使用Data.Vector进行动态编程

Question

am using Data.Vector and am currently in need of computing the contents of a vector for use in computing a cryptographic hash(Sha1). I created the following code.

dynamic :: a -> Int -> (Int -> Vector a -> a) -> Vector a
dynamic e n f = 
let 
    start = Data.Vector.replicate n e   
in step start 0
where
    step vector i = if i==n then vector
                    else step (vector // [(i,f i vector)]) (i+1)

I created this so that the function f filling out the vector has access to the partial results along the way. Surely something like this must already exist in Data.Vector, no?

The problem statement is the following: You are to solve a dynamic programming problem where the finished result is an array. You know the size of the array size and you have a recursive function for filling it out.

Answer 1

You probably already saw the function generate , which takes a size n and a function f of type Int -> a and then produces a Vector a of size n . What you probably weren't aware of is that when using this function you actually do have access to the partial results.

What I mean to say is that inside the function you pass to generate you can refer to the vector you're defining and due to Haskell's laziness it will work fine (unless you make it so that the different items of the vector depend on each other in a circular fashion, of course).

Example:

import Data.Vector

tenFibs = generate 10 fib
    where fib 0 = 0
          fib 1 = 1
          fib n = tenFibs ! (n-1) + tenFibs ! (n-2)

tenFibs is now a vector containing the first 10 Fibonacci numbers.

Answer 2

Maybe you could use one of Data.Vector's scan functions? http://hackage.haskell.org/packages/archive/vector/0.6.0.2/doc/html/Data-Vector.html#32