# Examples/Random list

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== Delete an element at random == |
== Delete an element at random == |
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− | <haskell> |
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unpick and unpick' are by osfameron and are from http://osfameron.vox.com/library/post/more-random-fun.html (no explicit license) |
unpick and unpick' are by osfameron and are from http://osfameron.vox.com/library/post/more-random-fun.html (no explicit license) |
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removeOne is by Chris Kuklewicz (BSD3 licence, 2007) |
removeOne is by Chris Kuklewicz (BSD3 licence, 2007) |
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− | > import System.Random |
+ | <haskell> |

− | > import Control.Monad.State.Lazy |
+ | import System.Random |

− | > import Debug.Trace -- for removeOne' demonstration |
+ | import Control.Monad.State.Lazy |

+ | import Debug.Trace -- for removeOne' demonstration |
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+ | </haskell> |
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− | The unpick function and its helper unpick' are strict in the entire |
+ | The unpick function and its helper unpick' are strict in the entire list being operated on (forcing it all into memory at once). And IO [a] cannot lazily return any initial values. |

− | list being operated on (forcing it all into memory at once). And IO |
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− | [a] cannot lazily return any initial values. |
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− | > unpick :: [a] -> IO [a] |
+ | <haskell> |

− | > unpick [] = undefined |
+ | unpick :: [a] -> IO [a] |

− | > unpick [x] = do return [] |
+ | unpick [] = undefined |

− | > unpick (x:xs) = do zs <- unpick' [] [x] xs 2 |
+ | unpick [x] = return [] |

− | > return (reverse zs) |
+ | unpick (x:xs) = do zs <- unpick' [] [x] xs 2 |

− | > |
+ | return (reverse zs) |

− | > unpick' :: (Num p, Random p) => [t] -> [t] -> [t] -> p -> IO [t] |
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− | > unpick' curr orig [] _ |
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− | > = do return curr |
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− | > unpick' curr orig (next:rest) prob |
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− | > = do r <- getStdRandom (randomR (1,prob)) |
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− | > let curr' = if r == 1 then orig else (next:curr) |
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− | > unpick' curr' (next:orig) rest (prob+1) |
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− | To run in the IO Monad just use (getStdRandom . removeOne) :: [a] -> IO [a]. |
+ | unpick' :: (Num p, Random p) => [t] -> [t] -> [t] -> p -> IO [t] |

+ | unpick' curr _ [] _ = return curr |
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+ | unpick' curr orig (next:rest) prob |
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+ | = do r <- getStdRandom (randomR (1,prob)) |
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+ | let curr' = if r == 1 then orig else (next:curr) |
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+ | unpick' curr' (next:orig) rest (prob+1) |
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+ | </haskell> |
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− | removeOne returns the output list lazily as soon as it has decided |
+ | To run in the IO Monad just use <hask>(getStdRandom . removeOne) :: [a] -> IO [a].</hask> |

− | not to delete any element in a prefix of the input list. |
+ | <hask>removeOne</hask> returns the output list lazily as soon as it has decided not to delete any element in a prefix of the input list. |

− | The resulting list is constructed efficiently, with no wasted |
+ | The resulting list is constructed efficiently, with no wasted intermediate list construction. <hask>removeOne</hask> allows any output it generates to be garbage collected, it holds no references to it. |

− | intermediate list construction. removeOne allows any output it |
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− | generates to be garbage collected, it holds no references to it. |
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− | "removeOne" is presented in curried form, without a binding for the |
+ | <hask>removeOne</hask> is presented in curried form, without a binding for the |

− | RandomGen g. The StdGen is hidden inside a State |
+ | RandomGen g. The StdGen is hidden inside a State monad. <hask>removeOne</hask> is designed for use with Strict.Lazy. It may not be optimal to use with <hask>Strict.Strict</hask>. |

− | monad. removeOne is designed for use with Strict.Lazy. It may not be |
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− | optimal to use with Strict.Strict. |
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− | Like "tail" this function is partial and will produce an error if |
+ | Like <hask>tail</hask> this function is partial and will produce an error if given the empty list. |

− | given the empty list. |
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− | > removeOne :: (RandomGen g) => [a] -> g -> ([a],g) |
+ | <haskell> |

− | > removeOne [] = error "Cannot removeOne from empty list" |
+ | removeOne :: (RandomGen g) => [a] -> g -> ([a],g) |

− | > removeOne whole@(_:xs) = runState (helper whole xs 0 1) where |
+ | removeOne [] = error "Cannot removeOne from empty list" |

+ | removeOne whole@(_:xs) = runState (helper whole xs 0 1) where |
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+ | </haskell> |
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− | The laziness is needed in helper to make "rest" a lazy thunk. The |
+ | The laziness is needed in helper to make <hask>rest</hsak> a lazy thunk. The |

− | "start" list parameter to helper is a suffix of "whole" that has the |
+ | <hask>start</hask> list parameter to helper is a suffix of <hask>whole</hask> that has the current candidate for deletion as its head. <hask>oldIndex</hask> is the index of the current candidate for deletion in the <hask>whole</hask> list. <hask>here</hask> is a suffix of <hask>whole</hask> with the <hask>index</hask><sup>th</sup> element of whole as its head. <hask>randomR</hask> decides if the head of <hask>here</hask> replaces the head of <hask>start</hask> as the candidate to remove. If it does replace the old candidate then a prefix of <hask>start</hask> of length <hask>(index-oldIndex)</hask> is immediately output, counted off by prependSome. |

− | current candidate for deletion as its head. "oldIndex" is the index |
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− | of the current candidate for deletion in the "whole" list. "here" is a |
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− | suffix of "whole" with the "index" element of whole as its head. The |
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− | randomR decides if the head of "here" replaces the head of "start" as |
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− | the candidate to remove. If it does replace the old candidate then |
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− | a prefix of "start" of length "(index-oldIndex)" is immediately |
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− | output, counted off by prependSome. |
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− | Assert "start" is never []. |
+ | Assert <hask>"start"</hask> is never <hask>[]</hask>. |

− | Assert 0 <= oldIndex < index. |
+ | Assert <hask>0 <= oldIndex < index</hask>. |

− | > helper start [] oldIndex index = return (tail start) |
+ | <haskell> |

− | > helper start here@(_:ys) oldIndex index = do |
+ | helper start [] oldIndex index = return (tail start) |

− | > r <- State (randomR (0,index)) |
+ | helper start here@(_:ys) oldIndex index = do |

− | > if r==0 then do rest <- helper here ys index $! succ index |
+ | r <- State (randomR (0,index)) |

− | > return (prependSome (index-oldIndex) start rest) |
+ | if r==0 then do rest <- helper here ys index $! succ index |

− | > else helper start ys oldIndex $! succ index |
+ | return (prependSome (index-oldIndex) start rest) |

+ | else helper start ys oldIndex $! succ index |
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+ | </haskell> |
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− | I assert that "prependSome n xs ys == take n xs ++ ys" but slightly |
+ | I assert that <hask>prependSome n xs ys == take n xs ++ ys</hask> but slightly |

− | optimized (without depending on the compiler). Assert n >= length xs. |
+ | optimized (without depending on the compiler). Assert <hask>n >= length xs</hask>. |

− | > prependSome :: Int -> [a] -> [a] -> [a] |
+ | <haskell> |

− | > prependSome 0 _ rest = rest |
+ | prependSome :: Int -> [a] -> [a] -> [a] |

− | > prependSome n (x:xs) rest = x : prependSome (pred n) xs rest |
+ | prependSome 0 _ rest = rest |

− | > prependSome _ [] _ = error "impossible error in removeOne.prependSome" |
+ | prependSome n (x:xs) rest = x : prependSome (pred n) xs rest |

+ | prependSome _ [] _ = error "impossible error in removeOne.prependSome" |
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+ | </haskell> |
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− | "removeOne'" is a tracing version for demonstration below: |
+ | <hask>removeOne</hask> is a tracing version for demonstration below: |

− | > removeOne' :: (Show a,RandomGen g) => [a] -> g -> ([a],g) |
+ | <haskell> |

− | > removeOne' [] _ = error "Cannot removeOne from empty list" |
+ | removeOne' :: (Show a,RandomGen g) => [a] -> g -> ([a],g) |

− | > removeOne' whole@(x:xs) g = runState (helper whole xs 0 1) g where |
+ | removeOne' [] _ = error "Cannot removeOne from empty list" |

− | > helper start [] oldIndex index = return (tail start) |
+ | removeOne' whole@(x:xs) g = runState (helper whole xs 0 1) g where |

− | > helper start here@(_:ys) oldIndex index = do |
+ | helper start [] oldIndex index = return (tail start) |

− | > r <- State (randomR (0,index)) |
+ | helper start here@(_:ys) oldIndex index = do |

− | > if r==0 then do rest <- helper here ys index $! succ index |
+ | r <- State (randomR (0,index)) |

− | > let rest' = trace "." rest |
+ | if r==0 then do rest <- helper here ys index $! succ index |

− | > return (prependSome (index-oldIndex) start rest') |
+ | let rest' = trace "." rest |

− | > else do let ys' = trace "_" ys |
+ | return (prependSome (index-oldIndex) start rest') |

− | > helper start ys' oldIndex $! succ index |
+ | else do let ys' = trace "_" ys |

+ | helper start ys' oldIndex $! succ index |
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+ | </haskell> |
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− | Use "removeOne'" to demonstrate when random decisions to drop |
+ | I will use <hask>removeOne</hask> to demonstrate when random decisions to drop |

− | elements are made. This also demonstrates that removeOne is lazy, |
+ | elements are made. This also demonstrates that <hask>removeOne</hask> is lazy, |

− | returning elements as soon as the removal decision has moved on to a |
+ | returning elements as soon as the removal decision has moved on to a |

− | later element (the "." is output instead of "_"). |
+ | later element (the "." is output instead of "_"). |

− | The element after the last "." is the one actually removed, |
+ | The element after the last "." is the one actually removed, |

− | defaulting to the first element. |
+ | defaulting to the first element. |

− | Since the probability of "." decreases, the average length of the |
+ | Since the probability of "." decreases, the average length of the run of output produced by <hask>appendSome</hask> increases as the list is processed. |

− | run of output produced by appendSome increases as the list is |
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− | processed. |
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+ | <haskell> |
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*Main> getStdRandom (removeOne' [1..10]) |
*Main> getStdRandom (removeOne' [1..10]) |
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[1. |
[1. |
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Line 164: | Line 164: | ||

,7,8,9. |
,7,8,9. |
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] |
] |
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+ | </haskell> |
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− | If I use ":m + Data.List" then I can demonstrate how fair the removal is: |
+ | If I use <hask>:m + Data.List Control.Monad</hask> then I can demonstrate how fair the removal is: |

− | *Main Data.List> sequence (replicate 1000 $ getStdRandom (removeOne [1..4])) >>= return . map length . group . sort |
+ | <haskell> |

+ | *Main Data.List Control.Monad> replicateM 1000 (getStdRandom (removeOne [1..4])) >>= return . map length . group . sort |
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[241,255,239,265] |
[241,255,239,265] |
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− | |||

− | where a perfect balance would be [250,250,250,250] |
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</haskell> |
</haskell> |
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+ | |||

+ | where a perfect balance would be <hask>[250,250,250,250]</hask> |

## Latest revision as of 21:09, 4 March 2011

## [edit] 1 Create a random list

Generate a random list of numbers, without using the System.Random.randoms method:

import System.Random import Data.List main = do seed <- newStdGen let rs = randomlist 10 seed print rs randomlist :: Int -> StdGen -> [Int] randomlist n = take n . unfoldr (Just . random)

## [edit] 2 Delete an element at random

unpick and unpick' are by osfameron and are from http://osfameron.vox.com/library/post/more-random-fun.html (no explicit license) removeOne is by Chris Kuklewicz (BSD3 licence, 2007)

import System.Random import Control.Monad.State.Lazy import Debug.Trace -- for removeOne' demonstration

The unpick function and its helper unpick' are strict in the entire list being operated on (forcing it all into memory at once). And IO [a] cannot lazily return any initial values.

unpick :: [a] -> IO [a] unpick [] = undefined unpick [x] = return [] unpick (x:xs) = do zs <- unpick' [] [x] xs 2 return (reverse zs) unpick' :: (Num p, Random p) => [t] -> [t] -> [t] -> p -> IO [t] unpick' curr _ [] _ = return curr unpick' curr orig (next:rest) prob = do r <- getStdRandom (randomR (1,prob)) let curr' = if r == 1 then orig else (next:curr) unpick' curr' (next:orig) rest (prob+1)

(getStdRandom . removeOne) :: [a] -> IO [a].

removeOne

removeOne

removeOne

removeOne

Strict.Strict

tail

removeOne :: (RandomGen g) => [a] -> g -> ([a],g) removeOne [] = error "Cannot removeOne from empty list" removeOne whole@(_:xs) = runState (helper whole xs 0 1) where

rest</hsak> a lazy thunk. The

<hask>start

<hask>start

whole

oldIndex

whole

here

whole

index

^{th}element of whole as its head.

randomR

here

start

start

(index-oldIndex)

"start"

[]

0 <= oldIndex < index

helper start [] oldIndex index = return (tail start) helper start here@(_:ys) oldIndex index = do r <- State (randomR (0,index)) if r==0 then do rest <- helper here ys index $! succ index return (prependSome (index-oldIndex) start rest) else helper start ys oldIndex $! succ index

prependSome n xs ys == take n xs ++ ys

n >= length xs

prependSome :: Int -> [a] -> [a] -> [a] prependSome 0 _ rest = rest prependSome n (x:xs) rest = x : prependSome (pred n) xs rest prependSome _ [] _ = error "impossible error in removeOne.prependSome"

removeOne

removeOne' :: (Show a,RandomGen g) => [a] -> g -> ([a],g) removeOne' [] _ = error "Cannot removeOne from empty list" removeOne' whole@(x:xs) g = runState (helper whole xs 0 1) g where helper start [] oldIndex index = return (tail start) helper start here@(_:ys) oldIndex index = do r <- State (randomR (0,index)) if r==0 then do rest <- helper here ys index $! succ index let rest' = trace "." rest return (prependSome (index-oldIndex) start rest') else do let ys' = trace "_" ys helper start ys' oldIndex $! succ index

removeOne

removeOne

returning elements as soon as the removal decision has moved on to a later element (the "." is output instead of "_").

The element after the last "." is the one actually removed, defaulting to the first element.

Since the probability of "." decreases, the average length of the run of output produced byappendSome

*Main> getStdRandom (removeOne' [1..10]) [1. _ _ ,2,3,4. _ _ _ _ ,5,6,7,8,9. ] *Main> getStdRandom (removeOne' [1..10]) _ _ [1,2,3. _ _ _ _ _ _ ,5,6,7,8,9,10] *Main> getStdRandom (removeOne' [1..10]) _ _ _ _ _ _ _ _ _ [2,3,4,5,6,7,8,9,10] *Main> getStdRandom (removeOne' [1..10]) [1. _ _ _ _ _ _ _ _ ,3,4,5,6,7,8,9,10] *Main> getStdRandom (removeOne' [1..10]) [1. ,2. _ _ _ _ _ _ _ ,4,5,6,7,8,9,10] *Main> getStdRandom (removeOne' [1..10]) [1. _ _ _ _ ,2,3,4,5,6. _ _ ,7,8,9. ]

:m + Data.List Control.Monad

*Main Data.List Control.Monad> replicateM 1000 (getStdRandom (removeOne [1..4])) >>= return . map length . group . sort [241,255,239,265]

[250,250,250,250]