Question

I am trying to write a tail-recursive function poly that will compute the value of a polynomial given a value and the list of coefficients. As in, if coeff is a list of coefficients (a0, a1, a2,...an) then (poly x coeff) should compute the value a0 + a1x +a2*x^2 + a3*x^3 + ...an*x^n

The functions is also expected to run in linear time (O(n))

My thoughts on this is to create a helper function that has an extra parameter (acc) that keeps track of where you are at in the list so you know what power to raise it to but I can’t think of how to do that

Answer 1

There is no need for a helper function to track where you are on the list, since you will only need to move forward one list element at a time till you reach the end. Here’s a possible skeleton

(define (poly coeff)
  (let loop ((power 0) (total 0) (clist coeff))
    (cond
       ((null? clist) ???)
       (else (loop (+ 1 power) (??????) (cdr clist))))))

That’s most of it done for you. All you really have to do is work out how you should do the calculating of exponents and addition. There are two basic options and I know which one I would choose (fewer cpu cycles).