Code Golf: Happy Primes!

Question

dc - 98 chars

$ cat happyprimes
[happy][sad]?dsI[[I~d*rd0<H+]dsHxd4<h]dshx[r]sr1=rP[ ][ non-]_1lI[1-d2>rdlIr%0<p]dspx-2=rP[prime]p
$ echo 1  |dc happyprimes
happy non-prime
$ echo 139|dc happyprimes
happy prime
$ echo 2  |dc happyprimes
sad prime
$ echo 440|dc happyprimes
happy non-prime
$ echo 78 |dc happyprimes
sad non-prime

Mathematica 115 108 107 102 100 99 91 87 Chars

---

87 characters

Print[If[Nest[Tr[IntegerDigits@#^2]&,#,9]>1,Sad,Happy],If[PrimeQ@#," "," non-"],prime]&

-- Mr.Wizard

---

Da monkey learnt a few tricks (91 chars)

 Print[
       If[Nest[Plus@@(IntegerDigits@ #^2) &, #, 9] > 1, Sad, Happy ],
       If[PrimeQ@#, " ", " non-"], prime
      ] &

Invoke with %[7]

Edit 5 - 99 Chars/

Nine iterations is enough. Thanks @Nabb, @mjschultz

h = Print[
    If[Nest[Plus @@ (IntegerDigits@#^2) &, #, 9] > 1, "Sad ", "Happy "]
   , If[PrimeQ@#, "", "non-"], "prime"] &

Edit 4 - 100 Chars/

Same as Edit 3, replacing 10^2 by 99 (allowing 84 digits for input values) ... Thanks, @Greg

h = Print[
    If[Nest[Plus @@ (IntegerDigits@#^2) &, #, 99] > 1, "Sad ", "Happy "]
   , If[PrimeQ@#, "", "non-"], "prime"] &

Edit 3 - 102 Chars/

Reworked the loop again.

It is interesting that the recursion depth until eventually reaching 1 is bounded by (15 + Number of digits of the argument). See here

So for numbers with less than 85 digits (I think this limit is pretty well into the OP's "Don't worry about handling big numbers" consideration) the following code works

h = Print[
    If[Nest[Plus @@ (IntegerDigits@#^2) &, #, 10^2] > 1, "Sad ", "Happy "]
   , If[PrimeQ@#, "", "non-"], "prime"] &

I changed the "NestWhile" for the shorter "Nest", and so, instead of specifying a stop condition for the recursion, is enough to hardcode the desired recursion depth (10^2).

It is not very efficient, but that's the golfer's life :D

Edit 2 - 107 Chars/

Reworked the Sad/Happy assignment

h = Print[
     If[NestWhile[Plus @@ (IntegerDigits@#^2) &, #, # > 4 &] > 1,"Sad ","Happy "]
    ,If[PrimeQ@#, "", "non-"]
    , "prime"] &

All spaces/newlines except on literals are optional and added for readability

Explanation:

The

    NestWhile[Plus @@ (IntegerDigits@#^2) &, #, # > 4 &]

Recurses applying "function" [Add up sum of digits squared] until the result is 4 or less. The function has the property that it stagnates at "1", or enters the cycle {4, 16, 37, 58, 89, 145, 42, 20, 4, ...}.

So, when the outcome is "1", the number is "Happy" and when the outcome is "4", it is "Sad".

If the result is "2", the number is also SAD, because it'll enter the SAD cycle in the next iteration (2^2 = 4).

If the result is 3, the cycle is 3->9->81->65->61->37->58->89->145-> .... (Enters the SAD loop).

So, we can stop the recursion when the result is 4 or less, knowing that only a result of "1" will lead to a Happy number.

Perhaps other solutions may take advantage of this fact.

In fact, the results 5 and 6 also lead to SAD numbers, but that gives us only an efficiency boost and not a golfing advantage (I guess).

Edit 1 - 108 Chars/

Reworked the Loop Control logic

    h = Print[
        NestWhile[Plus@@(IntegerDigits@#^2) &, #, #>4 &] /.{1 →"Happy ",_→"Sad "}
          , If[PrimeQ@#, "", "non-"]
          , "prime"] &

Original - 115 Chars/

h = Print[
    If[NestWhile[Plus @@ (IntegerDigits@#^2) &, #, Unequal, All] == 1
        ,"Happy ", "Sad "],      
    If[PrimeQ@#, "", "non-"], "prime"] &

The statement

NestWhile[Plus @@ (IntegerDigits@#^2) &, #, Unequal, All]

performs the recursive application of the sums of the digits squared, until some value repeats. The "Unequal,All" part takes care of the comparison across the preceding values list. Finally returns the repeated value, which is "1" for Happy Numbers.

Sample run

h[7]
Happy prime
h[2535301200456458802993406410753]
Sad non-prime

Looping (Slightly changing the Print statement)

1 Happy non-prime
2 Sad prime
3 Sad prime
4 Sad non-prime
5 Sad prime
6 Sad non-prime
7 Happy prime
8 Sad non-prime
9 Sad non-prime
10 Happy non-prime
11 Sad prime
12 Sad non-prime
13 Happy prime

GolfScript - 64 chars (works for 1)

~:@.{0\`{15&.*+}/}*1=!"happy sad "6/=@,{@\)%!},,2=4*"non-prime">

This program does n iterations to determine the happiness of the number, which is very wasteful for large numbers, but code-golf is not about conserving resources other than characters. The prime test is similarly inefficient - dividing n by all the values from 1 to n inclusive and checking that there are exactly two values with zero remainder. So while it is theoretically correct, running with really large numbers is not practical on real computers

GolfScript - 63 chars (fails for 1)

~:@9{0\`{15&.*+}/}*1=!"happy sad "6/=@,2>{@\%!},!4*"non-prime">

Python - 127 chars

Beating both perl answers at this moment!

l=n=input()
while l>4:l=sum(int(i)**2for i in`l`)
print['sad','happy'][l<2],'non-prime'[4*all(n%i for i in range(2,n))*(n>1):]

I also ported this answer to GolfScript and it is just over 1/2 the size!