We Keep Coding

Is it okay to hard-code complex math logic inside my code?

Is there a generally accepted best approach to coding complex math? For example:
double someNumber = .123 + .456 * Math.Pow(Math.E, .789 * Math.Pow((homeIndex + .22), .012));
Is this a point where hard-coding the numbers is okay? Or should each number have a constant associated with it? Or is there even another way, like storing the calculations in config and invoking them somehow?
There will be a lot of code like this, and I'm trying to keep it maintainable.
Note: The example shown above is just one line. There would be tens or hundreds of these lines of code. And not only could the numbers change, but the formula could as well.

Generally, there are two kinds of constants - ones with the meaning to the implementation, and ones with the meaning to the business logic.
It is OK to hard-code the constants of the first kind: they are private to understanding your algorithm. For example, if you are using a ternary search and need to divide the interval in three parts, dividing by a hard-coded 3 is the right approach.
Constants with the meaning outside the code of your program, on the other hand, should not be hard-coded: giving them explicit names gives someone who maintains your code after you leave the company non-zero chances of making correct modifications without having to rewrite things from scratch or e-mailing you for help.

"Is it okay"? Sure. As far as I know, there's no paramilitary police force rounding up those who sin against the one true faith of programming. (Yet.).
Is it wise?
Well, there are all sorts of ways of deciding that - performance, scalability, extensibility, maintainability etc.
On the maintainability scale, this is pure evil. It make extensibility very hard; performance and scalability are probably not a huge concern.
If you left behind a single method with loads of lines similar to the above, your successor would have no chance maintaining the code. He'd be right to recommend a rewrite.
If you broke it down like
public float calculateTax(person)
float taxFreeAmount = calcTaxFreeAmount(person)
float taxableAmount = calcTaxableAmount(person, taxFreeAmount)
float taxAmount = calcTaxAmount(person, taxableAmount)
return taxAmount
end
and each of the inner methods is a few lines long, but you left some hardcoded values in there - well, not brilliant, but not terrible.
However, if some of those hardcoded values are likely to change over time (like the tax rate), leaving them as hardcoded values is not okay. It's awful.
The best advice I can give is:
Spend an afternoon with Resharper, and use its automatic refactoring tools.
Assume the guy picking this up from you is an axe-wielding maniac who knows where you live.

I usually ask myself whether I can maintain and fix the code at 3 AM being sleep deprived six months after writing the code. It has served me well. Looking at your formula, I'm not sure I can.
Ages ago I worked in the insurance industry. Some of my colleagues were tasked to convert the actuarial formulas into code, first FORTRAN and later C. Mathematical and programming skills varied from colleague to colleague. What I learned was the following reviewing their code:
document the actual formula in code; without it, years later you'll have trouble remember the actual formula. External documentation goes missing, become dated or simply may not be accessible.
break the formula into discrete components that can be documented, reused and tested.
use constants to document equations; magic numbers have very little context and often require existing knowledge for other developers to understand.
rely on the compiler to optimize code where possible. A good compiler will inline methods, reduce duplication and optimize the code for the particular architecture. In some cases it may duplicate portions of the formula for better performance.
That said, there are times where hard coding just simplify things, especially if those values are well understood within a particular context. For example, dividing (or multiplying) something by 100 or 1000 because you're converting a value to dollars. Another one is to multiply something by 3600 when you'd like to convert hours to seconds. Their meaning is often implied from the greater context. The following doesn't say much about magic number 100:
public static double a(double b, double c)
{
return (b - c) * 100;
}
but the following may give you a better hint:
public static double calculateAmountInCents(double amountDue, double amountPaid)
{
return (amountDue - amountPaid) * 100;
}

As the above comment states, this is far from complex.
You can however store the Magic numbers in constants/app.config values, so as to make it easier for the next developer to maitain your code.
When storing such constants, make sure to explain to the next developer (read yourself in 1 month) what your thoughts were, and what they need to keep in mind.
Also ewxplain what the actual calculation is for and what it is doing.

Do not leave in-line like this.
Constant so you can reuse, easily find, easily change and provides for better maintaining when someone comes looking at your code for the first time.
You can do a config if it can/should be customized. What is the impact of a customer altering the value(s)? Sometimes it is best to not give them that option. They could change it on their own then blame you when things don't work. Then again, maybe they have it in flux more often than your release schedules.

Its worth noting that the C# compiler (or is it the CLR) will automatically inline 1 line methods so if you can extract certain formulas into one liners you can just extract them as methods without any performance loss.
EDIT:
Constants and such more or less depends on the team and the quantity of use. Obviously if you're using the same hard-coded number more than once, constant it. However if you're writing a formula that its likely only you will ever edit (small team) then hard coding the values is fine. It all depends on your teams views on documentation and maintenance.

If the calculation in your line explains something for the next developer then you can leave it, otherwise its better to have calculated constant value in your code or configuration files.
I found one line in production code which was like:
int interval = 1 * 60 * 60 * 1000;
Without any comment, it wasn't hard that the original developer meant 1 hour in milliseconds, rather than seeing a value of 3600000.
IMO May be leaving out calculations is better for scenarios like that.

Names can be added for documentation purposes. The amount of documentation needed depends largely on the purpose.
Consider following code:
float e = m * 8.98755179e16;
And contrast it with the following one:
const float c = 299792458;
float e = m * c * c;
Even though the variable names are not very 'descriptive' in the latter you'll have much better idea what the code is doing the the first one - arguably there is no need to rename the c to speedOfLight, m to mass and e to energy as the names are explanatory in their domains.
const float speedOfLight = 299792458;
float energy = mass * speedOfLight * speedOfLight;
I would argue that the second code is the clearest one - especially if programmer can expect to find STR in the code (LHC simulator or something similar). To sum up - you need to find an optimal point. The more verbose code the more context you provide - which might both help to understand the meaning (what is e and c vs. we do something with mass and speed of light) and obscure the big picture (we square c and multiply by m vs. need of scanning whole line to get equation).
Most constants have some deeper meening and/or established notation so I would consider at least naming it by the convention (c for speed of light, R for gas constant, sPerH for seconds in hour). If notation is not clear the longer names should be used (sPerH in class named Date or Time is probably fine while it is not in Paginator). The really obvious constants could be hardcoded (say - division by 2 in calculating new array length in merge sort).

Searching for partial substring within string in C#

Okay so I'm trying to make a basic malware scanner in C# my question is say I have the Hex signature for a particular bit of code
For example
{
System.IO.File.Delete(#"C:\Users\Public\DeleteTest\test.txt");
}
//Which will have a hex of 53797374656d2e494f2e46696c652e44656c657465284022433a5c55736572735c5075626c69635c44656c657465546573745c746573742e74787422293b
Gets Changed to -
{
System.IO.File.Delete(#"C:\Users\Public\DeleteTest\notatest.txt");
}
//Which will have a hex of 53797374656d2e494f2e46696c652e44656c657465284022433a5c55736572735c5075626c69635c44656c657465546573745c6e6f7461746573742e74787422293b
Keep in mind these bits will be within the entire Hex of the program - How could I go about taking my base signature and looking for partial matches that say have a 90% match therefore gets flagged.
I would do a wildcard but that wouldn't work for slightly more complex things where it might be coded slightly different but the majority would be the same. So is there a way I can do a percent match for a substring? I was looking into the Levenshtein Distance but I don't see how I'd apply it into this given scenario.
Thanks in advance for any input

Using an edit distance would be fine. You can take two strings and calculate the edit distance, which will be an integer value denoting how many operations are needed to take one string to the other. You set your own threshold based off that number.
For example, you may statically set that if the distance is less than five edits, the change is relevant.
You could also take the length of string you are comparing and take a percentage of that. Your example is 36 characters long, so (int)(input.Length * 0.88m) would be a valid threashold.

First, your program bits should match EXACTLY or else it has been modified or is corrupt. Generally, you will store an MD5 hash on the original binary and check the MD5 against new versions to see if they are 'the same enough' (MD5 can't guarantee a 100% match).
Beyond this, in order to detect malware in a random binary, you must know what sort of patterns to look for. For example, if I know a piece of malware injects code with some binary XYZ, I will look for XYZ in the bits of the executable. Patterns get much more complex than that, of course, as the malware bits can be spread out in chuncks. What is more interesting is that some viruses are self-morphing. This means that each time it runs, it modifies itself, meaning the scanner does not know an exact pattern to find. In these cases, the scanner must know the types of derivatives can be produced and look for all of them.
In terms of finding a % match, this operation is very time consuming unless you have constraints. By comparing 2 strings, you cannot tell which pieces were removed, added, or replaced. For instance, if I have a starting string 'ABCD', is 'AABCDD' a 100% match or less since content has been added? What about 'ABCDABCD'; here it matches twice. How about 'AXBXCXD'? What about 'CDAB'?
There are many DIFF tools in existence that can tell you what pieces of a file have been changed (which can lead to a %). Unfortunately, none of them are perfect because of the issues that I described above. You will find that you have false negatives, false positives, etc. This may be 'good enough' for you.
Before you can identify a specific algorithm that will work for you, you will have to decide what the restrictions of your search will be. Otherwise, your scan will be NP-hard, which leads to unreasonable running times (your scanner may run all day just to check one file).

I suggest you look into Levenshtein distance and Damerau-Levenshtein distance.
The former tells you how many add/delete operations are needed to turn one string into another; and the latter tells you how many add/delete/replace operations are needed to turn one string into another.
I use these quite a lot when writing programs where users can search for things, but they may not know the exact spelling.
There are code examples on both articles.

Creating a "spell check" that checks against a database with a reasonable runtime

I'm not asking about implementing the spell check algorithm itself. I have a database that contains hundreds of thousands of records. What I am looking to do is checking a user input against a certain column in a table for all these records and return any matches with a certain hamming distance (again, this question's not about determining hamming distance, etc.). The purpose, of course, is to create a "did you mean" feature, where a user searches a name, and if no direct matches are found in the database, a list of possible matches are returned.
I'm trying to come up with a way to do all of these checks in the most reasonable runtime possible. How can I check a user's input against all of these records in the most efficient way possible?
The feature is currently implemented, but the runtime is exceedingly slow. The way it works now is it loads all records from a user-specified table (or tables) into memory and then performs the check.
For what it's worth, I'm using NHibernate for data access.
I would appreciate any feedback on how I can do this or what my options are.

Calculating Levenshtein distance doesn't have to be as costly as you might think. The code in the Norvig article can be thought of as psuedocode to help the reader understand the algorithm. A much more efficient implementation (in my case, approx 300 times faster on a 20,000 term data set) is to walk a trie. The performance difference is mostly attributed to removing the need to allocate millions of strings in order to do dictionary lookups, spending much less time in the GC, and you also get better locality of reference so have fewer CPU cache misses. With this approach I am able to do lookups in around 2ms on my web server. An added bonus is the ability to return all results that start with the provided string easily.
The downside is that creating the trie is slow (can take a second or so), so if the source data changes regularly then you need to decide whether to rebuild the whole thing or apply deltas. At any rate, you want to reuse the structure as much as possible once it's built.

As Darcara said, a BK-Tree is a good first take. They are very easy to implement. There are several free implementations easily found via Google, but a better introduction to the algorithm can be found here: http://blog.notdot.net/2007/4/Damn-Cool-Algorithms-Part-1-BK-Trees.
Unfortunately, calculating the Levenshtein distance is pretty costly, and you'll be doing it a lot if you're using a BK-Tree with a large dictionary. For better performance, you might consider Levenshtein Automata. A bit harder to implement, but also more efficient, and they can be used to solve your problem. The same awesome blogger has the details: http://blog.notdot.net/2010/07/Damn-Cool-Algorithms-Levenshtein-Automata. This paper might also be interesting: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.16.652.

I guess the Levenshtein distance is more useful here than the Hamming distance.
Let's take an example: We take the word example and restrict ourselves to a Levenshtein distance of 1. Then we can enumerate all possible misspellings that exist:
1 insertion (208)
aexample
bexample
cexample
...
examplex
exampley
examplez
1 deletion (7)
xample
eample
exmple
...
exampl
1 substitution (182)
axample
bxample
cxample
...
examplz
You could store each misspelling in the database, and link that to the correct spelling, example. That works and would be quite fast, but creates a huge database.
Notice how most misspellings occur by doing the same operation with a different character:
1 insertion (8)
?example
e?xample
ex?ample
exa?mple
exam?ple
examp?le
exampl?e
example?
1 deletion (7)
xample
eample
exmple
exaple
examle
exampe
exampl
1 substitution (7)
?xample
e?ample
ex?mple
exa?ple
exam?le
examp?e
exampl?
That looks quite manageable. You could generate all these "hints" for each word and store them in the database. When the user enters a word, generate all "hints" from that and query the database.
Example: User enters exaple (notice missing m).
SELECT DISTINCT word
FROM dictionary
WHERE hint = '?exaple'
OR hint = 'e?xaple'
OR hint = 'ex?aple'
OR hint = 'exa?ple'
OR hint = 'exap?le'
OR hint = 'exapl?e'
OR hint = 'exaple?'
OR hint = 'xaple'
OR hint = 'eaple'
OR hint = 'exple'
OR hint = 'exale'
OR hint = 'exape'
OR hint = 'exapl'
OR hint = '?xaple'
OR hint = 'e?aple'
OR hint = 'ex?ple'
OR hint = 'exa?le'
OR hint = 'exap?e'
OR hint = 'exapl?'
exaple with 1 insertion == exa?ple == example with 1 substitution
See also: How does the Google “Did you mean?” Algorithm work?

it loads all records from a user-specified table (or tables) into memory and then performs the check
don't do that
Either
Do the match match on the back end
and only return the results you need.
or
Cache the records into memory early
on a take the working set hit and do
the check when you need it.

You will need to structure your data differently than a database can. Build a custom search tree, with all dictionary data needed, on the client. Although memory might become a problem if the dictionary is extremely big, the search itself will be very fast. O(nlogn) if I recall correctly.
Have a look at BK-Trees
Also, instead of using the Hamming distance, consider the Levenshtein distance

The answer you marked as correct..
Note: when i say dictionary.. in this post, i mean hash map .. map..
basically i mean a python dictionary
Another way you can improve its performance by creating an inverted index of words.
So rather than calculating the edit distance against whole db, you create 26 dictionary.. each has a key an alphabet. so english language has 26 alphabets.. so keys are "a","b".. "z"
So assume you have word in your db "apple"
So in the "a" dictionary : you add the word "apple"
in the "p" dictionary: you add the word "apple"
in the "l" dictionary: you add the word "apple"
in the "e" dictionary : you add the word "apple"
So, do this for all the words in the dictionary..
Now when the misspelled word is entered..
lets say aplse
you start with "a" and retreive all the words in "a"
then you start with "p" and find the intersection of words between "a" and "p"
then you start with "l" and find the intersection of words between "a", "p" and "l"
and you do this for all the alphabetss.
in the end you will have just the bunch of words which are made of alphabets "a","p","l","s","e"
In the next step, you calculate the edit distance between the input word and the bunch of words returned by the above steps.. thus drastically reducing your run time..
now there might be a case when nothing might be returned..
so something like "aklse".. there is a good chance that there is no word which is made of just these alphabets..
In this case, you will have to start reversing the above step to a stage where you have finite numbers of word left.
So somethng like start with *klse (intersection between words k, l,s,e) num(wordsreturned) =k1
then a*lse( intersection between words a,l,s,e)... numwords = k2
and so on..
choose the one which have higher number of words returned.. in this case, there is really no one answer.. as a lot of words might have same edit distance.. you can just say that if editdistance is greater than "k" then there is no good match...
There are many sophisticated algorithms built on top of this..
like after these many steps, use statistical inferences (probability the word is "apple" when the input is "aplse".. and so on) Then you go machine learning way :)

Analysis of Permutation Finder algorithm(pseudo code)

A SO post about generating all the permutations got me thinking about a few alternative approaches. I was thinking about using space/run-time trade offs and was wondering if people could critique this approach and possible hiccups while trying to implement it in C#.
The steps goes as follows:
Given a data-structure of homogeneous elements, count the number of elements in the structure.
Assuming the permutation consists of all the elements of the structure, calculate the factorial of the value from Step 1.
Instantiate a newer structure(Dictionary) of type <key(Somehashofcollection),Collection<data-structure of homogeneous elements>> and initialize a counter.
Hash(???) the seed structure from step 1, and insert the key/value pair of hash and collection into the Dictionary. Increment the counter by 1.
Randomly shuffle(???) the order of the seed structure, hash it and then try to insert it into the Dictionary from step 3.
If there is a conflict in hashes,repeat step 5 again to get a new order and hash and check for conflict. Upon successful insertion increment the counter by 1.
Repeat steps 5 & 6 until the counter equals the factorial calculated in step 2.
It seems like doing it this way using some sort of randomizer(which is a black box to me at the moment) might help with getting all the permutations within a decent timeframe for datasets of obscene sizes.
It will be great to get some feedback from the great minds of SO to further analyze this approach whose objective is to deviate from the traditional brute-force approach prevalent in algorithms of such nature and also the repercussions of implementing such an algorithm using C#.
Thanks

This method of generating all permutations does not fare well as compared to the standard known methods.
Say you had n items and M=n! permutations.
This method of generation is expected to generate M*lnM permutations before discovering all M.
(See this answer for a possible explanation: Programing Pearls - Random Select algorithm)
Also, what would the hash function be? For a reasonable hash function, we might have to start dealing with very large integer issues pretty soon (any n > 50 for sure, don't remember that exact cut-off point).
This method uses up a lot of memory too (the hashtable of all permutations).
Even assuming the hash is perfect, this method would take expected Omega(nMlogM) operations and guaranteed Omega(nM) space, while standard well-known methods can do it in O(M) time and O(n) space.
As a starting point I suggest one can read: Systematic Generation of All Permutations which is believe is O(nM) time and O(n) space and still much better than this method.
Note that if one has to generate all permutations, any algorithm will necessarily take Omega(M) steps and so the the method I refer to above is optimal!

It seems like a complicated way to randomise the order of the generated permutations. In terms of time efficiency, you can't do much better than the 'brute force' approach.

How do I determine if two similar band names represent the same band?

I'm currently working on a project that requires me to match our database of Bands and venues with a number of external services.
Basically I'm looking for some direction on the best method for determining if two names are the same. For Example:
Our database venue name - "The Pig and Whistle"
service 1 - "Pig and Whistle"
service 2 - "The Pig & Whistle"
etc etc
I think the main differences are going to be things like missing "the" or using "&" instead of "and" but there could also be things like slightly different spelling and words in different orders.
What algorithms/techniques are commonly used in this situation, do I need to filter noise words or do some sort of spell check type match?
Have you seen any examples of something simlar in c#?
UPDATE: In case anyone is interested in a c# example there is a heap you can access by doing a google code search for Levenshtein distance

The canonical (and probably the easiest) way to do this is to measure the Levenshtein distance between the two strings. If the distance is small relative to the size of the string, it's probably the same string. Note that if you have to compare a lot of very small strings it'll be harder to tell whether they're the same or not. It works better with longer strings.
A smarter approach might be to compare the Levenshtein distance between the two strings but to assign a distance of zero to the more obvious transformations, like "and"/"&", "Snoop Doggy Dogg"/"Snoop", etc.

I did something like this a while ago, I used the the Discogs database (which is public domain), which also tracks artist aliases;
You can either:
Use an API call (namevariations field).
Download the monthly data dumps (*_artists.xml.gz) & import it in your database. This contains the same data, but is obviously a lot faster.
One advantage of this over the Levenshtein distance) solution is that you'll get a lot less false matches.
For example, Ryan Adams and Bryan Adams have a score of 2, which is quite good (lower is better matches, Pig and Whistle and Pig & Whistle has a score of 3), yet they're obviously different people.
While you could make a smarter algorithm (which also looks at string length, for example), using the alias DB is a lot simpler & less error-phone; after implementing this, I could completely remove the solution that was suggested in the other answer & had better matches.

soundex may also be useful

In bioinformatics we use this to compare DNA- or protein sequences all the time.
There are plenty of algorithms, you probably want to look at global alignments.
In this respect the Needleman-Wunsch algorithm is probably what you seek.
If you have particularly long recurring strings to compare you might also want to consider heuristic searches like BLAST.