Following code is part of contnrs unit of FreePascal
constructor TFPCustomHashTable.Create;
begin
CreateWith(196613,#RSHash);
end;
I am curious about 196613. I know it is hash table size. Is there any particular reason why this value is used?
In my test, constructor took about 3-4 ms to execute, which in my particular situation is not accepted. I suspect this is related to this constant value.
Update:
My question are:
Why 196613 is chosen? Why not other prime number?
Does it affect constructor call execution time?
196613 is one of the numbers being recommended for hash tables sizes (prime and far away from powers of two), for more info see e.g. https://planetmath.org/goodhashtableprimes.
It affects the constructor call execution time, yes. You can always construct TFPCustomHashTable using CreateWith and pass a size of your choice (any number is fine, as resizing algorithm checks for suitable sizes anyways) as well as your own hash function (or the pre-defined RSHash):
MyHashTable:=TFPCustomHashTable.CreateWith(193,#RSHash);
Keep in mind though, that resizing a hash table is an expensive operation as it requires to recalculate the hash function for all elements, so starting with a too small value is neither a good idea.
I was reading up on the std::string class in C++ and noticed there are quite a few different constructors available giving us a wide set of initialization features. This got me wondering how a compiler picks which constructor to choose when given parameters, or in the case of overloads, how a compiler matches a function signature with a given set of parameters.
If we have the following functions declared in pseudo-code:
function f1(int numberHere) {
//....do something
}
function f1(int numberHere, string stringHere) {
//....do something
}
And I decide to call f1(4), there are obviously two options to choose from, but what if there are 10000 options/signatures? Would it take proportionally longer? If so, what takes longer? Does the compiler have some sneaky O(n) way to index overloads such that it can call the right one in O(1) time once the program is running or would it compile in O(1) no matter how many overloads exist but take longer to run the finished result because of on-the-fly signature matching?
Can this question even be answered effectively?
Thanks!
Matching function signatures is actually not different from any other search or lookup problem. There are three basic ways to do it depending on the data structure you are storing the available function signatures in:
Use an unsorted list or array and get O(n) time complexity.
Use a sorted array or a tree-like structure and get O(log(n)). (You can sort by type of 1st argument, then 2nd and so on, assuming that each type has an integer id assigned to it.)
Use a hash map and get O(1).
But I doubt that time complxity has any practical relevance in this case. It describes the asymptotic behaviour of algorithms for large values of n. Even for n=100, an unsorted array search might be faster than hash map lookup because it has less overhead.
And from a usability point of view it is a very bad idea to design an API having functions with 10 or even 100 overloads.
I recently had to use a GPS location API where each location object had among other things two properties altitude and verticalAccuracy. A negative verticalAccuracy signifies that altitude is invalid, whereas normally a smaller but positive value of verticalAccuracy actually means that altitude is more precise (since it's the vertical distance that it may be off by - I'll leave the discussion as to why this measure is called verticalAccuracy and not verticalInaccuracy for some other time).
This got me thinking: When is it a good idea to use sentinel values like this API does and when would it be better to explicitly make a separate hasValidAltitude property? Are there other options?
Sometimes, sentinel answers aren't really possible; maybe the function's range coincides with the codomain (range). This isn't the case with altitude, unless you allow negative altitudes (maybe in the future, there will be underwater cities). For instance, maybe we're talking about the intersection between lines (not a great example, since floating-points have a few built-in sentinels like +INF and NaN) or the precise integer quotient (without rounding, this is not guaranteed to exist... 7 and 3, for instance... here, the remainder after division can be viewed as either a sentinel or a "exact integer quotient exists" property). More generally, any reliable sentinel can be trivially used to construct a property-based mechanism.
Based on this, I'd recommend avoiding sentinels wherever this is possible and makes sense. My reasoning is that they are an internal implementation detail of the module, and should be encapsulated behind an information-hiding interface.
Can you suggest a precise definition for a 'value' within the context of programming without reference to specific encoding techniques or particular languages or architectures?
[Previous question text, for discussion reference: "What is value in programming? How to define this word precisely?"]
I just happened to be glancing through Pierce's "Types and Programming Languages" - he slips a reasonably precise definition of "value" in a programming context into the text:
[...] defines a subset of terms, called values, that are possible final results of evaluation
This seems like a rather tidy definition - i.e., we take the set of all possible terms, and the ones that can possibly be left over after all evaluation has taken place are values.
Based on the ongoing comments about "bits" being an unacceptable definition, I think this one is a little better (although possibly still flawed):
A value is anything representable on a piece of possibly-infinite Turing machine tape.
Edit: I'm refining this some more.
A value is a member of the set of possible interpretations of any possibly-infinite sequence of symbols.
That is equivalent to the earlier definition based on Turing machine tape, but it actually generalises better.
Here, I'll take a shot: A value is a piece of stored information (in the information-theoretical sense) that can be manipulated by the computer.
(I won't say that a value has meaning; a random number in a register may have no meaning, but it's still a value.)
In short, a value is some assigned meaning to a variable (the object containing the value)
For example type=boolean; name=help; variable=a storage location; value=what is stored in that location;
Further break down:
X = 2; where X is a variable while 2 is the value stored in X.
Have you checked the article in wikipedia?
In computer science, a value is a sequence of bits that is interpreted according to some data type. It is possible for the same sequence of bits to have different values, depending on the type used to interpret its meaning. For instance, the value could be an integer or floating point value, or a string.
Read the Wiki
Value = Value is what we call the "contents" that was stored in the variable
Variables = containers for storing data values
Example: Think of a folder named "Movies"(Variables) and inside of it are it contents which are namely; Pirates of the Carribean, Fantastic Beast, and Lala land, (this in turn is what we now call it's Values )
The word seems to get used in a number of contexts. The best I can figure is that they mean a variable that can't change. Isn't that what constants/finals (darn you Java!) are for?
An invariant is more "conceptual" than a variable. In general, it's a property of the program state that is always true. A function or method that ensures that the invariant holds is said to maintain the invariant.
For instance, a binary search tree might have the invariant that for every node, the key of the node's left child is less than the node's own key. A correctly written insertion function for this tree will maintain that invariant.
As you can tell, that's not the sort of thing you can store in a variable: it's more a statement about the program. By figuring out what sort of invariants your program should maintain, then reviewing your code to make sure that it actually maintains those invariants, you can avoid logical errors in your code.
It is a condition you know to always be true at a particular place in your logic and can check for when debugging to work out what has gone wrong.
The magic of wikipedia: Invariant (computer science)
In computer science, a predicate that,
if true, will remain true throughout a
specific sequence of operations, is
called (an) invariant to that
sequence.
This answer is for my 5 year old kid. Do not think of an invariant as a constant or fixed numerical value. But it can be. However, it is more than that.
Rather, an invariant is something like of a fixed relationship between varying entities. For example, your age will always be less than that compared to your biological parents. Both your age, and your parent's age changes in the passage of time, but the relationship that i mentioned above is an invariant.
An invariant can also be a numerical constant. For example, the value of pi is an invariant ratio between the circle's circumference over its diameter. No matter how big or small the circle is, that ratio will always be pi.
I usually view them more in terms of algorithms or structures.
For example, you could have a loop invariant that could be asserted--always true at the beginning or end of each iteration. That is, if your loop was supposed to process a collection of objects from one stack to another, you could say that |stack1|+|stack2|=c, at the top or bottom of the loop.
If the invariant check failed, it would indicate something went wrong. In this example, it could mean that you forgot to push the processed element onto the final stack, etc.
As this line states:
In computer science, a predicate that, if true, will remain true throughout a specific sequence of operations, is called (an) invariant to that sequence.
To better understand this hope this example in C++ helps.
Consider a scenario where you have to get some values and get the total count of them in a variable called as count and add them in a variable called as sum
The invariant (again it's more like a concept):
// invariant:
// we have read count grades so far, and
// sum is the sum of the first count grades
The code for the above would be something like this,
int count=0;
double sum=0,x=0;
while (cin >> x) {
++count;
sum+=x;
}
What the above code does?
1) Reads the input from cin and puts them in x
2) After one successful read, increment count and sum = sum + x
3) Repeat 1-2 until read stops ( i.e ctrl+D)
Loop invariant:
The invariant must be True ALWAYS. So initially you start out your code with just this
while(cin>>x){
}
This loop reads data from standard input and stores in x. Well and good. But the invariant becomes false because the first part of our invariant wasn't followed (or kept true).
// we have read count grades so far, and
How to keep the invariant true?
Simple! increment count.
So ++count; would do good!. Now our code becomes something like this,
while(cin>>x){
++count;
}
But
Even now our invariant (a concept which must be TRUE) is False because now we didn't satisfy the second part of our invariant.
// sum is the sum of the first count grades
So what to do now?
Add x to sum and store it in sum ( sum+=x) and the next time
cin>>x will read a new value into x.
Now our code becomes something like this,
while(cin>>x){
++count;
sum+=x;
}
Let's check
Whether code matches our invariant
// invariant:
// we have read count grades so far, and
// sum is the sum of the first count grades
code:
while(cin>>x){
++count;
sum+=x;
}
Ah!. Now the loop invariant is True always and code works fine.
The above example was taken and modified from the book Accelerated C++ by Andrew-koening and Barbara-E
Something that doesn't change within a block of code
All the answers here are great, but i felt that i can shed more light on the matter:
Invariant from a language point of view means something that never changes. The concept though comes actually from math, it's one of the popular proof techniques when combined with induction.
Here is how a proof goes, If you can find an invariant that is in the initial state, And that this invariant persists regardless of any [legal] transformation applied to the state, then you can prove that If a certain state does not have this invariant then it can never occur, no matter what sequence of transformations are applied to the initial state.
Now the previous way of thinking (again combined with induction) makes it possible to predicate the logic of computer software. Especially important when the execution goes in loops, in which an invariant can be used to prove that a certain loop will yield a certain result or that it will never change the state of a program in a certain way.
When invariant is used to predicate a loop logic its called loop invariant. It can be used outside loops, but for loops it is really important, because you often have a lot of possibilities, or an infinite number of possibilities.
Notice that i use the word "predicate" the logic of a computer software, and not prove. And that's because while in math invariant can be used as a proof, it can never prove that the computer software when executed will yield what is expected, due to the fact that the software is executed on top of many abstractions, that can never be proved that they will yield what is expected (think of the hardware abstraction for example).
Finally while theoretically and rigorously predicting software logic is only important for high critical applications like Medical, and Military ones. Invariant can still be used to aid the typical programmer when debugging. It can be used to know where at a certain location The program failed because it has failed to maintain a certain invariant - many of us use it anyway without giving a thought about it.
Class Invariant
Class Invariant is a condition which should be always true before and after calling relevant function
For example balanced tree has an Invariant which is called isBalanced. When you modify your tree through some methods (e.g. addNode, removeNode...) - isBalanced should be always true before and after modifying the tree
Following on from what it is, invariants are quite useful in writing clean code, since knowing conceptually what invariants should be present in your code allows you to easily decide how to organize your code to reach those aims. As mentioned ealier, they're also useful in debugging, as checking to see if the invariant's being maintained is often a good way of seeing if whatever manipulation you're attempting to perform is actually doing what you want it to.
It's typically a quantity that does not change under certain mathematical operations.
An example is a scalar, which does not change under rotations. In magnetic resonance imaging, for example, it is useful to characterize a tissue property by a rotational invariant, because then its estimation ideally does not depend on the orientation of the body in the scanner.
The ADT invariant specifes relationships
among the data fields (instance variables)
that must always be true before and after
the execution of any instance method.
There is an excellent example of an invariant and why it matters in the book Java Concurrency in Practice.
Although Java-centric, the example describes some code that is responsible for calculating the factors of a provided integer. The example code attempts to cache the last number provided, and the factors that were calculated to improve performance. In this scenario there is an invariant that was not accounted for in the example code which has left the code susceptible to race conditions in a concurrent scenario.