Whats wrong with this code? Why wont it sort?
let rec sort = function
| [] -> []
| [x] -> [x]
| x1::x2::xs -> if x1 <= x2 then x1 :: sort (x2::xs)
else x2 :: sort (x1::xs)
Suppost to take
sort [3;1;4;1;5;9;2;6;5];;
and return:
val it : int list = [1; 1; 2; 3; 4; 5; 5; 6; 9]
Your code is like one bubble cycle in bubble sort. It will take max element to the last position and some other bigger elements to the right.
Note that you are only traversing original list only once. It has linear complexity and we all know that sorting using only comparison has to be O(n*log n).
You can repeat that cycle more times if you want to sort this list.
think about what can end up in the first position ... right now it can only be the first or the second position in your list (the if inside the last case)
let rec ssort = function
[] -> []
| x::xs ->
let min, rest =
List.fold_left (fun (min,acc) x ->
if h<min then (h, min::acc)
else (min, h::acc))
(x, []) xs
in min::ssort rest
Related
Can anyone help me with this problem?
"Realize a function which duplicate each item in a list. You can use List.map"
IN F# sharp language.
And also
"Use the List.init function to generate a list of n random natural numbers between 0 and m."
let makeCopy elem Count =
match Count with
| 0 -> []
| 1 -> elem
let rec dupeElem row count =
match row with
| [] -> []
| hd::tl -> (makeCopy hd count) # dupeElem tl count
//let xs = [1; 2; 3]
//xs |> List.collect (fun x -> List.replicate 3 x)
//val it : int list = [1; 1; 2; 2; 3; 3]
Duplicating the items is pretty straight forward, you just need a recursive function that walks the list.
Generating the random numbers is where you can use List.init to create a new list. You can use the .NET Random class to generate the random numbers you're after.
This gives up the following functions:
let rec duplicateItems list =
match list with
| [] -> []
| head :: tail -> head :: head :: duplicateItems tail
let makeRandomList count upperBound =
let random = Random()
List.init count (fun i -> random.Next(0, upperBound))
You can now generate a random list and pipe it into the duplicate function:
let numbers = makeRandomList 10 20 |> duplicateItems
NOTE: duplicateItems is not tail recursive, so for really large lists this might be an issue. You can get around this by treating the data to duplicate as a sequence:
let duplicateSequence sequence =
seq {
for a in sequence do
yield a
yield a
}
Now we just need to pipe the result into Seq.toList:
let numbers = makeRandomList 10 20 |> duplicateSequence |> Seq.toList
We could also have written makeRandom to return a sequence rather than a list. This would have made the whole computation lazy up until the point we call Seq.toList.
which duplicate each item in a list. You can use List.map
I think your own solution with List.collect is fine. But here's one with List.map:
> let dupe x = List.map (fun s -> [s;s]) x |> List.concat
val dupe : x:'a list -> 'a list
> dupe [1;2;3];;
val it : int list = [1; 1; 2; 2; 3; 3]
Use the List.init function to generate a list of n random natural numbers between 0 and m
I'll show you the general idea, then you can work out the rest, I'm sure. This basically works:
> let rand n max = let r = Random() in List.init n (fun _ -> r.Next(0, max));;
val rand : n:int -> max:int -> int list
> rand 10 12;;
val it : int list = [11; 11; 10; 11; 6; 1; 3; 6; 8; 2]
I want to write a tail recursive function to multiply all the values in a list by 2 in F#. I know there is a bunch of ways to do this but i want to know if this is even a viable method. This is purely for educational purposes. I realize that there is a built in function to do this for me.
let multiply m =
let rec innerfunct ax = function
| [] -> printfn "%A" m
| (car::cdr) -> (car <- car*2 innerfunct cdr);
innerfunct m;;
let mutable a = 1::3::4::[]
multiply a
I get two errors with this though i doubt they are the only problems.
This value is not mutable on my second matching condition
and
This expression is a function value, i.e. is missing arguments. Its type is 'a list -> unit. for when i call length a.
I am fairly new to F# and realize im probably not calling the function properly but i cant figure out why. This is mostly a learning experience for me so the explanation is more important than just fixing the code. The syntax is clearly off, but can i map *2 to a list just by doing the equivalent of
car = car*2 and then calling the inner function on the cdr of the list.
There are a number of issues that I can't easily explain without showing intermediate code, so I'll try to walk through a commented refactoring:
First, we'll go down the mutable path:
As F# lists are immutable and so are primitive ints, we need a way to mutate that thing inside the list:
let mutable a = [ref 1; ref 3; ref 4]
Getting rid of the superfluous ax and arranging the cases a bit, we can make use of these reference cells:
let multiply m =
let rec innerfunct = function
| [] -> printfn "%A" m
| car :: cdr ->
car := !car*2
innerfunct cdr
innerfunct m
We see, that multiply only calls its inner function, so we end up with the first solution:
let rec multiply m =
match m with
| [] -> printfn "%A" m
| car :: cdr ->
car := !car*2
multiply cdr
This is really only for it's own purpose. If you want mutability, use arrays and traditional for-loops.
Then, we go up the immutable path:
As we learnt in the mutable world, the first error is due to car not being mutable. It is just a primitive int out of an immutable list. Living in an immutable world means we can only create something new out of our input. What we want is to construct a new list, having car*2 as head and then the result of the recursive call to innerfunct. As usual, all branches of a function need to return some thing of the same type:
let multiply m =
let rec innerfunct = function
| [] ->
printfn "%A" m
[]
| car :: cdr ->
car*2 :: innerfunct cdr
innerfunct m
Knowing m is immutable, we can get rid of the printfn. If needed, we can put it outside of the function, anywhere we have access to the list. It will always print the same.
We finish by also making the reference to the list immutable and obtain a second (intermediate) solution:
let multiply m =
let rec innerfunct = function
| [] -> []
| car :: cdr -> car*2 :: innerfunct cdr
innerfunct m
let a = [1; 3; 4]
printfn "%A" a
let multiplied = multiply a
printfn "%A" multiplied
It might be nice to also multiply by different values (the function is called multiply after all and not double). Also, now that innerfunct is so small, we can make the names match the small scope (the smaller the scope, the shorter the names):
let multiply m xs =
let rec inner = function
| [] -> []
| x :: tail -> x*m :: inner tail
inner xs
Note that I put the factor first and the list last. This is similar to other List functions and allows to create pre-customized functions by using partial application:
let double = multiply 2
let doubled = double a
All that's left now is to make multiply tail-recursive:
let multiply m xs =
let rec inner acc = function
| [] -> acc
| x :: tail -> inner (x*m :: acc) tail
inner [] xs |> List.rev
So we end up having (for educational purposes) a hard-coded version of let multiply' m = List.map ((*) m)
F# is a 'single-pass' compiler, so you can expect any compilation error to have a cascading effect beneath the error. When you have a compilation error, focus on that single error. While you may have more errors in your code (you do), it may also be that subsequent errors are only consequences of the first error.
As the compiler says, car isn't mutable, so you can assign a value to it.
In Functional Programming, a map can easily be implemented as a recursive function:
// ('a -> 'b) -> 'a list -> 'b list
let rec map f = function
| [] -> []
| h::t -> f h :: map f t
This version, however, isn't tail-recursive, since it recursively calls map before it cons the head onto the tail.
You can normally refactor to a tail-recursive implementation by introducing an 'inner' implementation function that uses an accumulator for the result. Here's one way to do that:
// ('a -> 'b) -> 'a list -> 'b list
let map' f xs =
let rec mapImp f acc = function
| [] -> acc
| h::t -> mapImp f (acc # [f h]) t
mapImp f [] xs
Here, mapImp is the last operation to be invoked in the h::t case.
This implementation is a bit inefficient because it concatenates two lists (acc # [f h]) in each iteration. Depending on the size of the lists to map, it may be more efficient to cons the accumulator and then do a single reverse at the end:
// ('a -> 'b) -> 'a list -> 'b list
let map'' f xs =
let rec mapImp f acc = function
| [] -> acc
| h::t -> mapImp f (f h :: acc) t
mapImp f [] xs |> List.rev
In any case, however, the only reason to do all of this is for the exercise, because this function is already built-in.
In all cases, you can use map functions to multiply all elements in a list by two:
> let mdouble = List.map ((*) 2);;
val mdouble : (int list -> int list)
> mdouble [1..10];;
val it : int list = [2; 4; 6; 8; 10; 12; 14; 16; 18; 20]
Normally, though, I wouldn't even care to define such function explicitly. Instead, you use it inline:
> List.map ((*) 2) [1..10];;
val it : int list = [2; 4; 6; 8; 10; 12; 14; 16; 18; 20]
You can use all the above map function in the same way.
Symbols that you are creating in a match statement are not mutable, so when you are matching with (car::cdr) you cannot change their values.
Standard functional way would be to produce a new list with the computed values. For that you can write something like this:
let multiplyBy2 = List.map (fun x -> x * 2)
multiplyBy2 [1;2;3;4;5]
This is not tail recursive by itself (but List.map is).
If you really want to change values of the list, you could use an array instead. Then your function will not produce any new objects, just iterate through the array:
let multiplyArrayBy2 arr =
arr
|> Array.iteri (fun index value -> arr.[index] <- value * 2)
let someArray = [| 1; 2; 3; 4; 5 |]
multiplyArrayBy2 someArray
I have this code:
let rec combinations acc listC =
match listC with
| [] -> acc
| h::t ->
let next = [h]::List.map (fun t -> h::t) acc # acc
combinations next t
It looks tail recursive, but I keep getting stack overflows with it. Any ideas on how to make it work?
combinations is tail recursive. Your problem is with the # operator. Appending a list with it iterates the whole list, so as your acc becomes large, you will get a SO.
You can see here, that the # operator is not tail recursive. The non-optimized version looks like: let rec (#) x y = match x with [] -> y | (h::t) -> h :: (t # y).
To get around this problem, there are a couple of options:
If you don't care about order, you could write a tail-recursive method to prepend the result like this:
let rec prepend lst1 lst2 =
match lst1 with
| [] -> lst2
| head::tail -> prepend tail (head::lst2)
> prepend [1;2;3;4] [5;6;7;8];;
val it : int list = [4; 3; 2; 1; 5; 6; 7; 8]
If you care about order, you could write a method to first reverse the list and then prepend it. The drawback of this, of course, is that it will require twice as much memory since you are allocating an additional list to hold the reversed version of the original list. You can reuse the previous function to write something like this:
let prepend2 lst1 lst2 =
prepend (prepend lst1 []) lst2
> prepend2 [1;2;3;4] [5;6;7;8];;
val it : int list = [1; 2; 3; 4; 5; 6; 7; 8]
I want a way to get rid of repeating pairs in an array. For my problem, the pairs will be consecutive, and there will be at most one repeating pair.
My current implementation seems too complicated. The elements 3 and 4 form what I'm calling a repeating pair in arr1 below. As a pair, they only appear once in the desired output, arr2. What are some more efficient ways?
let arr1=[|4; 2; 3; 4; 3; 4; 1|]
let n=arr1.Length
let iPlus2IsEqual=Array.map2 (fun x y -> x=y) arr1.[2..] arr1.[..(n-3)]
let consecutive=Array.map2 (fun x y -> x && y) iPlus2IsEqual.[1..] iPlus2IsEqual.[..(n-4)] |> Array.tryFindIndex (fun x -> x)
let dup=if consecutive.IsSome then consecutive.Value+1 else n-1
let arr2=if dup>=n-3 then arr1.[..dup] else Array.append arr1.[..dup] arr1.[(dup+3)..]
>
val arr2 : int [] = [|4; 2; 3; 4; 1|]
We can use recursion like so (it will get multiple repeats for free too)
let rec filterrepeats l =
match l with
|a::b::c::d::t when a=c && b=d -> a::b::(filterrepeats t)
|h::t ->h::(filterrepeats t)
|[] -> []
> filterrepeats [4;2;3;4;3;4;1];;
val it : int list = [4; 2; 3; 4; 1]
This works on lists, so you will need to add a call to Array.toList before you run it.
The above is not tail recursive as the compiler doesn't know what goes on the right hand side of h::(filterrepeats t) until after the function call. You can solve this by using an accumulator like so:
let rec filterrepeats l =
let rec loop l acc =
match l with
|a::b::c::d::t when a=c && b=d ->loop t (b::a::acc)
|h::t ->loop t (h::acc)
|[] -> acc
loop (List.rev l) []
For large arrays this is around 13x faster than your solution:
let inline tryFindDuplicatedPairIndex (xs: _ []) =
let rec loop i x0 x1 x2 =
if i < xs.Length-4 then
let x3 = xs.[i+3]
if x0=x2 && x1=x3 then Some i else
loop (i+1) x1 x2 x3
else None
if xs.Length < 4 then None else
loop 0 xs.[0] xs.[1] xs.[2]
let inline removeDuplicatedPair (xs: _ []) =
match tryFindDuplicatedPairIndex xs with
| None -> Array.copy xs
| Some i ->
let ys = Array.zeroCreate (xs.Length-2)
for j=0 to i-1 do
ys.[j] <- xs.[j]
for j=i+2 to xs.Length-1 do
ys.[j-2] <- xs.[j]
ys
I use inline and test elements individually (i.e. rather than as a tuple: (x0,x1) = (x2,x3)) to try to prevent = from being a generic equality test because that is very slow. I've reused previous array lookups from one iteration to the next. I copy the input array if the output is identical to the input and pre-allocate an array with n-2 elements otherwise. I've hand-rolled the copying to my pre-allocated array to avoid creating any garbage (e.g. instead of Array.append of two slices).
No stack overflow with large list (length >= 100K) and remove all duplicate pairs
let rec distinctPairs list =
List.foldBack (fun x (l,r) -> x::r, l) list ([],[])
|> fun (odds, evens) -> List.zip odds evens
|> Seq.distinct
Not very fast, 1M list take 500ms, anyway faster ?
Only work for list with even length
I have a sequence of integers representing dice in F#.
In the game in question, the player has a pool of dice and can choose to play one (governed by certain rules) and keep the rest.
If, for example, a player rolls a 6, 6 and a 4 and decides to play one the sixes, is there a simple way to return a sequence with only one 6 removed?
Seq.filter (fun x -> x != 6) dice
removes all of the sixes, not just one.
Non-trivial operations on sequences are painful to work with, since they don't support pattern matching. I think the simplest solution is as follows:
let filterFirst f s =
seq {
let filtered = ref false
for a in s do
if filtered.Value = false && f a then
filtered := true
else yield a
}
So long as the mutable implementation is hidden from the client, it's still functional style ;)
If you're going to store data I would use ResizeArray instead of a Sequence. It has a wealth of functions built in such as the function you asked about. It's simply called Remove. Note: ResizeArray is an abbreviation for the CLI type List.
let test = seq [1; 2; 6; 6; 1; 0]
let a = new ResizeArray<int>(test)
a.Remove 6 |> ignore
Seq.toList a |> printf "%A"
// output
> [1; 2; 6; 1; 0]
Other data type options could be Array
let removeOneFromArray v a =
let i = Array.findIndex ((=)v) a
Array.append a.[..(i-1)] a.[(i+1)..]
or List
let removeOneFromList v l =
let rec remove acc = function
| x::xs when x = v -> List.rev acc # xs
| x::xs -> remove (x::acc) xs
| [] -> acc
remove [] l
the below code will work for a list (so not any seq but it sounds like the sequence your using could be a List)
let rec removeOne value list =
match list with
| head::tail when head = value -> tail
| head::tail -> head::(removeOne value tail)
| _ -> [] //you might wanna fail here since it didn't find value in
//the list
EDIT: code updated based on correct comment below. Thanks P
EDIT: After reading a different answer I thought that a warning would be in order. Don't use the above code for infite sequences but since I guess your players don't have infite dice that should not be a problem but for but for completeness here's an implementation that would work for (almost) any
finite sequence
let rec removeOne value seq acc =
match seq.Any() with
| true when s.First() = value -> seq.Skip(1)
| true -> seq.First()::(removeOne value seq.Skip(1))
| _ -> List.rev acc //you might wanna fail here since it didn't find value in
//the list
However I recommend using the first solution which Im confident will perform better than the latter even if you have to turn a sequence into a list first (at least for small sequences or large sequences with the soughtfor value in the end)
I don't think there is any function that would allow you to directly represent the idea that you want to remove just the first element matching the specified criteria from the list (e.g. something like Seq.removeOne).
You can implement the function in a relatively readable way using Seq.fold (if the sequence of numbers is finite):
let removeOne f l =
Seq.fold (fun (removed, res) v ->
if removed then true, v::res
elif f v then true, res
else false, v::res) (false, []) l
|> snd |> List.rev
> removeOne (fun x -> x = 6) [ 1; 2; 6; 6; 1 ];
val it : int list = [1; 2; 6; 1]
The fold function keeps some state - in this case of type bool * list<'a>. The Boolean flag represents whether we already removed some element and the list is used to accumulate the result (which has to be reversed at the end of processing).
If you need to do this for (possibly) infinite seq<int>, then you'll need to use GetEnumerator directly and implement the code as a recursive sequence expression. This is a bit uglier and it would look like this:
let removeOne f (s:seq<_>) =
// Get enumerator of the input sequence
let en = s.GetEnumerator()
let rec loop() = seq {
// Move to the next element
if en.MoveNext() then
// Is this the element to skip?
if f en.Current then
// Yes - return all remaining elements without filtering
while en.MoveNext() do
yield en.Current
else
// No - return this element and continue looping
yield en.Current
yield! loop() }
loop()
You can try this:
let rec removeFirstOccurrence item screened items =
items |> function
| h::tail -> if h = item
then screened # tail
else tail |> removeFirstOccurrence item (screened # [h])
| _ -> []
Usage:
let updated = products |> removeFirstOccurrence product []