Recursion

Hi, I am having some trouble figuring out this recursion problem. Can anyone help?

Function Name: reversePascal Inputs (1): - (double) A vector of polynomial coefficients. Outputs (1): - (double) A vector of binomial coefficients. - (double) The exponent of the binomial.

 Function Description:
   Write a function called "reversePascal" that takes the coefficients to
   an arbitrarily long polynomial and condenses it into the form (ax+b)^n,
   or binomial form. The function should return [a b] as its first output,
   and n as its second. You MUST use recursion to solve this problem.

 Notes:
   - The input polynomial will always be reducible into a binomial.

 Test Cases:

[vec1 n1] = reversePascal([1 8 18 16 5]); vec1 => [1 5] n1 => 4

[vec2 n2] = reversePascal([5 16 18 8 1]); vec2 => [5 1] n2 => 4

[vec3 n3] = reversePascal([-1 -2 2 8 7 2]); vec3 => [-1 2] n3 => 5

   [vec4 n4] = reversePascal([-2 -2]);
       vec3 => [-2 -2]
       n3 => 1

Answer 1

[Geoff]

Well, the thing with recursion is you take a larger problem and make it slightly smaller. So, to begin with you test whether you need to break the problem down and if so, you make a single recursive call that simplifies the problem by one step.

Since this is a homework problem, we can't give you the answer, but we can try to point you in the right direction.

So consider this...

1. If the problem is reduced to its simplest form, just return the required answer.

2. If the problem is larger, recursively call your function with a slightly smaller problem (perhaps one less term?)

Remember that the result of (2) will always be the solution to the slightly smaller problem, so you have to adjust the result to account for that.

I hope that helps.