# memoization Classic List Threaded 4 messages Open this post in threaded view
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## memoization

 I know we can perform memoization in Haskell.  The well known recursive Fibonacci example works v. well.  f(10000) returns a virtually instant answer which would not be possible otherwise. My (probably naive) function to give the number of partitions of a number :- p = ((map p' [0 .. ]) !!)   where   p' 0 = 1   p' 1 = 1   p' n = sum [(((-1) ^ (k+1)) * ( p' (n-((k*(3*k-1)) `div` 2))  +  p' (n-((k*(3*k+1)) `div` 2)))) | k  <- [1 .. n]] It is an attempt to apply the Euler recurrence formula (no 11 in http://mathworld.wolfram.com/PartitionFunctionP.html ) It works but it is shockingly slow.  It is orders of magnitude slower than the Python memoized version which runs very fast. parts = {0:1, 1:1} def P(n):   if not n in parts:     parts[n] = sum ([( ((-1) ** (k+1)) * ( P(n-((k*(3*k-1))//2)) +   P(n-((k*(3*k+1))//2)) ) ) for k in xrange (1, n+1)])   return parts[n] Why?  Its as if memoization is being ignored in the haskell version.   How to fix?   _______________________________________________ Haskell-Cafe mailing list [hidden email] http://www.haskell.org/mailman/listinfo/haskell-cafe
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## Re: memoization

 On Sun, 2008-07-13 at 20:24 +0200, Logesh Pillay wrote: > I know we can perform memoization in Haskell.  The well known recursive > Fibonacci example works v. well.  f(10000) returns a virtually instant > answer which would not be possible otherwise. > > My (probably naive) function to give the number of partitions of a number :- > p = ((map p' [0 .. ]) !!) >   where >   p' 0 = 1 >   p' 1 = 1 >   p' n = sum [(((-1) ^ (k+1)) * ( p' (n-((k*(3*k-1)) `div` 2))  +  p' > (n-((k*(3*k+1)) `div` 2)))) | k  <- [1 .. n]] > > It is an attempt to apply the Euler recurrence formula (no 11 in > http://mathworld.wolfram.com/PartitionFunctionP.html ) > > It works but it is shockingly slow.  It is orders of magnitude slower > than the Python memoized version which runs very fast. > parts = {0:1, 1:1} > def P(n): >   if not n in parts: >     parts[n] = sum ([( ((-1) ** (k+1)) * ( P(n-((k*(3*k-1))//2)) +   > P(n-((k*(3*k+1))//2)) ) ) for k in xrange (1, n+1)]) >   return parts[n] > > Why?  Its as if memoization is being ignored in the haskell version.   That's because you aren't using it. > How to fix? Use your memoized function. _______________________________________________ Haskell-Cafe mailing list [hidden email] http://www.haskell.org/mailman/listinfo/haskell-cafe