Euclidean Algorithm

Chet — Sat, 04 Jul 2009 03:46:41 +0000

One of my favorite algorithms is the simple, elegant Euclidean algorithm for finding the greatest common denominator of two numbers. In ML or another functional language it really is beautiful:

1 2	fun gcd(a, 0) = a \| gcd(a, b) = gcd(b, a mod b);

Of course, the same can be done in Java iteratively:

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public int gcd(int a, int b){

    int c;

    while (b>0){

        c = a;

        a = b;

        b = c%b;

    }

    return a;

}

Or recursively:

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public int gcd(int a, int b){

    if(b==0){

        return a;

    }else{

        return gcd(b, a%b);

    }

}

Recursive Fibonacci

Chet — Sat, 04 Jul 2009 03:40:28 +0000

Here are two recursive fibonacci functions in ML I did for CS243. Can you tell which one is more efficient?

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fun fibonacci(n) = 

  let

      fun fib((a, b), i)=  

    if i=0 then b

        else fib((b, a + b), i-1);

           in

  fib((0, 1), n)

  end;

fun fibonacci(0) = 1

  | fibonacci(1) = 1

  | fibonacci(n) = fibonacci(n-1) + fibonacci(n-2);

CodeMocha » ml

Euclidean Algorithm

Recursive Fibonacci