I'm new to Julia language and I wanted to improve my understanding by implementing a double linked list.
Unfortunately it seems that there is no good existing library for this purpose.
The only good one is the single linked list (here).
There is one implementation of a double linked list (here). But this is 2 years old and I'm not sure if it is outdated or not. And it does not allow a real empty list. It is just a single element with a default value.
At the moment I would be able to implement the common stuff like push!, pop!, that's not the problem.
But I'm struggling with implementing a double linked list that could be empty.
My current approach uses Nullable for a optional value of the reference and value.
type ListNode{T}
prev::Nullable{ListNode{T}}
next::Nullable{ListNode{T}}
value::Nullable{T}
ListNode(v) = (x=new(); x.prev=Nullable{x}; x.next=Nullable{x}; x.value=Nullable(v); x)
ListNode(p, n, v) = new(p, n, v)
end
type List{T}
node::Nullable(ListNode{T})
List() = (start=new(Nullable(ListNode{T}())); node=start; start)
List(v) = (start=new(Nullable(ListNode{T}(v))); node=start; start)
end
But it seems like this is pretty ugly and inconvenient to work with.
My second approach would be to introduce a boolean variable (inside List{T}) which stores if a list is empty or not. Checking this boolean would me allow to simply handle push! and pop! to empty lists.
I tried to google a good solution but I didn't found one.
Can anyone give me a "julia style" solution for the double linked list?
Thanks,
felix
There is now a library containing various data structures, DataStructures.jl Some initial notes regarding the question. As of this writing, type is decrepitated. Instead, mutable struct should be used, for Julia 1.0 and beyond. Nullable is also decrepitated, and a Union of Nothing and the type in question can be used instead.
There exist a package called DataStructures.jl that provides what you need.
You can find a DoubleLinked list containing the functionality you need here:
mutable_list
Code snippets from the link above, defining a DoubleLinked list in Julia >= v 1.1:
mutable struct ListNode{T}
data::T
prev::ListNode{T}
next::ListNode{T}
function ListNode{T}() where T
node = new{T}()
node.next = node
node.prev = node
return node
end
function ListNode{T}(data) where T
node = new{T}(data)
return node
end
end
mutable struct MutableLinkedList{T}
len::Int
node::ListNode{T}
function MutableLinkedList{T}() where T
l = new{T}()
l.len = 0
l.node = ListNode{T}()
l.node.next = l.node
l.node.prev = l.node
return l
end
end
In addition to the DataStructures package, Chris Rackauckas' LinkedLists.jl is a good resource.
The source code is quite readable and you can always ask questions.
Related
Consider this F# code:
let isSalary employee =
let (fName,lName,Occupation,Department,SalaryType,
HoursPerWeek, AnnualSalary, HourlyWage
) = employee
SalaryType = "Salary"
if(employee.SalaryType = SalaryType) then
true
else
false
Im getting errors in here, any fixes to it?
First things first, please post error messages and a much more specific question. Thanks! But luckily, I can about deduce the error messages from this problem.
Next, if you want to mutate SalaryType after you've deconstructed your employee 8-tuple, you should write using the mutable keyword:
let mutable (fName, lName, Occupation, Department, SalaryType,
HoursPerWeek, AnnualSalary, HourlyWage) = employee
But you shouldn't. This is explained further below.
Next problem: there is no dot notation (no tuple.member) for accessing members of a tuple. It's only possible through deconstruction. So you can't employee.SalaryType.
Here's what looks to be the crux of the problem, and it's a mistake I made many times when I was learning functional programming, and it's a difficult paradigm shift to adapt to. You should not be attempting to mutate data, or in this case, variables. Variables, or values as they are called in F#, shouldn't change, as a broad rule. Functions should be pure.
What this means is that any parameters you pass into a function should not change after leaving the function. The parameter employee should be the same after you return to the calling scope.
There's a few syntactical errors you've made that make it pretty much impossible for me to deduce what you're trying to do in the first place. Please include this in the question.
Also, one last nitpick. As you know, the last expression in an F# function is it's return value. Instead of using an if statement, just return the condition you're testing, like this:
let ...
...
employee.SalaryType = SalaryType <- but remember, you can't use dot notation on tuples; this is just an example
Please read more on
https://learn.microsoft.com/en-us/dotnet/fsharp/language-reference/
this is a three part question on the use of the Python API to Z3 (Z3Py).
I thought I knew the difference between a constant and a variable but apparently not. I was thinking I could declare a sort and instantiate a variable of that sort as follows:
Node, (a1,a2,a3) = EnumSort('Node', ['a1','a2','a3'])
n1 = Node('n1') # c.f. x = Int('x')
But python throws an exception saying that you can't "call Node". The only thing that seems to work is to declare n1 a constant
Node, (a1,a2,a3) = EnumSort('Node', ['a1','a2','a3'])
n1 = Const('n1',Node)
but I'm baffled at this since I would think that a1,a2,a3 are the constants. Perhaps n1 is a symbolic constant, but how would I declare an actual variable?
How to create a constant set? I tried starting with an empty set and adding to it but that doesn't work
Node, (a1,a2,a3) = EnumSort('Node', ['a1','a2','a3'])
n1 = Const('n1',Node)
nodes = EmptySet(Node)
SetAdd(nodes, a1) #<-- want to create a set {a1}
solve([IsMember(n1,nodes)])
But this doesn't work Z3 returns no solution. On the other hand replacing the 3rd line with
nodes = Const('nodes',SetSort(Node))
is now too permissive, allowing Z3 to interpret nodes as any set of nodes that's needed to satisfy the formula. How do I create just the set {a1}?
Is there an easy way to create pairs, other than having to go through the datatype declaration which seems a bit cumbersome? eg
Edge = Datatype('Edge')
Edge.declare('pr', ('fst', Node), ('snd',Node))
Edge.create()
edge1 = Edge.pr(a1,a2)
Declaring Enums
Const is the right way to declare as you found out. It's a bit misleading indeed, but it is actually how all symbolic variables are created. For instance, you can say:
a = Const('a', IntSort())
and that would be equivalent to saying
a = Int('a')
It's just that the latter looks nicer, but in fact it's merely a function z3 folks defined that sort of does what the former does. If you like that syntax, you can do the following:
NodeSort, (a1,a2,a3) = EnumSort('Node', ['a1','a2','a3'])
def Node(nm):
return Const(nm, NodeSort)
Now you can say:
n1 = Node ('n1')
which is what you intended I suppose.
Inserting to sets
You're on the right track; but keep in mind that the function SetAdd does not modify the set argument. It just creates a new one. So, simply give it a name and use it like this:
emptyNodes = EmptySet(Node)
myNodes = SetAdd(emptyNodes, a1)
solve([IsMember(n1,myNodes)])
Or, you can simply substitute:
mySet = SetAdd(SetAdd(EmptySet(Node), a1), a2)
which would create the set {a1, a2}.
As a rule of thumb, the API tries to be always functional, i.e., no destructive updates to existing variables, but you instead create new values out of old.
Working with pairs
That's the only way. But nothing is stopping you from defining your own functions to simplify this task, just like we did with the Node function in the first part. After all, z3py is essentially Python library and z3 folks did a lot of work to make it nicer, but you also have the entire power of Python to simplify your life. In fact, many other interfaces to z3 from other languages (Scala, Haskell, O'Caml etc.) precisely do that to provide a much easier to work with API using the features of their respective host languages.
I'm trying to test equality of two collections in F# using FSUnit (specifically its Xunit branch) but failing horribly so far.
I have a function that returns an array of certain structs and would like to test whether the returned array is correct. The code I'm testing is in C# so it so the function can't return native F# lists.
The most promising approach I've tried is following:
[<Fact>]
let SimpleTest() =
let parser = new ExpressionParser()
parser.ParseExpression "2" |> should equal [new ParsedItem("2", ParsedItemType.Value)]
...but it results in the the test failing because of:
"Message> FSUnit.Xunit+MatchException: Exception of type 'FsUnit.Xunit+MatchException' was thrown.
Expected value: Equals [(2)]
Actual: was [2]
I can see that it's because the type of native F# list doesn't match a native array but have honestly no idea (nor have I found anything in documentation) how to do it differently (other then creating native array beforehand and populating it one by one...).
I've also tried some other approaches but they usually wouldn't even compile.
PS: I'm completely new to both F# and Xunit so I might be missing something absolutely obvious.
EDIT: A workaround that actually works better was suggested in comments (comparing string representations instead of the objects themselves) and while I will use that in my actual code I'd still appreciate a true solution to my problem above.
Although you can't easily return F# lists from your C# code, one option is to return arrays. These have structural equality, so you can simply compare them to determine if they are equal to each other:
open System.Linq
let csharpArray = Enumerable.Range(0, 10).ToArray()
let fsharpArray = [| 0..9 |]
These two arrays are equal:
> csharpArray = fsharpArray;;
val it : bool = true
If you don't want to return arrays, you can also return IEnumerable<T>, and convert to either lists or arrays in F#:
> let csharpEnumerable = Enumerable.Range(0, 10);;
val csharpEnumerable : System.Collections.Generic.IEnumerable<int>
> csharpEnumerable |> Seq.toList = [0..9];;
val it : bool = true
For a more comprehensive to introduction to unit testing with F#, you may want to view my Pluralsight course on the topic.
Ok, I've found the answer and it's simpler than I thought it'd be. First off the assentation works well the problem was in syntax and me not bothering to read the documentation on how to create an array in F# and just guessing it.
There were two things wrong. First [new ParsedItem("2", ParsedItemType.Value)] doesn't create an array it creates a list. That in itself wouldn't be a problem for FSUnit's should equal but it's enough to make simple structural equality test using = fail.
The second thing that was wrong was that I didn't really compare with [new ParsedItem("2", ParsedItemType.Value)] I compared with [new ParsedItem("2", ParsedItemType.Value), new ParsedItem("+", ParsedItemType.Operator), new ParsedItem("3", ParsedItemType.Value)] and that actually creates a list containing one touple. And that - unsurprisingly - didn't assert well :).
Simply reading the documentation and learning that an array is supposed to be created [|new ParsedItem("2", ParsedItemType.Value); new ParsedItem("+", ParsedItemType.Operator); new ParsedItem("3", ParsedItemType.Value)|] fixed the issue.
Anyway, thanks for the comments and the other answer. Though they didn't answer my question they increased my knowledge about F# and gave me a new idea how to test :).
I want to declare a graph of all states where the edges represent contiguous states. I think what I am trying to do might be called "tying the knot" (not sure about that though). It's not working like I expected, and I have a couple of questions.
First, I want a State type that has a string name and a list of contiguous states. But this declaration gives compiler error "...immediate cyclic reference...":
type State = string * (State list)
This way works:
type State(name:string, contigs: (State list)) =
let name = name
let contigs = contigs
But it's really not a requirement to name the members. A tuple is fine. How can I make that terse syntax work?
Second, the following code attempts to declare what should be three graphs of contiguous states (HI and AK are graphs consisting of a single node, all the remaining states constitute the last graph), followed by a list of all nodes. (For brevity I've only actually declared a handful of states here):
let rec hi = State("hi", [])
and mo = State("mo", [il ia])
and il = State("il", [mo])
and ia = State("ia", [mo])
and states = [hi,mo,il,ia]
This gives a variety of errors though including "mo will eventually be evaluated as part of it's own definition" and "expression was expected to have type 'a->'b but here has type State". I thought the 'rec' and 'and' keywords would allow this to work. Can I define this self referencing graph? If so, how?
The problem is your data structure and using invalid list element delimiters (should be semicolon). This works: (see edit)
type State =
| State of string * State list
let rec hi = State("hi", [])
and mo = State("mo", [il; ia])
and il = State("il", [mo])
and ia = State("ia", [mo])
let states = [hi; mo; il; ia]
Recursive references will be materialized as thunks (lazy). So you could, with a bit more typing do the same thing yourself with mutable lazys--just FYI--what you have is idiomatic.
EDIT
Intellisense didn't have a problem with it, but the compiler says
Recursive values cannot appear directly as a construction of the type 'List`1' within a recursive binding. This feature has been removed from the F# language. Consider using a record instead.
You can fix this by using seq instead of list.
type State =
| State of string * State seq
let rec hi = State("hi", [])
and mo = State("mo", seq { yield il; yield ia })
and il = State("il", seq { yield mo })
and ia = State("ia", seq { yield mo })
let states = [hi; mo; il; ia]
Although what Daniel says is correct I would contest the assertion that it is "idiomatic" because that does not produce a very useful data structure for representing graphs in the general case. Specifically, it only permits the addition of new vertices and edges from them but not adding or removing edges between existing vertices. In particular, this basically means your graph must be statically defined as a constant in your source code so you cannot load such a graph from disk easily.
The idiomatic purely functional representation of a graph is to replace dereferences with dictionary lookups. For example, represent the graph as a Map from vertices to Sets of vertices to which there are edges:
> let g =
Map["hi", set[]; "mo", set["il"; "ia"]; "il", set["mo"]; "ia", set["mo"]];;
val g : Map<string,Set<string>> =
map
[("hi", set []); ("ia", set ["mo"]); ("il", set ["mo"]);
("mo", set ["ia"; "il"])]
For example, you can lookup the vertices directly reachable via edges from mo like this:
> g.["mo"];;
val it : Set<string> = set ["ia"; "il"]
This is easier to debug than the mutable representation but it has significant disadvantages:
Lookup in a purely functional dictionary like Map is at least 200× slower than dereferencing a pointer for traversing graphs (according to a quick test here).
The garbage collector no longer reclaims unreachable subgraphs for you. The imperative solution is to use a weak dictionary but there are no known purely functional weak dictionaries.
So this is only feasible if performance and leaks will not be a problem. This is most commonly the case when your graphs are small or static.
Having had success with my last CLRS question, here's another:
In Introduction to Algorithms, Second Edition, p. 501-502, a linked-list representation of disjoint sets is described, wherein each list member the following three fields are maintained:
set member
pointer to next object
pointer back to first object (the set representative).
Although linked lists could be implemented by using only a single "Link" object type, the textbook shows an auxiliary "Linked List" object that contains a pointer to the "head" link and the "tail" link. Having a pointer to the "tail" facilitates the Union(x, y) operation, so that one need not traverse all of the links in a larger set x in order to start appending the links of the smaller set y to it.
However, to obtain a reference to the tail link, it would seem that each link object needs to maintain a fourth field: a reference to the Linked List auxiliary object itself. In that case, why not drop the Linked List object entirely and use that fourth field to point directly to the tail?
Would you consider this an omission in the text?
I just opened the text and the textbook description seems fine to me.
From what I understand the data-structure is something like:
struct Set {
LinkedListObject * head;
LinkedListObject * tail;
};
struct LinkedListObject {
Value set_member;
Set *representative;
LinkedListObject * next;
};
The textbook does not talk of any "auxillary" linked list structure in the book I have (second edition). Can you post the relevant paragraph?
Doing a Union would be something like:
// No error checks.
Set * Union(Set *x, Set *y) {
x->tail->next = y->head;
x->tail = y->tail;
LinkedListObject *tmp = y->head;
while (tmp) {
tmp->representative = x;
tmp = tmp->next;
}
return x;
}
why not drop the Linked List object entirely and use that fourth field to point directly to the tail?
An insight can be taken from path compression. There all the elements are supposed to point to head of list. If it doesn't happen then the find-set operation does that (by changing p[x] and returning that). You talk similarly of tail. So if such function is implemented only then can we use that.