Created
August 19, 2013 01:21
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A function to compute the permanent of a matrix in Haskell. The algorithm is not as efficient as it could be - it is using the Ryser formula for an O(n^2 * 2^n) runtime, where a O(n * 2^n) algorithm exists, which uses the same idea but adds Gray codes to compute the subsets in a better order, allowing a reuse of computations.
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{-# LANGUAGE FlexibleContexts #-} | |
import Data.Array.IArray (IArray, bounds) | |
import Data.Array.Unboxed (UArray) | |
import Data.Array.Base (unsafeAt) | |
import Data.Bits (popCount, testBit) | |
permanent :: (Integral a, IArray UArray a) => UArray (Int, Int) a -> a | |
permanent arr | n == m = (if even n then negate else id) (sum entries) | |
where | |
((0, 0), (n, m)) = bounds arr | |
n' = n + 1 | |
entries = do | |
i <- [1 .. 2^n' - 1] :: [Int] | |
let columnSums = map column [0 .. n] | |
bits = map (* n') $ filter (testBit i) [0 .. n] | |
column j = sum $ map (unsafeAt arr . (+ j)) bits | |
return . (if odd (popCount i) then negate else id) $ product columnSums |
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