For the last week I've been trying to figure out an algorithm for JPEG's zig-zag spacefilling curve. Specifically, I wanted an algorithm that maps all elements in an NxN matrix to a N*N array given their x and y values. I finally figured it out with the help of my analysis 101 TA. He's not a computer scientist, but he knows what pairing functions are. Anyway, after a few hours messing with perl, I made this subroutine:

sub getPos{
    ($x,$y,$s)=@_;($d=$x+$y)*($d++)/2
    +($d%2?$y:$x)-($d>$s)*($d-$s)**2
}
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To use it, you do something like this:

for(my $x = 0; $x < $size; $x++){
    for(my $y = 0; $y < $size; $y++){
        print getPos($x, $y, $size)."  ";
    }
    print "\n";
}
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For $size = 10 the loop will yield:

0  1  5  6  14  15  27  28  44  45  
2  4  7  13  16  26  29  43  46  63  
3  8  12  17  25  30  42  47  62  64  
9  11  18  24  31  41  48  61  65  78  
10  19  23  32  40  49  60  66  77  79  
20  22  33  39  50  59  67  76  80  89  
21  34  38  51  58  68  75  81  88  90  
35  37  52  57  69  74  82  87  91  96  
36  53  56  70  73  83  86  92  95  97  
54  55  71  72  84  85  93  94  98  99
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The body of getPos has 65 (non-whitespace) characters, any ideas on how to get it even smaller?

$==pop;print map{$y=$_;map(($d=$y+$_)*$d++/2-($d>$=)*($d-$=)**2+($d&1?
+$_:$y).$",@m),$/}@m=0..$=-1
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