how to optimize this recursion function with cache - recursion

When asked the question "palindromic decomposition", which is to separate an input string into a series of palindromic strings and return all the decompositions. I with my co worker provided different answers. And his approach is easily being optimized by returning each subproblem's result and caching them, While I dont know how to optimize my approach:
In [38]: def palindrome_decompose(s):
...: def sub_palindrome(offset, path):
...: if offset == len(s):
...: result.append(path)
...: return
...:
...: for i in range(offset, len(s)):
...: prefix = s[offset: i + 1]
...: if prefix == prefix[::-1]:
...: sub_palindrome(i + 1, path + [prefix])
...:
...: cache = {}
...: result = []
...: sub_palindrome(0, [])
...: return result
...:
I accidentally pass the intermediate result into the argument and only by reaching the bottom an answer is reached. If you have any idea to make it cached as well, please help me!
the input and out of this function:
s = 'aab'
return [['a','a','b'],['aa','b']]

Related

Type annotation for Callables with *args

I know how to type-annotate functions which take arguments.
def function(text: str, *args: int) -> None:
print(text)
for arg in args:
print(arg)
My problem, however, is that I don't know what this looks like when another function takes it as an input:
def introduce(foo: Callable[[str, XXX], None], text: str, *args: int) -> None:
print("Enter...")
foo(text, *args)
print("Exit...")
introduce(function, "Hello, World!", (1, 2, 3))
Naturally, the XXX represents whatever it is that *args is supposed to be. However, I can't figure that out, and I've been unable to intuit what belongs there. I don't think it would be int, as that would suggest exactly one proceeding value. Experimentation has failed me here.

currying multiple functions in parallel in F#

I'm trying to learn F# at the moment and have come up on a problem I can't solve and can't find any answers for on google.
Initially I wanted a log function that would work like the printf family of functions whereby I could provide a format string and a number of arguments (statically checked) but which would add a little metadata before printing it out. With googling, I found this was possible using a function like the following:
let LogToConsole level (format:Printf.TextWriterFormat<'T>) =
let extendedFormat = (Printf.TextWriterFormat<string->string->'T> ("%s %s: " + format.Value))
let date = DateTime.UtcNow.ToString "yyyy-MM-dd HH:mm:ss.fff"
let lvl = string level
printfn extendedFormat date lvl
having the printfn function as the last line of this function allows the varargs-like magic of the printf syntax whereby the partially-applied printfn method is returned to allow the caller to finish applying arguments.
However, if I have multiple such functions with the same signature, say LogToConsole, LogToFile and others, how could I write a function that would call them all keeping this partial-application magic?
Essential I'm looking for how I could implement a function MultiLog
that would allow me to call multiple printf-like functions from a single function call Such as in the ResultIWant function below:
type LogFunction<'T> = LogLevel -> Printf.TextWriterFormat<'T> -> 'T
let MultiLog<'T> (loggers:LogFunction<'T>[]) level (format:Printf.TextWriterFormat<'T>) :'T =
loggers
|> Seq.map (fun f -> f level format)
|> ?????????
let TheResultIWant =
let MyLog = MultiLog [LogToConsole; LogToFile]
MyLog INFO "Text written to %i outputs" 2
Perhaps the essence of this question can be caught more succintly: given a list of functions of the same signature how can I partially apply them all with the same arguments?
type ThreeArg = string -> int -> bool -> unit
let funcs: ThreeArg seq = [func1; func2; func3]
let MagicFunction = ?????
// I'd like this to be valid
let partiallyApplied = MagicFunction funcs "string"
// I'd also like this to be valid
let partiallyApplied = MagicFunction funcs "string" 255
// and this (fullyApplied will be `unit`)
let fullyApplied = MagicFunction funcs "string" 255 true
To answer the specific part of the question regarding string formatting, there is a useful function Printf.kprintf which lets you do what you need in a very simple way - the first parameter of the function is a continuation that gets called with the formatted string as an argument. In this continuation, you can just take the formatted string and write it to all the loggers you want. Here is a basic example:
let Loggers = [printfn "%s"]
let LogEverywhere level format =
Printf.kprintf (fun s ->
let date = DateTime.UtcNow.ToString "yyyy-MM-dd HH:mm:ss.fff"
let lvl = string level
for logger in Loggers do logger (sprintf "%s %s %s" date lvl s)) format
LogEverywhere "BAD" "hi %d" 42
I don't think there is a nice and simple way to do what you wanted to do in the more general case - I suspect you might be able to use some reflection or static member constraints magic, but fortunately, you don't need to in this case!
There is almost nothing to add to a perfect #TomasPetricek answer as he is basically a "semi-god" in F#. Another alternative, which comes to mind, is to use a computation expression (see, for example: https://fsharpforfunandprofit.com/series/computation-expressions.html). When used properly it does look like magic :) However, I have a feeling that it is a little bit too heavy for the problem, which you described.

Writing the function "once" in Elixir

I'm coming to Elixir from primarily a Javascript background. in JS, it's possible to write a higher order function "once" which returns a function that will invoke the passed in function only once, and returns the previous result on subsequent calls- the trick is manipulating variables that were captured via closure:
var once = (func) => {
var wasCalled = false, prevResult;
return (...args) => {
if (wasCalled) return prevResult;
wasCalled = true;
return prevResult = func(...args);
}
}
It seems to me that it's not possible to create this function in Elixir, due to its different variable rebinding behavior. Is there some other clever way to do it via pattern matching or recursion, or is it just not possible? Without macros that is, I'd imagine those might enable it. Thanks
Using the current process dictionary:
defmodule A do
def once(f) do
key = make_ref()
fn ->
case Process.get(key) do
{^key, val} -> val
nil ->
val = f.()
Process.put(key, {key, val})
val
end
end
end
end
Or if the function will be passed across processes, an ets table can be used:
# ... during application initialization
:ets.new(:cache, [:set, :public, :named_table])
defmodule A do
def once(f) do
key = make_ref()
fn ->
case :ets.lookup(:cache, key) do
[{^key, val}] -> val
[] ->
val = f.()
:ets.insert(:cache, {key, val})
val
end
end
end
end
Application.put_env / Application.get_env can also be used to hold global state, though usually is used for configuration settings.
It's not considered idiomatic in most cases, but you can do this with Agent:
defmodule A do
def once(fun) do
{:ok, agent} = Agent.start_link(fn -> nil end)
fn args ->
case Agent.get(agent, & &1) do
nil ->
result = apply(fun, args)
:ok = Agent.update(agent, fn _ -> {:ok, result} end)
result
{:ok, result} ->
result
end
end
end
end
Now if you run this:
once = A.once(fn sleep ->
:timer.sleep(sleep)
1 + 1
end)
IO.inspect once.([1000])
IO.inspect once.([1000])
IO.inspect once.([1000])
IO.inspect once.([1000])
You'll see that the first line is printed after 1 second, but the next 3 are printed instantly, because the result is fetched from the agent.
While both already given answers are perfectly valid, the most precise translation from your javascript is shown below:
defmodule M do
use GenServer
def start_link(_opts \\ []) do
GenServer.start_link(__MODULE__, nil, name: __MODULE__)
end
def init(_args) do
Process.sleep(1_000)
{:ok, 42}
end
def value() do
start_link()
GenServer.call(__MODULE__, :value)
end
def handle_call(:value, _from, state) do
{:reply, state, state}
end
end
(1..5) |> Enum.each(&IO.inspect(M.value(), label: to_string(&1)))
Use the same metric as in #Dogbert’s answer: the first value is printed with a delay, all subsequent are printed immediately.
This is an exact analog of your memoized function using GenServer stage. GenServer.start_link/3 returns one of the following:
{:ok, #PID<0.80.0>}
{:error, {:already_started, #PID<0.80.0>}}
That said, it is not restarted if it’s already started. I do not bother to check the returned value since we are all set in any case: if it’s the initial start, we call the heavy function, if we were already started, the vaklue is already at fingers in the state.

How to simulate Ruby's until loop in Elixir?

I'm converting a Ruby project to Elixir. How does Ruby's until loop translate to Elixir?
until scanner.eos? do
tokens << scan(line + 1)
end
Here's the full Ruby method:
def tokenize
#tokens = []
#lines.each_with_index do |text, line|
#scanner = StringScanner.new(text)
until #scanner.eos? do
#tokens << scan(line + 1)
end
end
#tokens
end
#lines is just a text file split by new lines. #lines = text.split("\n")
In Elixir, I've already converted the string scanner which looks like this: StringScanner.eos?(scanner):
#spec eos?(pid) :: boolean
def eos?(pid) when is_pid(pid) do
Also, in Elixir, tokens are tuples: #type token :: {:atom, any, {integer, integer}}. Where the {integer, integer} tuple is the line and position of the token.
This is the Elixir psuedo-code which doesn't quite work.
#spec scan(String.t, integer) :: token
def scan(text, line) when is_binary(text) and is_integer(line) do
string_scanner = StringScanner.new(text)
until StringScanner.eos?(string_scanner) do
result = Enum.find_value(#scanner_tokenizers, fn {scanner, tokenizer} ->
match = scanner.(string_scanner)
if match do
tokenizer.(string_scanner, match, line)
end
end)
IO.inspect result
end
StringScanner.stop(string_scanner)
result
end
Someone on the slack channel suggested using recursion, however they didn't elaborate with an example. I've seen recursion examples for summing / reducing which use accumulators etc. However, I don't see how that applies when evaluating a boolean.
Can anyone provide a working example which uses StringScanner.eos?(scanner)? Thanks.
It may be something like
def tokens(scanner) do
tokens(scanner, [])
end
defp tokens(scanner, acc) do
if StringScanner.eos?(scanner) do
acc
else
tokens(scanner, add_to_acc(scan_stuff(), acc))
end
end
At least this can be the general idea. As you'll see I kept a couple of functions very generic (scan_stuff/0 and add_to_acc/2) as I don't know how you mean to implement those; the first one is meant to do what scan(line + 1) does in the Ruby code, while the second one is meant to do what << does in the Ruby code (e.g., it could add the scanned stuff to the list of tokens or something similar).

Creating Sequence of Sequences is Causing a StackOverflowException

I'm trying to take a large file and split it into many smaller files. The location where each split occurs is based on a predicate returned from examining the contents of each given line (isNextObject function).
I have attempted to read in the large file via the File.ReadLines function so that I can iterate through the file one line at a time without having to hold the entire file in memory. My approach was to group the sequence into a sequence of smaller sub-sequences (one per file to be written out).
I found a useful function that Tomas Petricek created on fssnip called groupWhen. This function worked great for my initial testing on a small subset of the file, but a StackoverflowException is thrown when using the real file. I am not sure how to adjust the groupWhen function to prevent this (I'm still an F# greenie).
Here is a simplified version of the code showing only the relevant parts that will recreate the StackoverflowExcpetion::
// This is the function created by Tomas Petricek where the StackoverflowExcpetion is occuring
module Seq =
/// Iterates over elements of the input sequence and groups adjacent elements.
/// A new group is started when the specified predicate holds about the element
/// of the sequence (and at the beginning of the iteration).
///
/// For example:
/// Seq.groupWhen isOdd [3;3;2;4;1;2] = seq [[3]; [3; 2; 4]; [1; 2]]
let groupWhen f (input:seq<_>) = seq {
use en = input.GetEnumerator()
let running = ref true
// Generate a group starting with the current element. Stops generating
// when it founds element such that 'f en.Current' is 'true'
let rec group() =
[ yield en.Current
if en.MoveNext() then
if not (f en.Current) then yield! group() // *** Exception occurs here ***
else running := false ]
if en.MoveNext() then
// While there are still elements, start a new group
while running.Value do
yield group() |> Seq.ofList }
This is the gist of the code making use Tomas' function:
module Extractor =
open System
open System.IO
open Microsoft.FSharp.Reflection
// ... elided a few functions include "isNextObject" which is
// a string -> bool (examines the line and returns true
// if the string meets the criteria to that we are at the
// start of the next inner file)
let writeFile outputDir file =
// ... write out "file" to the file system
// NOTE: file is a seq<string>
let writeFiles outputDir (files : seq<seq<_>>) =
files
|> Seq.iter (fun file -> writeFile outputDir file)
And here is the relevant code in the console application that makes use of the functions:
let lines = inputFile |> File.ReadLines
writeFiles outputDir (lines |> Seq.groupWhen isNextObject)
Any ideas on the proper way to stop groupWhen from blowing the stack? I'm not sure how I would convert the function to use an accumulator (or to use a continuation instead, which I think is the correct terminology).
The problem with this is that the group() function returns a list, which is an eagerly evaluated data structure, which means that every time you call group() it has to run to the end, collect all results in a list, and return the list. This means that the recursive call happens within that same evaluation - i.e. truly recursively, - thus creating stack pressure.
To mitigate this problem, you could just replace the list with a lazy sequence:
let rec group() = seq {
yield en.Current
if en.MoveNext() then
if not (f en.Current) then yield! group()
else running := false }
However, I would consider less drastic approaches. This example is a good illustration of why you should avoid doing recursion yourself and resort to ready-made folds instead.
For example, judging by your description, it seems that Seq.windowed may work for you.
It's easy to overuse sequences in F#, IMO. You can accidentally get stack overflows, plus they are slow.
So (not actually answering your question),
personally I would just fold over the seq of lines using something like this:
let isNextObject line =
line = "---"
type State = {
fileIndex : int
filename: string
writer: System.IO.TextWriter
}
let makeFilename index =
sprintf "File%i" index
let closeFile (state:State) =
//state.writer.Close() // would use this in real code
state.writer.WriteLine("=== Closing {0} ===",state.filename)
let createFile index =
let newFilename = makeFilename index
let newWriter = System.Console.Out // dummy
newWriter.WriteLine("=== Creating {0} ===",newFilename)
// create new state with new writer
{fileIndex=index + 1; writer = newWriter; filename=newFilename }
let writeLine (state:State) line =
if isNextObject line then
/// finish old file here
closeFile state
/// create new file here and return updated state
createFile state.fileIndex
else
//write the line to the current file
state.writer.WriteLine(line)
// return the unchanged state
state
let processLines (lines: string seq) =
//setup
let initialState = createFile 1
// process the file
let finalState = lines |> Seq.fold writeLine initialState
// tidy up
closeFile finalState
(Obviously a real version would use files rather than the console)
Yes, it is crude, but it is easy to reason about, with
no unpleasant surprises.
Here's a test:
processLines [
"a"; "b"
"---";"c"; "d"
"---";"e"; "f"
]
And here's what the output looks like:
=== Creating File1 ===
a
b
=== Closing File1 ===
=== Creating File2 ===
c
d
=== Closing File2 ===
=== Creating File3 ===
e
f
=== Closing File3 ===

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