[taos-glug] Question 1.46
- From: Jonathan Bartlett <johnnyb@xxxxxxxxxx>
- To: taos-glug@xxxxxxxxxxxxx
- Date: Tue, 12 Aug 2003 14:29:39 -0700 (PDT)
Here's my answer to Q 1.46. I think it could be written better, but it
didn't occur to me how.
;This is the base procedure. It is only used as a gateway to the
;recursive
;procedure below (*NOTE - with Y-combinators you don't have to define a
;separate procedure - you can embed the recursive call within your
;function
;- but they are too evil to actually be of value). It takes a function
;check-guess, which checks it's guess, and improve-guess, which improves
;it.
(define iterative-improve (lambda (check-guess improve-guess)
(lambda (guess)
(iterative-improve-recursive check-guess improve-guess
guess)
)
))
(define iterative-improve-recursive (lambda (check-guess improve-guess
current-guess)
;Is the current guess good enough?
(if (check-guess current-guess)
;Yeah! It is! Return and we're done.
current-guess
;Nope, call this function again with an improved guess
(iterative-improve-recursive
check-guess
improve-guess
(improve-guess current-guess)
)
)
))
;Okay, here's the function that the user calls. They give a number
;to square and how precise they want their answer. The number is
;used as the initial guess
(define square-root (lambda (number precision)
(let
(
;Define the procedure to check guesses
;Basically, square the number, and see how
;close it is to the actual answer
(check-guess (lambda (guess)
(if (> (abs (- (* guess guess) number))
precision)
#f
#t
)
))
;Define a procedure which uses newton's method to
;get new guess for our square root
;It is the average of guess + number/guess
(improve-guess (lambda (guess)
(/ (+ guess (/ number guess)) 2)
))
)
;Remember, iterative-improve returns a procedure, and
;we then call that procedure with our first guess
((iterative-improve check-guess improve-guess) 5)
)
))
I don't know if it's the best solution, but it's the first I thought of.
Jon
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