ex_2_34.clj

(ns sicp.chapter-2.part-2.ex-2-34
  (:require
    [sicp.chapter-2.part-2.book-2-2 :as b22]))

; Exercise 2.34
;
; Evaluating a polynomial in x at a given value of x can be formulated as an accumulation.
; We evaluate the polynomial An*x^n + An-1*x^n-1 + ... + A0
;
; using a well-known algorithm called Horner’s rule, which structures the computation as
; (...(An*x + An-1)*x + ... + A1)*x + A0
;
; In other words, we start with An, multiply by x, add An−1, multiply by x,
; and so on, until we reach A0
;
; Fill in the following template to produce a procedure that evaluates a polynomial using
; Horner’s rule. Assume that the coefficients of the polynomial are arranged in a sequence, from A0
; through An.
;
; (define
;   (horner-eval x coefficient-sequence)
;   (accumulate
;    (lambda (this-coeff higher-terms)
;      ⟨??⟩)
;    0
;    coefficient-sequence))
; For example, to compute 1 + 3x + 5x3 + x5 at x = 2 you would evaluate
;
; (horner-eval 2 (list 1 3 0 5 0 1))

(defn horner-eval
  [x coefficient-sequence]
  (b22/accumulate
    (fn [this-coeff higher-terms] (+ (* higher-terms x) this-coeff))
    0
    coefficient-sequence))