Is it possible that Javascript keep same expression value? - javascript

I was wondering if javascript calculate (again) same expressions as it encounters them :
for example :
alert(new Date().getTime()+1-1+1-1+1-1+1-1+1-1+1-1+1-1+1-1+1-1+1-1-new Date().getTime())
output : 0
it's hard to test it like it but I thought that all the +/-1 will take it some time ( a tick) so I could see a difference.
But the answer is 0.
So ,
Is it zero because its just too fast or because JS treats the first new Date() as the same as the later one ?

GetTime() returns the number of milliseconds since the Unix epoch. Given that in theory an addition takes just one FLOP on a modern processor (which runs in the billions of FLOPS), I would say that it is extremely likely that the processor simply executes the entire statement in less than one millisecond.
Of course the way to really test this would be to run this billions of times in a loop and let the law of large numbers sort out the rest. To make things even easier, you could also try using alternating multiplication and division by an arbitrarily large number to make the execution take longer.
At any rate, keep in mind that in general, languages don't tend to optimise a function unless it always, or almost always makes sense to do so. In your specific case, how could the program reasonably assume that you aren't trying to measure how long the arithmetic takes? And what if you decomposed the single-line statement into several smaller statements? You would be doing the exact same thing... would it be reasonable in this case for the date/time function to act differently?
In short, I can think of many cases in which caching the date/time would cause serious problems in program execution. I can't imagine that the infinitesimally small performance boost provided by the caching would make up for them.

Yes, 10 + operations and 10 - operations are probably not going to take a millisecond. You can test it like this:
var c = (new Date().getTime() + calc() - new Date().getTime());
function calc() {
for (var i = 0; i < 100000000; i++) {}
return 0;
}
console.log(c);
And you really are going to get an output that doesn't equal zero.

To answer the crux of your question, which the other answers seem to be missing; no, it's not possible that the two calls to new Date() are optimized into the same thing. These two separate calls return distinct objects and for the engine to simply optimize the two distinct calls into one call would be completely invalid.
Consider, for example, if you had done this with a different method that returned a new Date object but this method included a 20 second delay in it (or an incremented return value each call) - the two getTime results should be thousands of ticks apart but your proposed "optimization" would cause them to return the same value.
What if the Date() function returned a random integer between 1 and 10,000?
There would be no way for the engine to know that the two calls should return the same value (which, incidentally, they shouldn't) without knowing what the returned values should be and, in order to know this, it would have to execute both methods anyway.
So, yes, it's because the calls are completed less than a millisecond apart.

That will depend on the JavaScript engine. If the code is being pre-compiled, your +/- 1 calculation might be optimized away.

Related

How does this code properly return its value? [duplicate]

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One of the topics that seems to come up regularly on mailing lists and online discussions is the merits (or lack thereof) of doing a Computer Science Degree. An argument that seems to come up time and again for the negative party is that they have been coding for some number of years and they have never used recursion.
So the question is:
What is recursion?
When would I use recursion?
Why don't people use recursion?
There are a number of good explanations of recursion in this thread, this answer is about why you shouldn't use it in most languages.* In the majority of major imperative language implementations (i.e. every major implementation of C, C++, Basic, Python, Ruby,Java, and C#) iteration is vastly preferable to recursion.
To see why, walk through the steps that the above languages use to call a function:
space is carved out on the stack for the function's arguments and local variables
the function's arguments are copied into this new space
control jumps to the function
the function's code runs
the function's result is copied into a return value
the stack is rewound to its previous position
control jumps back to where the function was called
Doing all of these steps takes time, usually a little bit more than it takes to iterate through a loop. However, the real problem is in step #1. When many programs start, they allocate a single chunk of memory for their stack, and when they run out of that memory (often, but not always due to recursion), the program crashes due to a stack overflow.
So in these languages recursion is slower and it makes you vulnerable to crashing. There are still some arguments for using it though. In general, code written recursively is shorter and a bit more elegant, once you know how to read it.
There is a technique that language implementers can use called tail call optimization which can eliminate some classes of stack overflow. Put succinctly: if a function's return expression is simply the result of a function call, then you don't need to add a new level onto the stack, you can reuse the current one for the function being called. Regrettably, few imperative language-implementations have tail-call optimization built in.
* I love recursion. My favorite static language doesn't use loops at all, recursion is the only way to do something repeatedly. I just don't think that recursion is generally a good idea in languages that aren't tuned for it.
** By the way Mario, the typical name for your ArrangeString function is "join", and I'd be surprised if your language of choice doesn't already have an implementation of it.
Simple english example of recursion.
A child couldn't sleep, so her mother told her a story about a little frog,
who couldn't sleep, so the frog's mother told her a story about a little bear,
who couldn't sleep, so the bear's mother told her a story about a little weasel...
who fell asleep.
...and the little bear fell asleep;
...and the little frog fell asleep;
...and the child fell asleep.
In the most basic computer science sense, recursion is a function that calls itself. Say you have a linked list structure:
struct Node {
Node* next;
};
And you want to find out how long a linked list is you can do this with recursion:
int length(const Node* list) {
if (!list->next) {
return 1;
} else {
return 1 + length(list->next);
}
}
(This could of course be done with a for loop as well, but is useful as an illustration of the concept)
Whenever a function calls itself, creating a loop, then that's recursion. As with anything there are good uses and bad uses for recursion.
The most simple example is tail recursion where the very last line of the function is a call to itself:
int FloorByTen(int num)
{
if (num % 10 == 0)
return num;
else
return FloorByTen(num-1);
}
However, this is a lame, almost pointless example because it can easily be replaced by more efficient iteration. After all, recursion suffers from function call overhead, which in the example above could be substantial compared to the operation inside the function itself.
So the whole reason to do recursion rather than iteration should be to take advantage of the call stack to do some clever stuff. For example, if you call a function multiple times with different parameters inside the same loop then that's a way to accomplish branching. A classic example is the Sierpinski triangle.
You can draw one of those very simply with recursion, where the call stack branches in 3 directions:
private void BuildVertices(double x, double y, double len)
{
if (len > 0.002)
{
mesh.Positions.Add(new Point3D(x, y + len, -len));
mesh.Positions.Add(new Point3D(x - len, y - len, -len));
mesh.Positions.Add(new Point3D(x + len, y - len, -len));
len *= 0.5;
BuildVertices(x, y + len, len);
BuildVertices(x - len, y - len, len);
BuildVertices(x + len, y - len, len);
}
}
If you attempt to do the same thing with iteration I think you'll find it takes a lot more code to accomplish.
Other common use cases might include traversing hierarchies, e.g. website crawlers, directory comparisons, etc.
Conclusion
In practical terms, recursion makes the most sense whenever you need iterative branching.
Recursion is a method of solving problems based on the divide and conquer mentality.
The basic idea is that you take the original problem and divide it into smaller (more easily solved) instances of itself, solve those smaller instances (usually by using the same algorithm again) and then reassemble them into the final solution.
The canonical example is a routine to generate the Factorial of n. The Factorial of n is calculated by multiplying all of the numbers between 1 and n. An iterative solution in C# looks like this:
public int Fact(int n)
{
int fact = 1;
for( int i = 2; i <= n; i++)
{
fact = fact * i;
}
return fact;
}
There's nothing surprising about the iterative solution and it should make sense to anyone familiar with C#.
The recursive solution is found by recognising that the nth Factorial is n * Fact(n-1). Or to put it another way, if you know what a particular Factorial number is you can calculate the next one. Here is the recursive solution in C#:
public int FactRec(int n)
{
if( n < 2 )
{
return 1;
}
return n * FactRec( n - 1 );
}
The first part of this function is known as a Base Case (or sometimes Guard Clause) and is what prevents the algorithm from running forever. It just returns the value 1 whenever the function is called with a value of 1 or less. The second part is more interesting and is known as the Recursive Step. Here we call the same method with a slightly modified parameter (we decrement it by 1) and then multiply the result with our copy of n.
When first encountered this can be kind of confusing so it's instructive to examine how it works when run. Imagine that we call FactRec(5). We enter the routine, are not picked up by the base case and so we end up like this:
// In FactRec(5)
return 5 * FactRec( 5 - 1 );
// which is
return 5 * FactRec(4);
If we re-enter the method with the parameter 4 we are again not stopped by the guard clause and so we end up at:
// In FactRec(4)
return 4 * FactRec(3);
If we substitute this return value into the return value above we get
// In FactRec(5)
return 5 * (4 * FactRec(3));
This should give you a clue as to how the final solution is arrived at so we'll fast track and show each step on the way down:
return 5 * (4 * FactRec(3));
return 5 * (4 * (3 * FactRec(2)));
return 5 * (4 * (3 * (2 * FactRec(1))));
return 5 * (4 * (3 * (2 * (1))));
That final substitution happens when the base case is triggered. At this point we have a simple algrebraic formula to solve which equates directly to the definition of Factorials in the first place.
It's instructive to note that every call into the method results in either a base case being triggered or a call to the same method where the parameters are closer to a base case (often called a recursive call). If this is not the case then the method will run forever.
Recursion is solving a problem with a function that calls itself. A good example of this is a factorial function. Factorial is a math problem where factorial of 5, for example, is 5 * 4 * 3 * 2 * 1. This function solves this in C# for positive integers (not tested - there may be a bug).
public int Factorial(int n)
{
if (n <= 1)
return 1;
return n * Factorial(n - 1);
}
Recursion refers to a method which solves a problem by solving a smaller version of the problem and then using that result plus some other computation to formulate the answer to the original problem. Often times, in the process of solving the smaller version, the method will solve a yet smaller version of the problem, and so on, until it reaches a "base case" which is trivial to solve.
For instance, to calculate a factorial for the number X, one can represent it as X times the factorial of X-1. Thus, the method "recurses" to find the factorial of X-1, and then multiplies whatever it got by X to give a final answer. Of course, to find the factorial of X-1, it'll first calculate the factorial of X-2, and so on. The base case would be when X is 0 or 1, in which case it knows to return 1 since 0! = 1! = 1.
Consider an old, well known problem:
In mathematics, the greatest common divisor (gcd) … of two or more non-zero integers, is the largest positive integer that divides the numbers without a remainder.
The definition of gcd is surprisingly simple:
where mod is the modulo operator (that is, the remainder after integer division).
In English, this definition says the greatest common divisor of any number and zero is that number, and the greatest common divisor of two numbers m and n is the greatest common divisor of n and the remainder after dividing m by n.
If you'd like to know why this works, see the Wikipedia article on the Euclidean algorithm.
Let's compute gcd(10, 8) as an example. Each step is equal to the one just before it:
gcd(10, 8)
gcd(10, 10 mod 8)
gcd(8, 2)
gcd(8, 8 mod 2)
gcd(2, 0)
2
In the first step, 8 does not equal zero, so the second part of the definition applies. 10 mod 8 = 2 because 8 goes into 10 once with a remainder of 2. At step 3, the second part applies again, but this time 8 mod 2 = 0 because 2 divides 8 with no remainder. At step 5, the second argument is 0, so the answer is 2.
Did you notice that gcd appears on both the left and right sides of the equals sign? A mathematician would say this definition is recursive because the expression you're defining recurs inside its definition.
Recursive definitions tend to be elegant. For example, a recursive definition for the sum of a list is
sum l =
if empty(l)
return 0
else
return head(l) + sum(tail(l))
where head is the first element in a list and tail is the rest of the list. Note that sum recurs inside its definition at the end.
Maybe you'd prefer the maximum value in a list instead:
max l =
if empty(l)
error
elsif length(l) = 1
return head(l)
else
tailmax = max(tail(l))
if head(l) > tailmax
return head(l)
else
return tailmax
You might define multiplication of non-negative integers recursively to turn it into a series of additions:
a * b =
if b = 0
return 0
else
return a + (a * (b - 1))
If that bit about transforming multiplication into a series of additions doesn't make sense, try expanding a few simple examples to see how it works.
Merge sort has a lovely recursive definition:
sort(l) =
if empty(l) or length(l) = 1
return l
else
(left,right) = split l
return merge(sort(left), sort(right))
Recursive definitions are all around if you know what to look for. Notice how all of these definitions have very simple base cases, e.g., gcd(m, 0) = m. The recursive cases whittle away at the problem to get down to the easy answers.
With this understanding, you can now appreciate the other algorithms in Wikipedia's article on recursion!
A function that calls itself
When a function can be (easily) decomposed into a simple operation plus the same function on some smaller portion of the problem. I should say, rather, that this makes it a good candidate for recursion.
They do!
The canonical example is the factorial which looks like:
int fact(int a)
{
if(a==1)
return 1;
return a*fact(a-1);
}
In general, recursion isn't necessarily fast (function call overhead tends to be high because recursive functions tend to be small, see above) and can suffer from some problems (stack overflow anyone?). Some say they tend to be hard to get 'right' in non-trivial cases but I don't really buy into that. In some situations, recursion makes the most sense and is the most elegant and clear way to write a particular function. It should be noted that some languages favor recursive solutions and optimize them much more (LISP comes to mind).
A recursive function is one which calls itself. The most common reason I've found to use it is traversing a tree structure. For example, if I have a TreeView with checkboxes (think installation of a new program, "choose features to install" page), I might want a "check all" button which would be something like this (pseudocode):
function cmdCheckAllClick {
checkRecursively(TreeView1.RootNode);
}
function checkRecursively(Node n) {
n.Checked = True;
foreach ( n.Children as child ) {
checkRecursively(child);
}
}
So you can see that the checkRecursively first checks the node which it is passed, then calls itself for each of that node's children.
You do need to be a bit careful with recursion. If you get into an infinite recursive loop, you will get a Stack Overflow exception :)
I can't think of a reason why people shouldn't use it, when appropriate. It is useful in some circumstances, and not in others.
I think that because it's an interesting technique, some coders perhaps end up using it more often than they should, without real justification. This has given recursion a bad name in some circles.
Recursion is an expression directly or indirectly referencing itself.
Consider recursive acronyms as a simple example:
GNU stands for GNU's Not Unix
PHP stands for PHP: Hypertext Preprocessor
YAML stands for YAML Ain't Markup Language
WINE stands for Wine Is Not an Emulator
VISA stands for Visa International Service Association
More examples on Wikipedia
Recursion works best with what I like to call "fractal problems", where you're dealing with a big thing that's made of smaller versions of that big thing, each of which is an even smaller version of the big thing, and so on. If you ever have to traverse or search through something like a tree or nested identical structures, you've got a problem that might be a good candidate for recursion.
People avoid recursion for a number of reasons:
Most people (myself included) cut their programming teeth on procedural or object-oriented programming as opposed to functional programming. To such people, the iterative approach (typically using loops) feels more natural.
Those of us who cut our programming teeth on procedural or object-oriented programming have often been told to avoid recursion because it's error prone.
We're often told that recursion is slow. Calling and returning from a routine repeatedly involves a lot of stack pushing and popping, which is slower than looping. I think some languages handle this better than others, and those languages are most likely not those where the dominant paradigm is procedural or object-oriented.
For at least a couple of programming languages I've used, I remember hearing recommendations not to use recursion if it gets beyond a certain depth because its stack isn't that deep.
A recursive statement is one in which you define the process of what to do next as a combination of the inputs and what you have already done.
For example, take factorial:
factorial(6) = 6*5*4*3*2*1
But it's easy to see factorial(6) also is:
6 * factorial(5) = 6*(5*4*3*2*1).
So generally:
factorial(n) = n*factorial(n-1)
Of course, the tricky thing about recursion is that if you want to define things in terms of what you have already done, there needs to be some place to start.
In this example, we just make a special case by defining factorial(1) = 1.
Now we see it from the bottom up:
factorial(6) = 6*factorial(5)
= 6*5*factorial(4)
= 6*5*4*factorial(3) = 6*5*4*3*factorial(2) = 6*5*4*3*2*factorial(1) = 6*5*4*3*2*1
Since we defined factorial(1) = 1, we reach the "bottom".
Generally speaking, recursive procedures have two parts:
1) The recursive part, which defines some procedure in terms of new inputs combined with what you've "already done" via the same procedure. (i.e. factorial(n) = n*factorial(n-1))
2) A base part, which makes sure that the process doesn't repeat forever by giving it some place to start (i.e. factorial(1) = 1)
It can be a bit confusing to get your head around at first, but just look at a bunch of examples and it should all come together. If you want a much deeper understanding of the concept, study mathematical induction. Also, be aware that some languages optimize for recursive calls while others do not. It's pretty easy to make insanely slow recursive functions if you're not careful, but there are also techniques to make them performant in most cases.
Hope this helps...
I like this definition:
In recursion, a routine solves a small part of a problem itself, divides the problem into smaller pieces, and then calls itself to solve each of the smaller pieces.
I also like Steve McConnells discussion of recursion in Code Complete where he criticises the examples used in Computer Science books on Recursion.
Don't use recursion for factorials or Fibonacci numbers
One problem with
computer-science textbooks is that
they present silly examples of
recursion. The typical examples are
computing a factorial or computing a
Fibonacci sequence. Recursion is a
powerful tool, and it's really dumb to
use it in either of those cases. If a
programmer who worked for me used
recursion to compute a factorial, I'd
hire someone else.
I thought this was a very interesting point to raise and may be a reason why recursion is often misunderstood.
EDIT:
This was not a dig at Dav's answer - I had not seen that reply when I posted this
1.)
A method is recursive if it can call itself; either directly:
void f() {
... f() ...
}
or indirectly:
void f() {
... g() ...
}
void g() {
... f() ...
}
2.) When to use recursion
Q: Does using recursion usually make your code faster?
A: No.
Q: Does using recursion usually use less memory?
A: No.
Q: Then why use recursion?
A: It sometimes makes your code much simpler!
3.) People use recursion only when it is very complex to write iterative code. For example, tree traversal techniques like preorder, postorder can be made both iterative and recursive. But usually we use recursive because of its simplicity.
Here's a simple example: how many elements in a set. (there are better ways to count things, but this is a nice simple recursive example.)
First, we need two rules:
if the set is empty, the count of items in the set is zero (duh!).
if the set is not empty, the count is one plus the number of items in the set after one item is removed.
Suppose you have a set like this: [x x x]. let's count how many items there are.
the set is [x x x] which is not empty, so we apply rule 2. the number of items is one plus the number of items in [x x] (i.e. we removed an item).
the set is [x x], so we apply rule 2 again: one + number of items in [x].
the set is [x], which still matches rule 2: one + number of items in [].
Now the set is [], which matches rule 1: the count is zero!
Now that we know the answer in step 4 (0), we can solve step 3 (1 + 0)
Likewise, now that we know the answer in step 3 (1), we can solve step 2 (1 + 1)
And finally now that we know the answer in step 2 (2), we can solve step 1 (1 + 2) and get the count of items in [x x x], which is 3. Hooray!
We can represent this as:
count of [x x x] = 1 + count of [x x]
= 1 + (1 + count of [x])
= 1 + (1 + (1 + count of []))
= 1 + (1 + (1 + 0)))
= 1 + (1 + (1))
= 1 + (2)
= 3
When applying a recursive solution, you usually have at least 2 rules:
the basis, the simple case which states what happens when you have "used up" all of your data. This is usually some variation of "if you are out of data to process, your answer is X"
the recursive rule, which states what happens if you still have data. This is usually some kind of rule that says "do something to make your data set smaller, and reapply your rules to the smaller data set."
If we translate the above to pseudocode, we get:
numberOfItems(set)
if set is empty
return 0
else
remove 1 item from set
return 1 + numberOfItems(set)
There's a lot more useful examples (traversing a tree, for example) which I'm sure other people will cover.
Well, that's a pretty decent definition you have. And wikipedia has a good definition too. So I'll add another (probably worse) definition for you.
When people refer to "recursion", they're usually talking about a function they've written which calls itself repeatedly until it is done with its work. Recursion can be helpful when traversing hierarchies in data structures.
An example: A recursive definition of a staircase is:
A staircase consists of:
- a single step and a staircase (recursion)
- or only a single step (termination)
To recurse on a solved problem: do nothing, you're done.
To recurse on an open problem: do the next step, then recurse on the rest.
In plain English:
Assume you can do 3 things:
Take one apple
Write down tally marks
Count tally marks
You have a lot of apples in front of you on a table and you want to know how many apples there are.
start
Is the table empty?
yes: Count the tally marks and cheer like it's your birthday!
no: Take 1 apple and put it aside
Write down a tally mark
goto start
The process of repeating the same thing till you are done is called recursion.
I hope this is the "plain english" answer you are looking for!
A recursive function is a function that contains a call to itself. A recursive struct is a struct that contains an instance of itself. You can combine the two as a recursive class. The key part of a recursive item is that it contains an instance/call of itself.
Consider two mirrors facing each other. We've seen the neat infinity effect they make. Each reflection is an instance of a mirror, which is contained within another instance of a mirror, etc. The mirror containing a reflection of itself is recursion.
A binary search tree is a good programming example of recursion. The structure is recursive with each Node containing 2 instances of a Node. Functions to work on a binary search tree are also recursive.
This is an old question, but I want to add an answer from logistical point of view (i.e not from algorithm correctness point of view or performance point of view).
I use Java for work, and Java doesn't support nested function. As such, if I want to do recursion, I might have to define an external function (which exists only because my code bumps against Java's bureaucratic rule), or I might have to refactor the code altogether (which I really hate to do).
Thus, I often avoid recursion, and use stack operation instead, because recursion itself is essentially a stack operation.
You want to use it anytime you have a tree structure. It is very useful in reading XML.
Recursion as it applies to programming is basically calling a function from inside its own definition (inside itself), with different parameters so as to accomplish a task.
"If I have a hammer, make everything look like a nail."
Recursion is a problem-solving strategy for huge problems, where at every step just, "turn 2 small things into one bigger thing," each time with the same hammer.
Example
Suppose your desk is covered with a disorganized mess of 1024 papers. How do you make one neat, clean stack of papers from the mess, using recursion?
Divide: Spread all the sheets out, so you have just one sheet in each "stack".
Conquer:
Go around, putting each sheet on top of one other sheet. You now have stacks of 2.
Go around, putting each 2-stack on top of another 2-stack. You now have stacks of 4.
Go around, putting each 4-stack on top of another 4-stack. You now have stacks of 8.
... on and on ...
You now have one huge stack of 1024 sheets!
Notice that this is pretty intuitive, aside from counting everything (which isn't strictly necessary). You might not go all the way down to 1-sheet stacks, in reality, but you could and it would still work. The important part is the hammer: With your arms, you can always put one stack on top of the other to make a bigger stack, and it doesn't matter (within reason) how big either stack is.
Recursion is the process where a method call iself to be able to perform a certain task. It reduces redundency of code. Most recurssive functions or methods must have a condifiton to break the recussive call i.e. stop it from calling itself if a condition is met - this prevents the creating of an infinite loop. Not all functions are suited to be used recursively.
hey, sorry if my opinion agrees with someone, I'm just trying to explain recursion in plain english.
suppose you have three managers - Jack, John and Morgan.
Jack manages 2 programmers, John - 3, and Morgan - 5.
you are going to give every manager 300$ and want to know what would it cost.
The answer is obvious - but what if 2 of Morgan-s employees are also managers?
HERE comes the recursion.
you start from the top of the hierarchy. the summery cost is 0$.
you start with Jack,
Then check if he has any managers as employees. if you find any of them are, check if they have any managers as employees and so on. Add 300$ to the summery cost every time you find a manager.
when you are finished with Jack, go to John, his employees and then to Morgan.
You'll never know, how much cycles will you go before getting an answer, though you know how many managers you have and how many Budget can you spend.
Recursion is a tree, with branches and leaves, called parents and children respectively.
When you use a recursion algorithm, you more or less consciously are building a tree from the data.
In plain English, recursion means to repeat someting again and again.
In programming one example is of calling the function within itself .
Look on the following example of calculating factorial of a number:
public int fact(int n)
{
if (n==0) return 1;
else return n*fact(n-1)
}
Any algorithm exhibits structural recursion on a datatype if basically consists of a switch-statement with a case for each case of the datatype.
for example, when you are working on a type
tree = null
| leaf(value:integer)
| node(left: tree, right:tree)
a structural recursive algorithm would have the form
function computeSomething(x : tree) =
if x is null: base case
if x is leaf: do something with x.value
if x is node: do something with x.left,
do something with x.right,
combine the results
this is really the most obvious way to write any algorith that works on a data structure.
now, when you look at the integers (well, the natural numbers) as defined using the Peano axioms
integer = 0 | succ(integer)
you see that a structural recursive algorithm on integers looks like this
function computeSomething(x : integer) =
if x is 0 : base case
if x is succ(prev) : do something with prev
the too-well-known factorial function is about the most trivial example of
this form.
function call itself or use its own definition.

How to generically solve the problem of generating incremental integer IDs in JavaScript

I have been thinking about this for a few days trying to see if there is a generic way to write this function so that you don't ever need to worry about it breaking again. That is, it is as robust as it can be, and it can support using up all of the memory efficiently and effectively (in JavaScript).
So the question is about a basic thing. Often times when you create objects in JavaScript of a certain type, you might give them an ID. In the browser, for example with virtual DOM elements, you might just give them a globally unique ID (GUID) and set it to an incrementing integer.
GUID = 1
let a = createNode() // { id: 1 }
let b = createNode() // { id: 2 }
let c = createNode() // { id: 3 }
function createNode() {
return { id: GUID++ }
}
But what happens when you run out of integers? Number.MAX_SAFE_INTEGER == 2⁵³ - 1. That is obviously a very large number: 9,007,199,254,740,991 quadrillions perhaps. Many billions of billions. But if JS can reach 10 million ops per second lets say in a pick of the hat way, then that is about 900,719,925s to reach that number, or 10416 days, or about 30 years. So in this case if you left your computer running for 30 years, it would eventually run out of incrementing IDs. This would be a hard bug to find!!!
If you parallelized the generation of the IDs, then you could more realistically (more quickly) run out of the incremented integers. Assuming you don't want to use a GUID scheme.
Given the memory limits of computers, you can only create a certain number of objects. In JS you probably can't create more than a few billion.
But my question is, as a theoretical exercise, how can you solve this problem of generating the incremented integers such that if you got up to Number.MAX_SAFE_INTEGER, you would cycle back from the beginning, yet not use the potentially billions (or just millions) that you already have "live and bound". What sort of scheme would you have to use to make it so you could simply cycle through the integers and always know you have a free one available?
function getNextID() {
if (i++ > Number.MAX_SAFE_INTEGER) {
return i = 0
} else {
return i
}
}
Random notes:
The fastest overall was Chrome 11 (under 2 sec per billion iterations, or at most 4 CPU cycles per iteration); the slowest was IE8 (about 55 sec per billion iterations, or over 100 CPU cycles per iteration).
Basically, this question stems from the fact that our typical "practical" solutions will break in the super-edge case of running into Number.MAX_SAFE_INTEGER, which is very hard to test. I would like to know some ways where you could solve for that, without just erroring out in some way.
But what happens when you run out of integers?
You won't. Ever.
But if JS can reach 10 million ops per second [it'll take] about 30 years.
Not much to add. No computer will run for 30 years on the same program. Also in this very contrived example you only generate ids. In a realistic calculation you might spend 1/10000 of the time to generate ids, so the 30 years turn into 300000 years.
how can you solve this problem of generating the incremented integers such that if you got up to Number.MAX_SAFE_INTEGER, you would cycle back from the beginning,
If you "cycle back from the beginning", they won't be "incremental" anymore. One of your requirements cannot be fullfilled.
If you parallelized the generation of the IDs, then you could more realistically (more quickly) run out of the incremented integers.
No. For the ids to be strictly incremental, you have to share a counter between these parallelized agents. And access to shared memory is only possible through synchronization, so that won't be faster at all.
If you still really think that you'll run out of 52bit, use BigInts. Or Symbols, depending on your usecase.

How to determine Big-o complexity if it only depends on values of input rather than input size?

I just saw javascript code about sorting which uses setTimeout as shown
var list = [2, 5, 10, 4, 8, 32];
var result = [];
list.forEach( n => setTimeout(() => result.push(n), n));
It is interesting because in js setTimeout is asynchronous so if you wait for sufficient time, result will be sorted array. It is deterministic depends on only values of data but not the size of the input so I have no idea how to determine Big-O (time complexity) of this approach.
TLDR; it depends on how you define the complexity of setTimeout()
When discussing algorithmic complexity, we have to answer the following questions:
What are my inputs?
What is a unit of work in the hypothetical machine that my algorithm runs in?
In some cases, how we define our inputs is dependent on what the algorithm is doing and how we defined our unit of work. The problem is complicated when using built-in functions as we have to define the complexity of those functions so we can take them into account and calculate the overall complexity of the algorithm.
What is the complexity of setTimeout()? That's up for interpretation. I find it helpful to give setTimeout() a complexity of O(n), where n is the number of milliseconds passed to the function. In this case I've decided that each millisecond that is counted internally by setTimeout() represents one unit of work.
Given that setTimeout() has complexity O(n), we must now determine how it fits into the rest of our algorithm. Because we are looping through list and calling setTimeout() for each member of the list, we multiply n with another variable, let's call it k to represent the size of the list.
Putting it all together, the algorithm has complexity O(k * n), where k is the length of the numbers given, and n is the maximum value in the list.
Does this complexity make sense? Let's do a sanity check by interpreting the results of our analysis:
Our algorithm takes longer as we give it more numbers ✓
Our algorithm takes longer as we give it larger numbers ✓
Notice that the key to this conclusion was determining the complexity of setTimeout(). Had we given it a constant O(1) complexity, our end result would have been O(k), which IMO is misleading.
Edit:
Perhaps a more correct interpretation of setTimeout()'s contribution to our complexity is O(n) for all inputs, where n is the maximum value of a given list, regardless of how many times it is called.
In the original post, I made the assumption that setTimeout() would run n times for each item in the list, but this logic is slightly flawed as setTimeout() conceptually "caches" previous values, so if it is called with setTimeout(30), setTimeout(50), and setTimeout(100), it will run 100 units of work (as opposed to 180 units of work, which was the case in the original post).
Given this new "cached" interpretation of setTimeout(), the complexity is O(k + n), where k is the length of the list, and n is the maximum value in the list.
Fun fact:
This happens to have the same complexity as Counting Sort, whose complexity is also a function of list size and max list value

WebAudio setTargetAtTime: formula to convert-time constant to seconds

I've found I like the sound of setTargetAtTime() applied to gain. So I'd like to do this:
gainNode.gain.setTargetAtTime(0, audioContext.currentTime, timeConst)
oscillator.stop(audioContext.currentTime + timeConstToSeconds(timeConst));
So that the oscillator stops when the sound is functionally inaudible.
What is an effective timeConstToSeconds() function for this?
And/or, what is an effective formula for the reverse operation? (input seconds, return time constant.)
The spec tells you exactly how setTargetAtTime works: https://webaudio.github.io/web-audio-api/#dom-audioparam-settargetattime
As a rough general rule, these kinds of exponential approaches are generally considered to have converged to the final value after 5 or 10 time constants, so
function timeConstToSeconds(t) {
return 10*t;
}
Change 10 to some other appropriate value for what you consider to be close enough.

Javascript perf, weird results

I want to know what is the better way to code in javascript for my nodejs project, so I did this:
function clas(){
}
clas.prototype.index = function(){
var i = 0;
while(i < 1000){
i++;
}
}
var t1 = new clas();
var f = 0;
var d1 = new Date();
while(f < 1000){
t1.index();
f++;
}
console.log("t1: "+(new Date()-d1)+"ms");
f=0;
var d2 = new Date();
while(f < 1000){
var t2 = new clas();
t2.index();
f++;
}
console.log("t2: "+(new Date()-d2)+"ms");
on my browser, the first and the second are the same... 1ms and with nodejs, i have t1 = 15ms and t2 = 1ms, why? why the first take more time than the second as he doesn't initialise my class?
Here are several issues. Your example shows that you have very little experience in benchmarking or system performance. That is why I recommend brushing up on the very basics, and until you got some more feel for it, don't try optimizing at all. Optimizing prematurely is generally a bad thing. If done by someone who does not know anything about performance optimization in the first place, "optimizations" end up being pure noise: Some work and some don't, pretty much at random.
For completeness, here are some things that are wrong with your test case:
First of all, 1000 is not enough for a performance test. You want to do iterations in the order of millions for your CPU to actually spend a remarkable amount of time on it.
Secondly, for benchmarking, you want to use a high performance timer. The reason as to why node gives you 15ms, is because it uses a coarse-grained system timer whose smallest unit is about 15ms, which most probably corresponds to your system's scheduling granularity.
Thirdly, regarding your actual question: Allocating a new object inside your loop, if not necessary, is almost always a bad choice for performance. There is a lot going on under the hood, including the possibility of heap allocations. However, in your simple case, most run-times will probably optimize away most of the overhead, for two reasons:
Your test case is too simple, and the optimizer can easily optimize simple code segments, but has a much harder time in real situations.
Your test case is transient. If the optimizer is smart enough, it will detect that, and it will skip the entire loop.
It is because node does jut-in-time ( JIT )compilation optimizations to the code.
by JIT-optimization, we mean that the node tries to optimize the code when it is executed.
So... the first call the the function is taking more time, and node realizes that it can optimize this for-loop, as it does nothing at all. Whereas for all other calls the optimized loop is executed.
So... subsequent calls will take less time.
You can try by changing the order. The first call will take the more time.
Where as in some browser's the code is optimized ahead-of-time (ie. before running the code).

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