I am trying to fill a list with random numbers and am having diffculty getting the random number part. What I have right now prints out a random number 10 times, what I want is to print out 10 different random numbers
let a = (new System.Random()).Next(1, 1000)
let listOfSquares = [ for i in 1 .. 10->a]
printfn "%A" listOfSquares
any tips or suggestions?
Your code is simply getting one random number and using it ten times.
This extension method might be useful:
type System.Random with
/// Generates an infinite sequence of random numbers within the given range.
member this.GetValues(minValue, maxValue) =
Seq.initInfinite (fun _ -> this.Next(minValue, maxValue))
Then you can use it like this:
let r = System.Random()
let nums = r.GetValues(1, 1000) |> Seq.take 10
let genRandomNumbers count =
let rnd = System.Random()
List.init count (fun _ -> rnd.Next ())
let l = genRandomNumbers 10
printfn "%A" l
When I write a random something dispenser I like to use the same random number generator for each call to the dispenser. You can do that in F# with closures (a combination of Joel's and ildjarn's answer).
Example:
let randomWord =
let R = System.Random()
fun n -> System.String [|for _ in 1..n -> R.Next(26) + 97 |> char|]
In this way, a single instance of Random is 'baked into' the function, reusing it with each call.
There are two problems:
1) In F# functions are supposed to be pure so a function without arguments is considered as final value.
To declare impure function "without arguments", let it take one argument of type unit
let a () = (new System.Random()).Next(1, 1000)
and call it passing unit argument
let list = [ for i in 1 .. 10 -> a () ]
Source
2) New System.Random() instance is created each time when a is called. This results in getting same numbers. To fix this, create the instance only once
let random = new System.Random()
let a () = random.Next(1, 1000)
let list = [ for i in 1 .. 10 -> a ()]
This isn't specific to F#, read explanation for C# for better understanding
You could also avoid declaring an impure function as said by Pavel and just run:
let rnd = Random()
let rndList = [for i in 0..100 do rnd.Next(1000)]
I think one should be careful how to initialize System.Random as it uses the current time as seed. One instance should be enough for the whole app. Injecting random into functions has the advantage that you can use a fixed seed and reproduce with semi randomness, e.g. for testing your logic.
let rnd = System.Random()
let genRandomNumbers random count =
List.init count (fun _ -> random.Next ())
let getRandomNumbersSeeded = getRandomNumbers rnd
let l = getRandomNumbersSeeded 10
printfn "%A" l
Related
I'm trying to learn F# but I'm stuck with a very simple thing.
I would like to create a list with uniques random values that I can display on a console. Let say Random from 1 to 100 and 10 elements in the list.
I've seen here this code F# getting a list of random numbers :
let genRandomNumbers count =
let rnd = System.Random()
List.init count (fun _ -> rnd.Next (1, 100))
let l = genRandomNumbers 10
printfn "%A" l
But how can I make theses numbers be differents ? This is not exactly a duplicate question because I don't find a way to be sure that each number is unique ; Random.Next can generate same numbers...
Here's a very simple solution:
let genRandomNumbers count =
let rnd = System.Random()
let initial = Seq.initInfinite (fun _ -> rnd.Next (1, 100))
initial
|> Seq.distinct
|> Seq.take(count)
|> Seq.toList
Note the Seq.distinct does exactly what you want to get the unique values. Also note that you'll get an issue if you try to get a count larger than 99 because there aren't that many distinct values between 1 and 99!
In F#, I receive an error when I write the following code:
let records = {1..100}
let middleElement= records |> Seq.length / 2
The type 'int' does not match the type ''a -> int'
I know this error is basic.
But I'm new to F# and really don't know what I need to do to resolve this error.
You need to add parentheses:
let middleElement = (records |> Seq.length) / 2
In your version, the compiler reads your code as
let middleElement = records |> (Seq.length / 2)
... and it gets confused, because it thinks you are trying to divide the length function by 2!
I endorse Tomas Petricek's answer, but you could also write it this way. :-)
let records = {1..100}
let middleElement = records |> Seq.length |> (/) <| 2
This says, take the records, feed them to the length function. Feed the result as the first argument to the divide (/) function. This will result in a function which takes an int and returns an int (int -> int). We then feed 2 to that function to get 50.
[Edit] I just realized that this might be even clearer
let records = {1..100}
let middleElement = let length = records |> Seq.length in length / 2;;
I am attempting to generate a series of guesses for the second Taxicab number. What I want to do is is call the Attempt function on a series of integers in a finite sequence. I have my two questions about implementation in the comments.
A taxi cab number, in case your wondering, is the least number that satisfied the sum of 2 unique cubes in for n unique sets of 2 unique cubes. Ta(2) is 1729.
[<EntryPoint>]
let main argv =
let Attempt (start : int) =
let stop = start+20
let integerList = [start..stop]
let list = List.init 3 (fun x -> integerList.[x])
//Is there a simple way to make initialize the list with random indices of integerList?
let Cube x = x*x*x
let newlist = list |> List.map (fun x -> Cube x)
let partitionList (x : List<int>) (y : int) = List.sum [x.[y];x.[y+1]]
let intLIST = [0..2]
let partitionList' = [for i in intLIST do yield partitionList newlist i]
let x = Set.ofList partitionList'
let y = Set.ofList partitionList'
//I was going to try to use some kind of equality operator to determine whether the two sets were equal, which could tell me whether we had actually found a Taxicab number by the weakened definition.
System.Console.Write(list)
System.Console.Write(newlist)
let rnd = System.Random()
//My primary question is how can I convert a random to an integer to use in start for the function Attempt?
System.Console.ReadKey() |> ignore
printfn("%A") argv
0
Dirty way to initialize list with random indexes of another list:
let randomIndexes count myList =
let rand = System.Random()
seq {
for n = 1 to count do
yield rand.Next(List.length myList) }
|> Seq.distinct
//|> Seq.sort // if you need them sorted
|> List.ofSeq
let result = randomIndexes 5 [3;2;4;5]
printfn "%A" result
I am using F# Canopy to complete some web testing. I am trying to create and load a random number with or without letters, not that important and use it to paste to my website.
The code I am currently using is
let genRandomNumbers count =
let rnd = System.Random()
List.init count
let l = genRandomNumbers 1
"#CompanyName" << l()
The #CompanyName is the ID of the element I am trying to pass l into. As it stands I am receiving the error 'The expression was expected to have type string but here it has type a list.
Any help would be greatly appreciated.
The << operator in canopy writes a string to the selector (I haven't used it but the documentation looks pretty clear), but your function returns a list. If you want the random string to work, you could do something like this (not tested code)
let randomNumString n = genRandomNumbers n |> List.map string |> List.reduce (+)
This maps your random list to strings then concats all the strings together using the first element as the accumulator seed. You could also do a fold
let randomNumString n = genRandomNumbers n
|> List.fold (fun acc i -> acc + (string i)) ""
Putting it all together
let rand = new System.Random()
let genRandomNumbers count = List.init count (fun _ -> rand.Next())
let randomNumString n = genRandomNumbers n |> List.map string |> List.reduce (+)
"#CompanyName" << (randomNumString 1)
In general, F# won't do any type promotion for you. Since the << operator wants a string on the right hand side, you need to map your list to a string somehow. That means iterating over each element, converting the number to a string, and adding all the elements together into one final string.
IE,
What am I doing wrong here? Does it have to to with lists, sequences and arrays and the way the limitations work?
So here is the setup: I'm trying to generate some primes. I see that there are a billion text files of a billion primes. The question isn't why...the question is how are the guys using python calculating all of the primes below 1,000,000 in milliseconds on this post...and what am I doing wrong with the following F# code?
let sieve_primes2 top_number =
let numbers = [ for i in 2 .. top_number do yield i ]
let sieve (n:int list) =
match n with
| [x] -> x,[]
| hd :: tl -> hd, List.choose(fun x -> if x%hd = 0 then None else Some(x)) tl
| _ -> failwith "Pernicious list error."
let rec sieve_prime (p:int list) (n:int list) =
match (sieve n) with
| i,[] -> i::p
| i,n' -> sieve_prime (i::p) n'
sieve_prime [1;0] numbers
With the timer on in FSI, I get 4.33 seconds worth of CPU for 100000... after that, it all just blows up.
Your sieve function is slow because you tried to filter out composite numbers up to top_number. With Sieve of Eratosthenes, you only need to do so until sqrt(top_number) and remaining numbers are inherently prime. Suppose we havetop_number = 1,000,000, your function does 78498 rounds of filtering (the number of primes until 1,000,000) while the original sieve only does so 168 times (the number of primes until 1,000).
You can avoid generating even numbers except 2 which cannot be prime from the beginning. Moreover, sieve and sieve_prime can be merged into a recursive function. And you could use lightweight List.filter instead of List.choose.
Incorporating above suggestions:
let sieve_primes top_number =
let numbers = [ yield 2
for i in 3..2..top_number -> i ]
let rec sieve ns =
match ns with
| [] -> []
| x::xs when x*x > top_number -> ns
| x::xs -> x::sieve (List.filter(fun y -> y%x <> 0) xs)
sieve numbers
In my machine, the updated version is very fast and it completes within 0.6s for top_number = 1,000,000.
Based on my code here: stackoverflow.com/a/8371684/124259
Gets the first 1 million primes in 22 milliseconds in fsi - a significant part is probably compiling the code at this point.
#time "on"
let limit = 1000000
//returns an array of all the primes up to limit
let table =
let table = Array.create limit true //use bools in the table to save on memory
let tlimit = int (sqrt (float limit)) //max test no for table, ints should be fine
let mutable curfactor = 1;
while curfactor < tlimit-2 do
curfactor <- curfactor+2
if table.[curfactor] then //simple optimisation
let mutable v = curfactor*2
while v < limit do
table.[v] <- false
v <- v + curfactor
let out = Array.create (100000) 0 //this needs to be greater than pi(limit)
let mutable idx = 1
out.[0]<-2
let mutable curx=1
while curx < limit-2 do
curx <- curx + 2
if table.[curx] then
out.[idx]<-curx
idx <- idx+1
out
There have been several good answers both as to general trial division algorithm using lists (#pad) and in choice of an array for a sieving data structure using the Sieve of Eratosthenes (SoE) (#John Palmer and #Jon Harrop). However, #pad's list algorithm isn't particularly fast and will "blow up" for larger sieving ranges and #John Palmer's array solution is somewhat more complex, uses more memory than necessary, and uses external mutable state so is not different than if the program were written in an imperative language such as C#.
EDIT_ADD: I've edited the below code (old code with line comments) modifying the sequence expression to avoid some function calls so as to reflect more of an "iterator style" and while it saved 20% of the speed it still doesn't come close to that of a true C# iterator which is about the same speed as the "roll your own enumerator" final F# code. I've modified the timing information below accordingly. END_EDIT
The following true SoE program only uses 64 KBytes of memory to sieve primes up to a million (due to only considering odd numbers and using the packed bit BitArray) and still is almost as fast as #John Palmer's program at about 40 milliseconds to sieve to one million on a i7 2700K (3.5 GHz), with only a few lines of code:
open System.Collections
let primesSoE top_number=
let BFLMT = int((top_number-3u)/2u) in let buf = BitArray(BFLMT+1,true)
let SQRTLMT = (int(sqrt (double top_number))-3)/2
let rec cullp i p = if i <= BFLMT then (buf.[i] <- false; cullp (i+p) p)
for i = 0 to SQRTLMT do if buf.[i] then let p = i+i+3 in cullp (p*(i+1)+i) p
seq { for i = -1 to BFLMT do if i<0 then yield 2u
elif buf.[i] then yield uint32(3+i+i) }
// seq { yield 2u; yield! seq { 0..BFLMT } |> Seq.filter (fun i->buf.[i])
// |> Seq.map (fun i->uint32 (i+i+3)) }
primesSOE 1000000u |> Seq.length;;
Almost all of the elapsed time is spent in the last two lines enumerating the found primes due to the inefficiency of the sequence run time library as well as the cost of enumerating itself at about 28 clock cycles per function call and return with about 16 function calls per iteration. This could be reduced to only a few function calls per iteration by rolling our own iterator, but the code is not as concise; note that in the following code there is no mutable state exposed other than the contents of the sieving array and the reference variable necessary for the iterator implementation using object expressions:
open System
open System.Collections
open System.Collections.Generic
let primesSoE top_number=
let BFLMT = int((top_number-3u)/2u) in let buf = BitArray(BFLMT+1,true)
let SQRTLMT = (int(sqrt (double top_number))-3)/2
let rec cullp i p = if i <= BFLMT then (buf.[i] <- false; cullp (i+p) p)
for i = 0 to SQRTLMT do if buf.[i] then let p = i+i+3 in cullp (p*(i+1)+i) p
let nmrtr() =
let i = ref -2
let rec nxti() = i:=!i+1;if !i<=BFLMT && not buf.[!i] then nxti() else !i<=BFLMT
let inline curr() = if !i<0 then (if !i= -1 then 2u else failwith "Enumeration not started!!!")
else let v = uint32 !i in v+v+3u
{ new IEnumerator<_> with
member this.Current = curr()
interface IEnumerator with
member this.Current = box (curr())
member this.MoveNext() = if !i< -1 then i:=!i+1;true else nxti()
member this.Reset() = failwith "IEnumerator.Reset() not implemented!!!"
interface IDisposable with
member this.Dispose() = () }
{ new IEnumerable<_> with
member this.GetEnumerator() = nmrtr()
interface IEnumerable with
member this.GetEnumerator() = nmrtr() :> IEnumerator }
primesSOE 1000000u |> Seq.length;;
The above code takes about 8.5 milliseconds to sieve the primes to a million on the same machine due to greatly reducing the number of function calls per iteration to about three from about 16. This is about the same speed as C# code written in the same style. It's too bad that F#'s iterator style as I used in the first example doesn't automatically generate the IEnumerable boiler plate code as C# iterators do, but I guess that is the intention of sequences - just that they are so damned inefficient as to speed performance due to being implemented as sequence computation expressions.
Now, less than half of the time is expended in enumerating the prime results for a much better use of CPU time.
What am I doing wrong here?
You've implemented a different algorithm that goes through each possible value and uses % to determine if it needs to be removed. What you're supposed to be doing is stepping through with a fixed increment removing multiples. That would be asymptotically.
You cannot step through lists efficiently because they don't support random access so use arrays.