# Memoization

### From HaskellWiki

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'''Memoization''' is a technique for storing values of a function instead of recomputing them each time the function is called. | '''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 number]]s. | ||

+ | |||

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

+ | Try <hask>slow_fib 30</hask>, not too much higher than that and it hangs. | ||

+ | <haskell> | ||

+ | slow_fib :: Integer -> Integer | ||

+ | slow_fib 1 = 1 | ||

+ | slow_fib 2 = 1 | ||

+ | slow_fib n = slow_fib (n-2) + slow_fib (n-1) | ||

+ | </haskell> | ||

+ | |||

+ | The memoized version is much faster. | ||

+ | Try <hask>memoized_fib 10000</hask>. | ||

+ | |||

+ | <haskell> | ||

+ | 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 ..] !!) | ||

+ | </haskell> | ||

+ | |||

== See also == | == See also == |

## Revision as of 20:02, 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.

Tryslow_fib 30

slow_fib :: Integer -> Integer slow_fib 1 = 1 slow_fib 2 = 1 slow_fib n = slow_fib (n-2) + slow_fib (n-1)

The memoized version is much faster.

Trymemoized_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 ..] !!)