Comments on: Project Euler in F# – Problem 53 – Dynamic Programming

By: Steffen Forkmann

Steffen Forkmann — Tue, 09 Dec 2008 17:18:12 +0000

@GrahameTheHornist:

Thank you. I tried your solution on my computer and with 16ms it is the fastest so far. Well done.

By: GrahameTheHornist

GrahameTheHornist — Tue, 09 Dec 2008 16:56:33 +0000

let euler53() =
    let binomial (* n k *) =
        let binomials = Array2.create 101 101 1I
        fun n k -> 
            let b = binomials.[n-1, k] + binomials.[n-1, k-1]
            binomials.[n, k] <- b
            binomials.[n, n-k] <- b
            b
        
    let rec nLoop n acc = if n > 100 then acc 
                                     else kLoop n 1 acc
    and kLoop n k acc =
        if k > n/2 
            then nLoop (n+1) acc
        elif binomial n k > 1000000I 
            then nLoop (n+1) (acc + n-1 - 2*(k-1))
        else kLoop n (k+1) acc                  
                      
    nLoop 1 0

By: Steffen Forkmann

Steffen Forkmann — Tue, 09 Dec 2008 08:10:15 +0000

Thanks Grahame. But I think something went wrong. Where is the definition of the nLoop?

(i added a

 for code formatting)

By: Claudio

Claudio — Tue, 09 Dec 2008 08:09:51 +0000

Great post!
Dynamic programming is exactly what I had in mind when I asked for optimization strategies.

By: GrahameTheHornist

GrahameTheHornist — Mon, 08 Dec 2008 23:48:28 +0000

Shoot, no formatting! Sorry about that.

By: GrahameTheHornist

GrahameTheHornist — Mon, 08 Dec 2008 23:47:24 +0000

Great efficiency improvements! I wrote the following version of your algorithm, using recursion instead of an imperative style and also using (k-1) instead of c. My version seems to be a little more efficient.

let euler53() =
    let binomial (* n k *) =
        let binomials = Array2.create 101 101 1I
        fun n k -> 
            let b = binomials.[n-1, k] + binomials.[n-1, k-1]
            binomials.[n, k] <- b
            binomials.[n, n-k]  100 then acc 
                                     else kLoop n 1 acc
    and kLoop n k acc =
        if k > n/2 
            then nLoop (n+1) acc
        elif binomial n k > 1000000I 
            then nLoop (n+1) (acc + n-1 - 2*(k-1))
        else kLoop n (k+1) acc                  
                      
    nLoop 1 0