## Median Of Five

### December 4, 2012

Our solution requires six comparisons:

`(define (median5 lt? a b c d e)`

(when (lt? b a)

(let ((t a)) (set! a b) (set! b t)))

(when (lt? e d)

(let ((t d)) (set! d e) (set! e t)))

(when (lt? d a)

(let ((t a)) (set! a d) (set! d t))

(let ((t b)) (set! b e) (set! e t)))

(if (lt? b c)

(if (lt? b d)

(if (lt? c d) c d)

(if (lt? b e) b e))

(if (lt? d c)

(if (lt? c e) c e)

(if (lt? b d) b d))))

There is discussion of the algorithm and a brief bit of explanation at http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi?board=riddles_cs;action=display;num=1061827085.

This function is easy to test: generate all permutations of the list (1 2 3 4 5) and assert that the median of each of them is 3:

`> (for-each (lambda (perm) (assert (apply median < perm) 3))`

(permutations '(1 2 3 4 5)))

Testing uses `assert`

from the Standard Prelude, and you can see the complete program, including the permutation generator, at http://programmingpraxis.codepad.org/4CinTQQM.

Pages: 1 2

I made thos Python version already for the previous exercise, but did not post it.

[...] today’s Programming Praxis exercise, our goal is to determine to median of five numbers using only six [...]

My Haskell solution (see http://bonsaicode.wordpress.com/2012/12/04/programming-praxis-median-of-five/ for a version with comments):

[...] Pages: 1 2 [...]