I have a code where in i compare a large data, say a source of a web page against some words in a file. What is the best algorithm to be used?
There can be 2 scenarios:
If I have a large amount of words to compare against the source, In which case, for a normal string search algorithm, it would have to take a word, compare against the data, take the next and compare against the data and so on until all is complete.
I have only a couple of words in the file and the normal string search would be ok, but still need to reduce the time as much as possible.
What algorithm is best? I know about Boyer-Moore and also Rabin-Karp search algorithms.
Although Boyer-Moore search seems fast, I would also like names of other algorithms and their comparisons.
In both cases, I think you probably want to construct a patricia trie (also called radix tree). Most importantly, lookup time would be O(k), where k is the max length of a string in the trie.
Note that Boyer-Moore is to search a text (several words) within a text.
If all you want is identifying some individual words, then it's much easier to:
put each searched word in a dictionary structure (whatever it is)
look-up each word of the text in the dictionary
This most notably mean that you read the text as a stream, and need not hold it all in memory at once (which works great with the typical example of a file cursor).
As for the structure of the dictionary, I would recommend a simple hash table. Works great memory-wise compared to tree structures.
Related
I have list of seed strings, about 100 predefined strings. All strings contain only ASCII characters.
std::list<std::wstring> seeds{ L"google", L"yahoo", L"stackoverflow"};
My app constantly receives a lot of strings which can contain any characters. I need check each received line and decide whether it contain any of seeds or not. Comparison must be case insensitive.
I need the fastest possible algorithm to test received string.
Right now my app uses this algo:
std::wstring testedStr;
for (auto & seed : seeds)
{
if (boost::icontains(testedStr, seed))
{
return true;
}
}
return false;
It works well, but I'm not sure that this is the most efficient way.
How is it possible to implement the algorithm in order to achieve better performance?
This is a Windows app. App receives valid std::wstring strings.
Update
For this task I implemented Aho-Corasick algo. If someone could review my code it would be great - I do not have big experience with such algorithms. Link to implementation: gist.github.com
If there are a finite amount of matching strings, this means that you can construct a tree such that, read from root to leaves, similar strings will occupy similar branches.
This is also known as a trie, or Radix Tree.
For example, we might have the strings cat, coach, con, conch as well as dark, dad, dank, do. Their trie might look like this:
A search for one of the words in the tree will search the tree, starting from a root. Making it to a leaf would correspond to a match to a seed. Regardless, each character in the string should match to one of their children. If it does not, you can terminate the search (e.g. you would not consider any words starting with "g" or any words beginning with "cu").
There are various algorithms for constructing the tree as well as searching it as well as modifying it on the fly, but I thought I would give a conceptual overview of the solution instead of a specific one since I don't know of the best algorithm for it.
Conceptually, an algorithm you might use to search the tree would be related to the idea behind radix sort of a fixed amount of categories or values that a character in a string might take on at a given point in time.
This lets you check one word against your word-list. Since you're looking for this word-list as sub-strings of your input string, there's going to be more to it than this.
Edit: As other answers have mentioned, the Aho-Corasick algorithm for string matching is a sophisticated algorithm for performing string matching, consisting of a trie with additional links for taking "shortcuts" through the tree and having a different search pattern to accompany this. (As an interesting note, Alfred Aho is also a contributor to the the popular compiler textbook, Compilers: Principles, Techniques, and Tools as well as the algorithms textbook, The Design And Analysis Of Computer Algorithms. He is also a former member of Bell Labs. Margaret J. Corasick does not seem to have too much public information on herself.)
You can use Aho–Corasick algorithm
It builds trie/automaton where some vertices marked as terminal which would mean string has seeds.
It's built in O(sum of dictionary word lengths) and gives the answer in O(test string length)
Advantages:
It's specifically works with several dictionary words and check time doesn't depend on number of words (If we not consider cases where it doesn't fit to memory etc)
The algorithm is not hard to implement (comparing to suffix structures at least)
You may make it case insensitive by lowering each symbol if it's ASCII (non ASCII chars don't match anyway)
You should try a pre-existing regex utility, it may be slower than your hand-rolled algorithm but regex is about matching multiple possibilities, so it is likely it will be already several times faster than a hashmap or a simple comparison to all strings. I believe regex implementations may already use the Aho–Corasick algorithm mentioned by RiaD, so basically you will have at your disposal a well tested and fast implementation.
If you have C++11 you already have a standard regex library
#include <string>
#include <regex>
int main(){
std::regex self_regex("google|yahoo|stackoverflow");
regex_match(input_string ,self_regex);
}
I expect this to generate the best possible minimum match tree, so I expect it to be really fast (and reliable!)
One of the faster ways is to use suffix tree https://en.wikipedia.org/wiki/Suffix_tree, but this approach has huge disadvantage - it is difficult data structure with difficult constructing. This algorithm allows to build tree from string in linear complexity https://en.m.wikipedia.org/wiki/Ukkonen%27s_algorithm
Edit: As Matthieu M. pointed out, the OP asked if a string contains a keyword. My answer only works when the string equals the keyword or if you can split the string e.g. by the space character.
Especially with a high number of possible candidates and knowing them at compile time using a perfect hash function with a tool like gperf is worth a try. The main principle is, that you seed a generator with your seed and it generates a function that contains a hash function which has no collisions for all seed values. At runtime you give the function a string and it calculates the hash and then it checks if it is the only possible candidate corresponding to the hashvalue.
The runtime cost is hashing the string and then comparing against the only possible candidate (O(1) for seed size and O(1) for string length).
To make the comparison case insensitive you just use tolower on the seed and on your string.
Because number of string is not big (~100), you can use next algo:
Calculate max length of word you have. Let it be N.
Create int checks[N]; array of checksum.
Let's checksum will be sum of all characters in searching phrase. So, you can calculate such checksum for each word from your list (that is known at compile time), and create std::map<int, std::vector<std::wstring>>, where int is checksum of string, and vector should contain all your strings with that checksum.
Create array of such maps for each length (up to N), it can be done at compile time also.
Now move over big string by pointer. When pointer points to X character, you should add value of X char to all checks integers, and for each of them (numbers from 1 to N) remove value of (X-K) character, where K is number of integer in checks array. So, you will always have correct checksum for all length stored in checks array.
After that search on map does there exists strings with such pair (length & checksum), and if exists - compare it.
It should give false-positive result (when checksum & length is equal, but phrase is not) very rare.
So, let's say R is length of big string. Then looping over it will take O(R).
Each step you will perform N operations with "+" small number (char value), N operations with "-" small number (char value), that is very fast. Each step you will have to search for counter in checks array, and that is O(1), because it's one memory block.
Also each step you will have to find map in map's array, that will also be O(1), because it's also is one memory block.
And inside map you will have to search for string with correct checksum for log(F), where F is size of map, and it will usually contain no more then 2-3 strings, so we can in general pretend that it is also O(1).
Also you can check, and if there is no strings with same checksum (that should happens with high chance with just 100 words), you can discard map at all, storing pairs instead of map.
So, finally that should give O(R), with quite small O.
This way of calculating checksum can be changed, but it's quite simple and completely fast, with really rare false-positive reactions.
As a variant on DarioOO’s answer, you could get a possibly faster implementation of a regular expression match, by coding a lex parser for your strings. Though normally used together with yacc, this is a case where lex on its own does the job, and lex parsers are usually very efficient.
This approach might fall down if all your strings are long, as then an algorithm such as Aho-Corasick, Commentz-Walter or Rabin-Karp would probably offer significant improvements, and I doubt that lex implementations use any such algorithm.
This approach is harder if you have to be able to configure the strings without reconfiguration, but since flex is open source you could cannibalise its code.
Assuming I have the following text:
today was a good day and today was a sunny day.
I break up this text into lines, seperated by white spaces, which is
Today
was
a
good
etc.
Now I use the vector data structure to simple count the number of words in a text via .size(). That's done.
However, I also want to check If a word comes up more than once, and if so, how many time. In my example "today" comes up 2 times.
I want to store that "today" and append a 2/x (depending how often it comes up in a large text). Now that's not just for "today" but for every word in the text. I want to look up how often a word appears, append an counter, and sort it (the word + counters) in descending order (that's another thing, but
not important right now).
I'm not sure which data structure to use here. Map perhaps? But I can't add counters to map.
Edit: This is what I've done so far: http://pastebin.com/JncR4kw9
You should use a map. Infact, you should use an unordered_map.
unordered_map<string,int> will give you a hash table which will use strings as keys, and you can augment the integer to keep count.
unordered_map has the advantage of O(1) lookup and insertion over the O(logn) lookup and insertion of a map. This is because the former uses an array as a container whereas the latter uses some implementation of trees (red black, I think).
The only disadvantage of an unordered_map is that as mentioned in its name, you can't iterate over all the elements in lexical order. This should be clear from the explanation of their structure above. However, you don't seem to need such a traversal, and hence it shouldn't be an issue.
unordered_map<string,int> mymap;
mymap[word]++; // will increment the counter associated with the count of a word.
Why not use two data structures? The vector you have now, and a map, using the string as the key, and an integer as data, which then will be the number of times the word was found in the text.
Sort the vector in alphabetical order.
Scan it and compare every word to those that follow, until you find a different one, and son on.
a, a, and, day, day, sunny, today, today, was, was
2 1 2 1 2 2
A better option to consider is Radix Tree, https://en.wikipedia.org/wiki/Radix_tree
Which is quite memory efficient, and in case of large text input, it will perform better than alternative data structures.
One can store the frequencies of a word in the nodes of tree. Also it will reap the benefits of "locality of reference[For any text document]" too.
I have 300 strings to be stored and searched for and that most of them are identical in terms of characters and lenght. For Example i have string "ABC1","ABC2","ABC3" and so on. and another set like sample1,sample2,sample3. So i am kinda confused as of how to store them like to use an array or a hash table. My main concern is the time i take to search for a string when i need to get one out from the storage. If i use an array i will have to do a string compare on all the index for me to arrive at one. Now if i go and impliment a hash table i will have to take care of collisions(obvious) and that i will have to impliment chaining for storing identical strings.
So i am kind of looking for some suggestions weighing the pros and cons of each and arrive at the best practice
Because the keys are short tend to have a common prefix you should consider radix data structures such as the Patricia trie and Ternary Search Tree (google these, you'll find lots of examples) Time for searching these structures tends to be O(1) with respect to # of entries and O(n) with respect to length of the keys. Beware, however that long strings can use lots of memory.
Search time is similar to hash maps if you don't consider collision resolution which is not a problem in a radix search. Note that I am considering the time to compute the hash as part of the cost of a hash map. People tend to forget it.
One downside is radix structures are not cache-friendly if your keys tend to show up in random order. As someone mentioned, if the search time is really important: measure the performance of some alternative approaches.
This depends on how much your data is changing. With that I mean, if you have 300 index strings which are referencing to another string, how often does those 300 index strings change?
You can use a std::map for quick lookups, but the map will require more resource when it is created the first time (compared to a array, vector or list).
I use maps mostly for some kind of dynamic lookup tables (for example: ip to socket).
So in your case it will look like this:
std::map<std::string, std::string> my_map;
my_map["ABC1"] = "sample1";
my_map["ABC2"] = "sample2";
std::string looked_up = my_map["ABC1"];
I am starting to read about Trie. I got also references from friends here in: Tutorials on Trie
I am not clear on the following:
It seems that to go on and use a Trie one assumes that all the input strings that will be the search space and used to build the Trie are separated in distinct word boundaries.
E.g. all the example tutorials I have seen use input such as:
S={ball, bid, byte, car, cat, mac, map etc...}
Then we build the trie from S and do our searches (really fast)
My question is: How did we end up with S to begin with?
I mean before starting to read about tries I imagined that S would be an arbitrarily long text e.g. A Shakespeare passage.
Then using a Trie we could find things really fast.
But it seems this is not the case.
Is the assumption here that the input passage (of Shakespeare for example) is pre-processed first extracting all the words to get S?
So if one wants to search for patterns (same way as you do when you Google and see all pages having also spaces in your search query) a Trie is not appropriate?
When can we know if a Trie is the data structure that we can actually use?
Tries are useful where you have a fixed dictionary you want to look up quickly. Compared to a hashtable it may require less storage for a large dictionary but may well take longer to look up. One example place I have used it is for mapping URLs to operations on a web server were there may be inheritance of functionality based on the prefix. Here recursing down a trie enables appropriate lookup of all of the methods that need to be called for a particular url. It would also be efficient for storing a dictionary.
For doing text searches you would typically represent documents using a token vector of leximes with weights (perhaps based on occurance frequency), and then search against that to get a ranking of documents against a particular search vector. There a number of standard libraries to do this which I would suggest using rather than writing your own - particularly for removing stopwords, dealing with synonyms and stemming.
We can use tries for sub string searching in linear time, without pre processing the string every time. You can get a best tutorial on suffix tree generation #
Ukkonen's suffix tree algorithm in plain English?
As the other examples have said, a trie is useful because it provides fast string look-ups (or, more generally, look-ups for any sequence). Some examples of where I've used tries:
My answer to this question uses a (slightly modified) trie for matching sentences: it is a trie based on a sequence of words, rather than a sequence of characters. (The other answers to that question probably demonstrate the trie in action more clearly.)
I've also used a trie in a game which had a large number of rooms with names (the total number and the names were defined at run time), each of these names has to be unique and one had to be able to search for a room with a given name quickly. A hash table could also have been used, but in some ways a trie is simpler to implement and faster when using strings. (My trie implementation ended up being ~50 lines of C.)
The trie tag probably has many more examples.
There are multiple ways to use tries. The typical example is a lookup such as the one you have presented. However Tries can also be used to fully index a complete text. Either you use the Ukkonen suffix tree algorithm, to produce a suffix trie, or you explicetly construct the suffix trie by storing suffixes (much slower than Ukkonens algorithm, but also much simpler). As this is preprocessing, which needs to be done only once speed is not that crucial.
For this you would just take your text, insert the full text, then chop of the first letter, insert the resulting text, chop of second letter, insert...
So if we have the text "The Text" we would insert the following set:
{"The Text", "he Text", "e Text", " Text", "Text", "ext", "xt", "t"}
In the resulting suffix trie we can easily search for any kind of prefix. Also this is space efficient, because we do not need to store the whole string, since common prefixes are stored only once.
If you need to store much longer strings space efficiently it is best not only to store prefixes together but also suffixes. In that case you could build up a directed acyclic word graph (DAWG), which is very similar to a trie in conception.
So a trie in that sense allows finding arbitrary substrings, including partial words. If you are only interested in storing words, a different data structure should be used, for example a inverted list (if order is important) or a vector space based retrieval algorithm (in case word order does not matter).
Say I have a file with words:
Apple
Bacon
Phone
And so on, there are about 2000 words.
I then have a string:
I was eating some Apple-bacon when the phoNe rang.
I'm trying to find a fast way to result in:
I was eating some *****-***** when the ***** rang.
I'm basically trying to censor a chat box. I'm just wondering if there is a better way than iterating through a vector. I'm only using the standard library so a boost hashmap is not a possibility.
I'm using C++ 98.
I'm just wondering if there is a better way than iterating through a vector.
Use either binary_search on a sorted vector or std::set for guaranteed O(lg n) lookup time. lg(2000) = 7.6, a 263-fold speed increase in theory, disregarding any constant factors.
(Though this is really a better fit for regular expressions.)
If the string to be censored is very long you may try to optimize by iterating the string only once.
Construct a tree with the letters from the list of words you are searching from and write a function that use this map to find words. The design is complicated but for long strings and many words to search will be probably fastest.
Example:
words: Ape, Ace, Apa, By,
Tree
A B
/ | |
p c y
/| |
e a e
search:
1) iterate trough every char in string for top level chars (A or B)
2) if found check if next letter is child of first.
note that iterating chars in string is done anyway for each strchr and is fast because of the branch prediction and should be a primitive implementation of regexp.
There are several alternatives to speed up the search.
One of the simpler approaches if you already have a vector of words, is to sort the vector and to do a binary_search
Trie search is probably the best way. Build a tree of all words in the dictionary and compare input from top. When sees non alphabet letter, reset and start from the top of the tree again
The first attempt would be to tokenize the phrase and look up every word in a map or a set.
However, if you have a server which has to process a lot of messages, you could think about implementing it a bit more clever. Walk through the string, character by character and search inside some better datastructure like those:
suffix tree of all the words, or
hashvalues of all the words
Then replace the characters in place with a *.
Suffix tree should be really fast, but wastes a lot of memory. Hashvalues might be faster than a set implementation, but you have to come up with a clever algorithm.