Converting a recursive function that return 2 recursion to Iteration

Question

I always have problem trying to convert a recursive algorithm which i created that returns 2 recursive call until the base case is met.

It's easy to like track back what each recursive call do but converting them to iteration is a little confusing.

For example this recursive function

BEGIN SEQ(n)
   if (n == 1)
     return 3;
   
  else if (n == 2)
     return 2;

  else 
     return SEQ(n - 2) + SEQ(n - 1)

This is rather straight forward when i try to rubber duck my way through the recursive which produces the follow process

SEQ(6) = SEQ(4) + SEQ(5)

SEQ(5) = SEQ(3) + SEQ(4)

SEQ(4) = SEQ(2) + SEQ(3)

SEQ(3) = SEQ(1) + SEQ(2)

SEQ(2) = 2

…

SEQ(3) = 3 + 2 = 5

SEQ(4) = 2 + 5 = 7

SEQ(5) = 5 + 7 = 12

SEQ(6) = 7 + 12 = 19

However, i can't seems to figure out an iteration way that return exactly how the recursive does

The algorithm does not quite match the example. Did you mean return SEQ(n-2) + SEQ(n-1) in the last line? — Henry
– Henry, Commented Nov 10, 2016 at 5:31
Apart from the starting values this is built in the same way as the fibonacci sequence. Any iterative program you find for that is easy to modify. — Henry
– Henry, Commented Nov 10, 2016 at 5:36

αNerd · Accepted Answer · 2016-11-10 05:46:09Z

4

Your iteration method in C# could look like this:

public static int SEQ(int n)
{
    if (n == 1)
    {
        return 3;
    }

    if (n == 2)
    {
        return 2;
    }
    var first = 3;
    var second = 2;

    for (var i = 3; i <= n; i++)
    {
        second += first;
        first = second - first;
    }


    return second;
}

edited Nov 10, 2016 at 5:46

answered Nov 10, 2016 at 5:39

αNerd

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