## Puzzle

Q&A's, tips, howto's
cameyo
Posts: 102
Joined: Sun Mar 27, 2011 3:07 pm

### Puzzle

Write a function f so that f (f (n)) = -n for every integer n.

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``````Examples:
(f (f -1)) = 1
(f (f 1)) = -1
(f (f 4)) = -4
(f (f -4)) = 4
(f (f 0)) = 0``````
I'll post the solution the next week :-)

fdb
Posts: 49
Joined: Sat Nov 09, 2013 8:49 pm

### Re: Puzzle

The simplest i could think of is:

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``````(define-macro (f n)
(- (n 1)))
``````
But i do not know if macro's are allowed!

cameyo
Posts: 102
Joined: Sun Mar 27, 2011 3:07 pm

### Re: Puzzle

Hi fdb, nice solution :-)
However it is possible to solve the puzzle using a "normal" function with any programming language.

ralph.ronnquist
Posts: 216
Joined: Mon Jun 02, 2014 1:40 am
Location: Melbourne, Australia

### Re: Puzzle

Yes, quite challenging. Especially with the (implied) constraint that f is restricted to integers, as arguments and values (otherwise it's all too easy). Perhaps the following is acceptable?

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``````(define (f n)
(if (= n) 0 (> n)
(if (odd? n) (inc n) (- (dec n)))
(if (odd? n) (dec n) (- (inc n)))))``````

fdb
Posts: 49
Joined: Sat Nov 09, 2013 8:49 pm

### Re: Puzzle

ah yes to easy when n doesn't need to be a number...

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``````(define (f n)
(if (number? n)
(list n)
(- (n 0))))
``````

cameyo
Posts: 102
Joined: Sun Mar 27, 2011 3:07 pm

### Re: Puzzle

@ralph.ronnquist: you right :-)
@fbd: another good lisp-style solution
Solution:
One method is to separate the sign and magnitude of the number by the parity of the number.
We have three cases:
1) If the number is even, it keeps the same sign and moves 1 closer to 0
(subtract 1 from a positive even number and add 1 to a negative even number).
2) If the number is odd, it changes sign and moves 1 farther from 0
(multiply by -1 and subtract 1 from a positive odd number and multiply by -1 and add 1 to a negative even number)
3) If the number is 0 do nothing (it has no sign)

Code: Select all

``````(define (f n)
(cond ((and (> n 0) (even? n)) (- n 1))
((and (> n 0) (odd? n))  (- (- n) 1))
((and (< n 0) (even? n)) (+ n 1))
((and (< n 0) (odd? n))  (+ (- n) 1))
(true 0)))
(f (f 1))
;-> -1
(f (f -1))
;-> 1
(f (f 3))
;-> -3
(f (f -3))
;-> 3
(f (f 0))
;-> 0``````
Thanks fdb and ralph.ronnquist