obscurity. The knowledge that it's an integer sequence is probably a crib that any competent attacker would be able to take advantage of.
I've given some more thought to the idea of the extra database field. One advantage of the extra field is that it makes it a lot more straightforward for future programmers who are trying to familiarise themselves with the system by looking at the database. Otherwise they'd have to dig through the source code (or documentation, ahem) to work out how a request to a given url is resolved to a given record in the database.
If I allow the extra database field, then some of the other assumptions in the question become irrelevant (for example the transformation doesn't need to be reversible). That becomes a different question, so I'll leave it there.
I find that simple XOR encryption is best suited for URL obfuscation. You can continue using whatever serial number you are using without change. Further XOR encryption doesn't increase the length of source string. If your text is 22 bytes, the encrypted string will be 22 bytes too. It's not easy enough as to be guessed like rot 13 but not heavy weight like DSE/RSA.
Search the net for PHP XOR encryption to find some implementation. The first one I found is here.
I've toyed with this sort of thing myself, in my amateurish way, and arrived at a kind of kooky number scrambling algorithm, involving mixed radices. Basically I have a function that maps a number between 0-N to another number in the 0-N range. For URLS I then map that number to a couple of english words. (words are easier to remember).
A simplified version of what I do, without mixed radices: You have a number that is 32 bits, so ahead of time, have a passkey which is 32-bits long, and XOR the passkey with your input number. Then shuffle the bits around in a determinate reordering. (possibly based on your passkey).
The nice thing about this is
No collisions, as long as you shuffle and xor the same way each time
No need to store the obfuscated keys in the database
Still use your ordered IDS internally, since you can reverse the obfuscation
You can repeat the operation several times to get more obfuscated results.
if you're up for the mixed radix version, it's basically the same, except that I add the steps of converting the input to a mixed raddix number, using the maximum range's prime factors as the digit's bases. Then I shuffle the digits around, keeping the bases with the digits, and turn it back into a standard integer.
You might find it useful to revisit the idea of using a GUID, because you can construct GUIDs in a way that isn't subject to collision.
Check out the Wikipedia page on GUIDs - the "Type 1" algorithm uses both the MAC address of the PC, and the current date/time as inputs. This guarantees that collisions are simply impossible.
Alternatively, if you create a GUID column in your database as an alternative-key (keep using your auto-increment primary keys), define it as unique. Then, if your GUID generation approach does give a duplicate, you'll get an appropriate error on insert that you can handle.
I saw this question yesterday: how reddit generates an alphanum id
I think it's a reasonably good method (and particularily clever)
it uses Python
def to_base(q, alphabet):
if q < 0: raise ValueError, "must supply a positive integer"
l = len(alphabet)
converted = []
while q != 0:
q, r = divmod(q, l)
converted.insert(0, alphabet[r])
return "".join(converted) or '0'
def to36(q):
return to_base(q, '0123456789abcdefghijklmnopqrstuvwxyz')
Add a char(10) field to your order table... call it 'order_number'.
After you create a new order, randomly generate an integer from 1...9999999999. Check to see if it exists in the database under 'order_number'. If not, update your latest row with this value. If it does exist, pick another number at random.
Use 'order_number' for publicly viewable URLs, maybe always padded with zeros.
There's a race condition concern for when two threads attempt to add the same number at the same time... you could do a table lock if you were really concerned, but that's a big hammer. Add a second check after updating, re-select to ensure it's unique. Call recursively until you get a unique entry. Dwell for a random number of milliseconds between calls, and use the current time as a seed for the random number generator.
Swiped from here.
UPDATED As with using the GUID aproach described by Bevan, if the column is constrained as unique, then you don't have to sweat it. I guess this is no different that using a GUID, except that the customer and Customer Service will have an easier time referring to the order.
I've found a much simpler way. Say you want to map N digits, pseudorandomly to N digits. you find the next highest prime from N, and you make your function
prandmap(x) return x * nextPrime(N) % N
this will produce a function that repeats (or has a period) every N, no number is produced twice until x=N+1. It always starts at 0, but is pseudorandom thereafter.
I honestly thing encrypting/decrypting query string data is a bad approach to this problem. The easiest solution is sending data using POST instead of GET. If users are clicking on links with querystring data, you have to resort to some javascript hacks to send data by POST (keep accessibility in mind for users with Javascript turned off). This doesn't prevent users from viewing source, but at the very least it keeps sensitive from being indexed by search engines, assuming the data you're trying to hide really that sensitive in the first place.
Another approach is to use a natural unique key. For example, if you're issuing invoices to customers on a monthly basis, then "yyyyMM[customerID]" uniquely identifies a particular invoice for a particular user.
From your description, personally, I would start off by working with whatever standard encryption library is available (I'm a Java programmer, but I assume, say, a basic AES encryption library must be available for PHP):
on the database, just key things as you normally would
whenever you need to transmit a key to/from a client, use a fairly strong, standard encryption system (e.g. AES) to convert the key to/from a string of garbage. As your plain text, use a (say) 128-byte buffer containing: a (say) 4-byte key, 60 random bytes, and then a 64-byte medium-quality hash of the previous 64 bytes (see Numerical Recipes for an example)-- obviously when you receive such a string, you decrypt it then check if the hash matches before hitting the DB. If you're being a bit more paranoid, send an AES-encrypted buffer of random bytes with your key in an arbitrary position, plus a secure hash of that buffer as a separate parameter. The first option is probably a reasonable tradeoff between performance and security for your purposes, though, especially when combined with other security measures.
the day that you're processing so many invoices a second that AES encrypting them in transit is too performance expensive, go out and buy yourself a big fat server with lots of CPUs to celebrate.
Also, if you want to hide that the variable is an invoice ID, you might consider calling it something other than "invoice_id".