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Would an implementation of the programming language Brainfuck, still be turing complete if its memory cells were 1bit in capacity, instead of the usual 8bit?
The + and - instructions become identical, however this need not be a problem.
I see no issue with, for example 4bit memory cells, but I cannot work out if this scales all the way to single bit values.
Yes, the resulting language would still be Turing-complete. In fact, several such languages exist. One of them is Boolfuck. It does exactly what you suggest: have each cell be a single bit and get rid of -, because it's redundant. It also uses ; instead . for output. The official website contains a reduction from Brainfuck to Boolfuck which proves Boolfuck's Turing-completeness. I'm reiterating the reduction here to make the answer self-contained:
Brain. Bool.
+ >[>]+<[+<]>>>>>>>>>[+]<<<<<<<<<
- >>>>>>>>>+<<<<<<<<+[>+]<[<]>>>>>>>>>[+]<<<<<<<<<
< <<<<<<<<<
> >>>>>>>>>
, >,>,>,>,>,>,>,>,<<<<<<<<
. >;>;>;>;>;>;>;>;<<<<<<<<
[ >>>>>>>>>+<<<<<<<<+[>+]<[<]>>>>>>>>>[+<<<<<<<<[>]+<[+<]
] >>>>>>>>>+<<<<<<<<+[>+]<[<]>>>>>>>>>]<[+<]
Other bit-based Brainfuck-derivatives include Smallfuck and BitChanger. This article may also be of interest to you, which goes through several steps of minimising the Brainfuck language by removing redundancy (including using bits instead of bytes).
When people talk about the use of "magic numbers" in computer programming, what do they mean?
Magic numbers are any number in your code that isn't immediately obvious to someone with very little knowledge.
For example, the following piece of code:
sz = sz + 729;
has a magic number in it and would be far better written as:
sz = sz + CAPACITY_INCREMENT;
Some extreme views state that you should never have any numbers in your code except -1, 0 and 1 but I prefer a somewhat less dogmatic view since I would instantly recognise 24, 1440, 86400, 3.1415, 2.71828 and 1.414 - it all depends on your knowledge.
However, even though I know there are 1440 minutes in a day, I would probably still use a MINS_PER_DAY identifier since it makes searching for them that much easier. Whose to say that the capacity increment mentioned above wouldn't also be 1440 and you end up changing the wrong value? This is especially true for the low numbers: the chance of dual use of 37197 is relatively low, the chance of using 5 for multiple things is pretty high.
Use of an identifier means that you wouldn't have to go through all your 700 source files and change 729 to 730 when the capacity increment changed. You could just change the one line:
#define CAPACITY_INCREMENT 729
to:
#define CAPACITY_INCREMENT 730
and recompile the lot.
Contrast this with magic constants which are the result of naive people thinking that just because they remove the actual numbers from their code, they can change:
x = x + 4;
to:
#define FOUR 4
x = x + FOUR;
That adds absolutely zero extra information to your code and is a total waste of time.
"magic numbers" are numbers that appear in statements like
if days == 365
Assuming you didn't know there were 365 days in a year, you'd find this statement meaningless. Thus, it's good practice to assign all "magic" numbers (numbers that have some kind of significance in your program) to a constant,
DAYS_IN_A_YEAR = 365
And from then on, compare to that instead. It's easier to read, and if the earth ever gets knocked out of alignment, and we gain an extra day... you can easily change it (other numbers might be more likely to change).
There's more than one meaning. The one given by most answers already (an arbitrary unnamed number) is a very common one, and the only thing I'll say about that is that some people go to the extreme of defining...
#define ZERO 0
#define ONE 1
If you do this, I will hunt you down and show no mercy.
Another kind of magic number, though, is used in file formats. It's just a value included as typically the first thing in the file which helps identify the file format, the version of the file format and/or the endian-ness of the particular file.
For example, you might have a magic number of 0x12345678. If you see that magic number, it's a fair guess you're seeing a file of the correct format. If you see, on the other hand, 0x78563412, it's a fair guess that you're seeing an endian-swapped version of the same file format.
The term "magic number" gets abused a bit, though, referring to almost anything that identifies a file format - including quite long ASCII strings in the header.
http://en.wikipedia.org/wiki/File_format#Magic_number
Wikipedia is your friend (Magic Number article)
Most of the answers so far have described a magic number as a constant that isn't self describing. Being a little bit of an "old-school" programmer myself, back in the day we described magic numbers as being any constant that is being assigned some special purpose that influences the behaviour of the code. For example, the number 999999 or MAX_INT or something else completely arbitrary.
The big problem with magic numbers is that their purpose can easily be forgotten, or the value used in another perfectly reasonable context.
As a crude and terribly contrived example:
while (int i != 99999)
{
DoSomeCleverCalculationBasedOnTheValueOf(i);
if (escapeConditionReached)
{
i = 99999;
}
}
The fact that a constant is used or not named isn't really the issue. In the case of my awful example, the value influences behaviour, but what if we need to change the value of "i" while looping?
Clearly in the example above, you don't NEED a magic number to exit the loop. You could replace it with a break statement, and that is the real issue with magic numbers, that they are a lazy approach to coding, and without fail can always be replaced by something less prone to either failure, or to losing meaning over time.
Anything that doesn't have a readily apparent meaning to anyone but the application itself.
if (foo == 3) {
// do something
} else if (foo == 4) {
// delete all users
}
Magic numbers are special value of certain variables which causes the program to behave in an special manner.
For example, a communication library might take a Timeout parameter and it can define the magic number "-1" for indicating infinite timeout.
The term magic number is usually used to describe some numeric constant in code. The number appears without any further description and thus its meaning is esoteric.
The use of magic numbers can be avoided by using named constants.
Using numbers in calculations other than 0 or 1 that aren't defined by some identifier or variable (which not only makes the number easy to change in several places by changing it in one place, but also makes it clear to the reader what the number is for).
In simple and true words, a magic number is a three-digit number, whose sum of the squares of the first two digits is equal to the third one.
Ex-202,
as, 2*2 + 0*0 = 2*2.
Now, WAP in java to accept an integer and print whether is a magic number or not.
It may seem a bit banal, but there IS at least one real magic number in every programming language.
0
I argue that it is THE magic wand to rule them all in virtually every programmer's quiver of magic wands.
FALSE is inevitably 0
TRUE is not(FALSE), but not necessarily 1! Could be -1 (0xFFFF)
NULL is inevitably 0 (the pointer)
And most compilers allow it unless their typechecking is utterly rabid.
0 is the base index of array elements, except in languages that are so antiquated that the base index is '1'. One can then conveniently code for(i = 0; i < 32; i++), and expect that 'i' will start at the base (0), and increment to, and stop at 32-1... the 32nd member of an array, or whatever.
0 is the end of many programming language strings. The "stop here" value.
0 is likewise built into the X86 instructions to 'move strings efficiently'. Saves many microseconds.
0 is often used by programmers to indicate that "nothing went wrong" in a routine's execution. It is the "not-an-exception" code value. One can use it to indicate the lack of thrown exceptions.
Zero is the answer most often given by programmers to the amount of work it would take to do something completely trivial, like change the color of the active cell to purple instead of bright pink. "Zero, man, just like zero!"
0 is the count of bugs in a program that we aspire to achieve. 0 exceptions unaccounted for, 0 loops unterminated, 0 recursion pathways that cannot be actually taken. 0 is the asymptote that we're trying to achieve in programming labor, girlfriend (or boyfriend) "issues", lousy restaurant experiences and general idiosyncracies of one's car.
Yes, 0 is a magic number indeed. FAR more magic than any other value. Nothing ... ahem, comes close.
rlynch#datalyser.com
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Although I know the basic concepts of binary representation, I have never really written any code that uses binary arithmetic and operations.
I want to know
What are the basic concepts any
programmer should know about binary
numbers and arithmetic ? , and
In what "practical" ways can binary
operations be used in programming. I
have seen some "cool" uses of shift
operators and XOR etc. but are there
some typical problems where using binary
operations is an obvious choice.
Please give pointers to some good reference material.
If you are developing lower-level code, it is critical that you understand the binary representation of various types. You will find this particularly useful if you are developing embedded applications or if you are dealing with low-level transmission or storage of data.
That being said, I also believe that understanding how things work at a low level is useful even if you are working at much higher levels of abstraction. I have found, for example, that my ability to develop efficient code is improved by understanding how things are represented and manipulated at a low level. I have also found such understanding useful in working with debuggers.
Here is a short-list of binary representation topics for study:
numbering systems (binary, hex, octal, decimal, ...)
binary data organization (bits, nibbles, bytes, words, ...)
binary arithmetic
other binary operations (AND,OR,XOR,NOT,SHL,SHR,ROL,ROR,...)
type representation (boolean,integer,float,struct,...)
bit fields and packed data
Finally...here is a nice set of Bit Twiddling Hacks you might find useful.
Unless you're working with lower level stuff, or are trying to be smart, you never really get to play with binary stuff.
I've been through a computer science degree, and I've never used any of the binary arithmetic stuff we learned since my course ended.
Have a squizz here: http://www.swarthmore.edu/NatSci/echeeve1/Ref/BinaryMath/BinaryMath.html
You must understand bit masks.
Many languages and situations require the use of bit masks, for example flags in arguments or configs.
PHP has its error level which you control with bit masks:
error_reporting = E_ALL & ~E_NOTICE
Or simply checking if an int is odd or even:
isOdd = myInt & 1
I believe basic know-hows on binary operations line AND, OR, XOR, NOT would be handy as most of the programming languages support these operations in the form of bit-wise operators.
These operations are also used in image processing and other areas in graphics.
One important use of XOR operation which I can think of is Parity check. Check this http://www.cs.umd.edu/class/sum2003/cmsc311/Notes/BitOp/xor.html
cheers
The following are things I regularly appreciate knowing in my quite conventional programming work:
Know the powers of 2 up to 2^16, and know that 2^32 is about 4.3 billion. Know them well enough so that if you see the number 2147204921 pop up somewhere your first thought is "hmm, that looks pretty close to 2^31" -- that's a very effective module for your bug radar.
Be able to do simple arithmetic; e.g. convert a hexadecimal digit to a nybble and back.
Have some vague idea of how floating-point numbers are represented in binary.
Understand standard conventions that you might encounter in other people's code related to bit twiddling (flags get ORed together to make composite values and AND checks if one's set, shift operators pack and unpack numbers into different bytes, XOR something twice and you get the same something back, that kind of thing.)
Further knowledge is mostly gravy unless you work with significant performance constraints or do other less common work.
At the absolute bare minimum you should be able to implement a bit mask solution. The tasks associated with bit mask operations should ensure that you at least understand binary at a superficial level.
From the top of my head, here are some examples of where I've used bitwise operators to do useful stuff.
A piece of javascript that needed one of those "check all" boxes was something along these lines:
var check = true;
for(var i = 0; i < elements.length; i++)
check &= elements[i].checked;
checkAll.checked = check;
Calculate the corner points of a cube.
Vec3f m_Corners[8];
void corners(float a_Size){
for(size_t i = 0; i < 8; i++){
m_Corners[i] = a_Size * Vec3f(axis(i, Vec3f::X), axis(i, Vec3f::Y), axis(i, Vec3f::Z));
}
}
float axis(size_t a_Corner, int a_Axis) const{
return ((a_Corner >> a_Axis) & 1) == 1
? -.5f
: +.5f;
}
Draw a Sierpinski triangle
for(int y = 0; y < 512; y++)
for(int x = 0; x < 512; x++)
if(x & y) pixels[x + y * w] = someColor;
else pixels[x + y * w] = someOtherColor;
Finding the next power of two
int next = 1 << ((int)(log(number) / log(2));
Checking if a number is a power of two
bool powerOfTwo = number & (number - 1);
The list can go on and on, but for me these are (except for Sierpinksi) everyday examples. Once you'll understand and work with it though, you'll encounter it in more and more places such as the corners of a cube.
You don't specifically mention (nor rule out!-) floating point binary numbers and arithmetic, so I won't miss the opportunity to flog one of my favorite articles ever (seriously: I sometimes wish I could make passing a strict quiz on it a pre-req of working as a programmer...;-).
The most important thing every programmer should know about binary numbers and arithmetic is : Every number in a computer is represented in some kind of binary encoding, and all arithmetic on a computer is binary arithmetic.
The consequences of this are many:
Floating point "bugs" when doing math with IEEE floating point binary numbers (Which is all numbers in javascript, and quite a few in JAVA, and C)
The upper and lower bounds of representable numbers for each type
The performance cost of multiplication/division/square root etc operations (for embedded systems
Precision loss, and accumulation errors
and more. This is stuff you need to know even if you never do a bitwise xor, or not, or whatever in your life. You'll still run into these things.
This really depends on the language you're using. Recent languages such as C# and Java abstract the binary representation from you -- this makes working with binary difficult and is not usually the best way to do things anyway in these languages.
Middle and low level languages like C and C++, however, require you to understand quite a bit about how the numbers are stored underneath -- especially regarding endianness.
Binary knowledge is also useful when implementing a cross platform protcol of some sort .... for example, on x86 machines, byte order is little endian. but most network protocols want big endian numbers. Therefore you have to realize you need to do the conversion for things to go smoothly. Many RFCs, such as this one -> https://www.rfc-editor.org/rfc/rfc4648 require binary knowledge to understand.
In short, it's completely dependent on what you're trying to do.
Billy3
It's handy to know the numbers 256 and 65536. It's handy to know how two's complement negative numbers work.
Maybe you won't run into a lot of binary. I still use it pretty often, but maybe out of habit.
A good familiarity with bitwise operations should make you more facile with boolean algebra, and I think that's important for every programmer--you want to be able to quickly simplify complex logic expressions.
Absolute minimum is, that "2" is not a binary digit and 10b is smaller than 3.
If you never do low-level programming (like C in embedded systems), never have to use a debugger, and never have to work with real numbers, then I suppose you could get by without knowing binary. But knowing binary will make you a stronger programmer, even if indirectly.
Once you venture into those areas you will need to know binary (and its ``sister'' base, hexadecimal). Without knowing it:
Embedded systems programming would be impossible.
Debugging would be hard because you wouldn't know what you were looking at in memory.
Numerical calculations with decimals would give you answers you don't understand.
I learned to twiddle bits back when c and asm were still used for "mainstream" programming. Although I no longer have much use for that knowledge, I recently used it to solve a real-world business problem.
We use a fax service that posts a message back to us when the fax has been sent or failed after x number of retries. The only way I had to identify the fax was a 15 character field. We wanted to consolidate this into one URL for all of our clients. Before we consolidated, all we had to fit in this field was the FaxID PK (32 bit int) column which we just sent as a string.
Now we had to identify the client (a 4 character code) and the database (32 bit int) underneath the client. I was able to do this using base 64 encoding. Without understanding the binary representation of numbers and characters, I probably would never have even thought of this solution.
Some useful information about the number system.
Binary | base 2
Hexadecimal | base 16
Decimal | base 10
Octal | base 8
These are the most common.
Converting them is faily easy.
112 base 8 = (1 x 8^2) + (2 x 8^1) + (4 x 8^0)
74 base 10 = (7 x 10^1) + (4 x 10^0)
The AND, OR, XOR, and etc. are used in logic gates. Search boolean algebra, something well worth the time knowing.
Say for instance, you have 11001111 base 2 and you want to extract the last four only.
Truth table for AND:
P | Q | R
T | T | T
T | F | F
F | F | F
F | T | F
You can use 11001111 base 2 AND 00111111 base 2 = 00001111 base 2
There are plenty of resources on the internet.
What do you think about one line functions? Is it bad?
One advantage I can think of is that it makes the code more comprehensive (if you choose a good name for it). For example:
void addint(Set *S, int n)
{
(*S)[n/CHAR_SIZE] |= (unsigned char) pow(2, (CHAR_SIZE - 1) - (n % CHAR_SIZE));
}
One disadvantage I can think of is that it slows the code (pushing parameters to stack, jumping to a function, popping the parameters, doing the operation, jumping back to the code - and only for one line?)
is it better to put such lines in functions or to just put them in the code? Even if we use them only once?
BTW, I haven't found any question about that, so forgive me if such question had been asked before.
Don't be scared of 1-line functions!
A lot of programmers seem to have a mental block about 1-line functions, you shouldn't.
If it makes the code clearer and cleaner, extract the line into a function.
Performance probably won't be affected.
Any decent compiler made in the last decade (and perhaps further) will automatically inline a simple 1-line function. Also, 1-line of C can easily correspond to many lines of machine code. You shouldn't assume that even in the theoretical case where you incur the full overhead of a function call that this overhead is significant compared to your "one little line". Let alone significant to the overall performance of your application.
Abstraction Leads to Better Design. (Even for single lines of code)
Functions are the primary building blocks of abstract, componentized code, they should not be neglected. If encapsulating a single line of code behind a function call makes the code more readable, do it. Even in the case where the function is called once. If you find it important to comment one particular line of code, that's a good code smell that it might be helpful to move the code into a well-named function.
Sure, that code may be 1-line today, but how many different ways of performing the same function are there? Encapsulating code inside a function can make it easier to see all the design options available to you. Maybe your 1-line of code expands into a call to a webservice, maybe it becomes a database query, maybe it becomes configurable (using the strategy pattern, for example), maybe you want to switch to caching the value computed by your 1-line. All of these options are easier to implement and more readily thought of when you've extracted your 1-line of code into its own function.
Maybe Your 1-Line Should Be More Lines.
If you have a big block of code it can be tempting to cram a lot of functionality onto a single line, just to save on screen real estate. When you migrate this code to a function, you reduce these pressures, which might make you more inclined to expand your complex 1-liner into more straightforward code taking up several lines (which would likely improve its readability and maintainability).
I am not a fan of having all sort of logic and functionality banged into one line. The example you have shown is a mess and could be broken down into several lines, using meaningful variable names and performing one operation after another.
I strongly recommend, in every question of this kind, to have a look (buy it, borrow it, (don't) download it (for free)) at this book: Robert C. Martin - Clean Code. It is a book every developer should have a look at.
It will not make you a good coder right away and it will not stop you from writing ugly code in the future, it will however make you realise it when you are writing ugly code. It will force you to look at your code with a more critical eye and to make your code readable like a newspaper story.
If used more than once, definitely make it a function, and let the compiler do the inlining (possibly adding "inline" to the function definition). (<Usual advice about premature optimization goes here>)
Since your example appears to be using a C(++) syntax you may want to read up on inline functions which eliminate the overhead of calling a simple function. This keyword is only recommendation to the compiler though and it may not inline all functions that you mark, and may choose to inline unmarked functions.
In .NET the JIT will inline methods that it feels is appropiate, but you have no control over why or when it does this, though (as I understand it) debug builds will never inline since that would stop the source code matching the compiled application.
What language? If you mean C, I'd also use the inline qualifier. In C++, I have the option of inline, boost.lamda or and moving forward C++0x native support for lamdas.
There is nothing wrong with one line functions. As mentioned it is possible for the compiler to inline the functions which will remove any performance penalty.
Functions should also be preferred over macros as they are easier to debug, modify, read and less likely to have unintended side effects.
If it is used only once then the answer is less obvious. Moving it to a function can make the calling function simpler & clearer by moving some of the complexity into the new function.
If you use the code within that function 3 times or more, then I would recommend to put that in a function. Only for maintainability.
Sometimes it's not a bad idea to use the preprocessor:
#define addint(S, n) (*S)[n/CHAR_SIZE] |= (unsigned char) pow(2, (CHAR_SIZE - 1) - (n % CHAR_SIZE));
Granted, you don't get any kind of type checking, but in some cases this can be useful. Macros have their disadvantages and their advantages, and in a few cases their disadvantages can become advantages. I'm a fan of macros in appropriate places, but it's up to you to decide when is appropriate. In this case, I'm going to go out on a limb and say that, whatever you end up doing, that one line of code is quite a bit.
#define addint(S, n) do { \
unsigned char c = pow(2, (CHAR_SIZE -1) - (n % CHAR_SIZE)); \
(*S)[n/CHAR_SIZE] |= c \
} while(0)
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What is the clearest explanation of what computer scientists mean by "the naive implementation"? I need a good clear example which will illustrate — ideally, even to non-technical people — that the naive implementation may technically be a functioning solution to the problem, but practically be utterly unusable.
I'd try to keep it away from computers altogether. Ask your audience how they find an entry in a dictionary. (A normal dictionary of word definitions.)
The naive implementation is to start at the very beginning, and look at the first word. Oh, that's not the word we're looking for - look at the next one, etc. It's worth pointing out to the audience that they probably didn't even think of that way of doing things - we're smart enough to discount it immediately! It is, however, about the simplest way you could think of. (It might be interesting to ask them whether they can think of anything simpler, and check that they do really understand why it's simpler than the way we actually do it.)
The next implementation (and a pretty good one) is to start in the middle of the dictionary. Does the word we're looking for come before or after that? If it's before, turn to the page half way between the start and where we are now - otherwise, turn to the page half way between where we are now and the end, etc - binary chop.
The actual human implementation is to use our knowledge of letters to get very rapidly to "nearly the right place" - if we see "elephant" then we'll know it'll be "somewhere near the start" maybe about 1/5th of the way through. Once we've got to E (which we can do with very, very simple comparisons) we find EL etc.
StackOverflow's Jeff Atwood had a great example of a naive algorithm related to shuffling an array.
Doing it the most straightforward, least tricky way available. One example is selection sort.
In this case naive does not mean bad or unusable. It just means not particularly good.
Taking Jon Skeet's advice to heart you can describe selection sort as:
Find the highest value in the list and put it first
Find the next highest value and add it to the list
Repeat step 2 until you run out of list
It is easy to do and easy to understand, but not necessarily the best.
another naive implementation would be the use of recursion in computing for an integer's factorial in an imperative language. a more efficient solution in that case is to just use a loop.
What's the most obvious, naive algorithm for exponentiation that you could think of?
base ** exp is base * base * ... * base, exp times:
double pow(double base, int exp) {
double result = 1;
for (int i = 0; i < exp; i++)
result *= base;
return result;
}
It doesn't handle negative exponents, though. Remembering that base ** exp == 1 / base ** (-exp) == (1 / base) ** (-exp):
double pow(double base, int exp) {
double result = 1;
if (exp < 0) {
base = 1 / base;
exp = -exp;
}
for (int i = 0; i < exp; i++)
result *= base;
return result;
}
It's actually possible to compute base ** exp with less than exp multiplications, though!
double pow(double base, int exp) {
double result = 1;
if (exp < 0) {
base = 1 / base;
exp = -exp;
}
while (exp) {
if (exp % 2) {
result *= base;
exp--;
}
else {
base *= base;
exp /= 2;
}
}
return result * base;
}
This takes advantage of the fact that base ** exp == (base * base) ** (exp / 2) if exp is even, and will only require about log2(exp) multiplications.
I took the time to read your question a little closer, and I have the perfect example.
a good clear example which will illustrate -- ideally, even to non-technical people -- that the naive implementation may technically be a functioning solution to the problem, but practically be utterly unusable.
Try Bogosort!
If bogosort were used to sort a deck of cards, it would consist of checking if the deck were in order, and if it were not, one would throw the deck into the air, pick up the cards up at random, and repeat the process until the deck is sorted.
"Naive implementation" is almost always synonymous with "brute-force implementation". Naive implementations are often intuitive and the first to come to mind, but are also often O(n^2) or worse, thus taking too long too be practical for large inputs.
Programming competitions are full of problems where the naive implementation will fail to run in an acceptable amount of time, and the heart of the problem is coming up with an improved algorithm that is generally much less obvious but runs much more quickly.
Naive implementation is:
intuitive;
first to come in mind;
often inffective and/or buggy incorner cases;
Let's say that someone figures out how to extract a single field from a database and then proceeds to write a web page in PHP or any language that makes a separate query on the database for each field on the page. It works, but will be incredibly slow, inefficient, and difficult to maintain.
Naive doesn't mean bad or unusable - it means having certain qualities which pose a problem in a specific context and for a specific purpose.
The classic example of course is sorting. In the context of sorting a list of ten numbers, any old algorithm (except pogo sort) would work pretty well. However, when we get to the scale of thousands of numbers or more, typically we say that selection sort is the naive algorithm because it has the quality of O(n^2) time which would be too slow for our purposes, and that the non-naive algorithm is quicksort because it has the quality of O(n lg n) time which is fast enough for our purposes.
In fact, the case could be made that in the context of sorting a list of ten numbers, quicksort is the naive algorithm, since it will take longer than selection sort.
Determining if a number is prime or not (primality test) is an excellent example.
The naive method just check if n mod x where x = 2..square root(n) is zero for at least one x. This method can get really slow for very large prime numbers and it is not feasible to use in cryptography.
On the other hand there are a couple of probability or fast deterministic tests. These are too complicated to explain here but you might want to check the relevant Wikipedia article on the subject for more information: http://en.wikipedia.org/wiki/Primality_test
Bubble sort over 100,000 thousand entries.
The intuitive algorithms you normally use to sort a deck of cards (insertion sort or selection sort, both O(n^2)) can be considered naive, because they are easy to learn and implement, but would not scale well to a deck of, say, 100000 cards :D . In a general setting, there are faster (O(n log n)) ways to sort a list.
Note, however, that naive does not necessarily mean bad. There are situations where insertion sort is a good choice (say, when you have an already sorted big deck and few unsorted cards to add).
(Haven't seen a truly naive implementation posted yet so...)
The following implementation is "naive", because it does not cover the edge cases, and will break in other cases. It is very simple to understand, and can convey a programming message.
def naive_inverse(x):
return 1/x
It will:
Break on x=0
Do a bad job when passed an integer
You could make it more "mature" by adding these features.
A O(n!) algorithm.
foreach(object o in set1)
{
foreach(object p in set1)
{
// codez
}
}
This will perform fine with small sets and then exponentially worse with larger ones.
Another might be a naive Singleton that doesn't account for threading.
public static SomeObject Instance
{
get
{
if(obj == null)
{
obj = new SomeObject();
}
return obj;
}
}
If two threads access that at the same time it's possible for them to get two different versions. Leading to seriously weird bugs.