Using only abs(n), addition, and subtraction; is it possible to construct a function that works the same as min(a,b)?

My intuition says it might be possible, but I can't seem to figure out a way.

4/21/2009 6:07:15 PM

without doing a lot of checking doesn't this work? i'm assuming if statements are allowed

newmin(a, b){
if (a==b) { return a }
if ((a-b) < (b-a)) { return a }
{ else return b }
}

4/21/2009 6:11:20 PM

Well, I guess I should have said, do it in one line; as if with an inline #define function. Or in an SQL query....

but just figured it out myself it's pretty simple. needs division though.

the motivation for needing this in the first place is because Oracle doesn't have min(a,b) built-in



[Edited on April 21, 2009 at 6:25 PM. Reason : click edit post for solution.]

4/21/2009 6:20:58 PM

omar's would work if you abs(a) and abs(b)

[Edited on April 21, 2009 at 6:50 PM. Reason : icwydt, concise but not especially readable]

4/21/2009 6:49:40 PM

Quote :

"newmin(a, b){ if (a==b) { return a } if ((a-b) < (b-a)) { return a } { else return b } } "

Why not just:

if ( (a-b) > (b-a) ) then { return b } else { return a }

if((a-b) > (b-a), b, a)

4/21/2009 7:27:35 PM

it has a CASE expression which can do if-then

[Edited on April 21, 2009 at 7:40 PM. Reason : it's more like "case when condition then thing"]

4/21/2009 7:39:13 PM

^^ good call - i missed that my first time through

4/22/2009 9:40:54 AM

you guys check me on this, but this is one without conditionals:

min(a,b) = 0.5*(a+b-abs(a-b))

[Edited on April 22, 2009 at 10:43 AM. Reason : simpler]

4/22/2009 10:42:20 AM

has multiplication but other than that looks good

4/22/2009 10:52:43 AM

i don't think there's a way to do it without multiplication. i think i even had this as a challenge problem in high school (and it said you could use abs, +, - and *). here's max if you're interested:

max(a,b) = 0.5*(abs(a-b) + a + b)

4/22/2009 10:55:52 AM