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Exercise 2.34 horner-eval.rkt
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Exercise 2.34 horner-eval.rkt
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#lang racket
; 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) + .... + a1.x + a0
; using a well-known algorithm called Horner's rule, which structures the computation as
; ( ... (an.x + a(n-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))
; SOLUTION
(define (horner-eval x coefficient-sequence)
(accumulate
(lambda (this-coeff higher-terms)
(+ this-coeff (* x higher-terms))
)
0
coefficient-sequence
)
)
(define (accumulate op initial sequence)
(if (null? sequence)
initial
(op (car sequence) (accumulate op initial (cdr sequence)))
)
)
; Tests
Welcome to DrRacket, version 6.11 [3m].
Language: racket, with debugging; memory limit: 128 MB.
> (horner-eval 2 (list 1 3 0 5 0 1))
79