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Memoization

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(Fibonacci, memoization with a simple list)
(same base case)
Line 9: Line 9:
 
<haskell>
 
<haskell>
 
slow_fib :: Integer -> Integer
 
slow_fib :: Integer -> Integer
  +
slow_fib 0 = 0
 
slow_fib 1 = 1
 
slow_fib 1 = 1
slow_fib 2 = 1
 
 
slow_fib n = slow_fib (n-2) + slow_fib (n-1)
 
slow_fib n = slow_fib (n-2) + slow_fib (n-1)
 
</haskell>
 
</haskell>
Line 20: Line 20:
 
memoized_fib :: Integer -> Integer
 
memoized_fib :: Integer -> Integer
 
memoized_fib =
 
memoized_fib =
let fib' 0 = 0
+
let fib 0 = 0
fib' 1 = 1
+
fib 1 = 1
fib' n = memoized_fib (n-2) + memoized_fib (n-1)
+
fib n = memoized_fib (n-2) + memoized_fib (n-1)
in (map fib' [0 ..] !!)
+
in (map fib [0 ..] !!)
 
</haskell>
 
</haskell>
   

Revision as of 20:09, 5 August 2007


Memoization is a technique for storing values of a function instead of recomputing them each time the function is called.

A classic example is the recursive computation of Fibonacci numbers.

The immediate implementation of Fibonacci numbers without memoization is horribly slow.

Try
slow_fib 30
, not too much higher than that and it hangs.
slow_fib :: Integer -> Integer
slow_fib 0 = 0
slow_fib 1 = 1
slow_fib n = slow_fib (n-2) + slow_fib (n-1)

The memoized version is much faster.

Try
memoized_fib 10000
.
memoized_fib :: Integer -> Integer
memoized_fib =
   let fib 0 = 0
       fib 1 = 1
       fib n = memoized_fib (n-2) + memoized_fib (n-1)
   in  (map fib [0 ..] !!)


See also