My friend sent me this:
It pretty much forced me to write spiral.php and spiral.sh to generate this:
print('1')
print('7 8 9')
print('6 1 2')
print('5 4 3')
print('21 22 23 24 25')
print('20 7 8 9 10')
print('19 6 1 2 11')
print('18 5 4 3 12')
print('17 16 15 14 13')
print('43 44 45 46 47 48 49')
print('42 21 22 23 24 25 26')
print('41 20 7 8 9 10 27')
print('40 19 6 1 2 11 28')
print('39 18 5 4 3 12 29')
print('38 17 16 15 14 13 30')
print('37 36 35 34 33 32 31')
print('73 74 75 76 77 78 79 80 81')
print('72 43 44 45 46 47 48 49 50')
print('71 42 21 22 23 24 25 26 51')
print('70 41 20 7 8 9 10 27 52')
print('69 40 19 6 1 2 11 28 53')
print('68 39 18 5 4 3 12 29 54')
print('67 38 17 16 15 14 13 30 55')
print('66 37 36 35 34 33 32 31 56')
print('65 64 63 62 61 60 59 58 57')
print('111 112 113 114 115 116 117 118 119 120 121')
print('110 73 74 75 76 77 78 79 80 81 82')
print('109 72 43 44 45 46 47 48 49 50 83')
print('108 71 42 21 22 23 24 25 26 51 84')
print('107 70 41 20 7 8 9 10 27 52 85')
print('106 69 40 19 6 1 2 11 28 53 86')
print('105 68 39 18 5 4 3 12 29 54 87')
print('104 67 38 17 16 15 14 13 30 55 88')
print('103 66 37 36 35 34 33 32 31 56 89')
print('102 65 64 63 62 61 60 59 58 57 90')
print('101 100 99 98 97 96 95 94 93 92 91')
print('157 158 159 160 161 162 163 164 165 166 167 168 169')
print('156 111 112 113 114 115 116 117 118 119 120 121 122')
print('155 110 73 74 75 76 77 78 79 80 81 82 123')
print('154 109 72 43 44 45 46 47 48 49 50 83 124')
print('153 108 71 42 21 22 23 24 25 26 51 84 125')
print('152 107 70 41 20 7 8 9 10 27 52 85 126')
print('151 106 69 40 19 6 1 2 11 28 53 86 127')
print('150 105 68 39 18 5 4 3 12 29 54 87 128')
print('149 104 67 38 17 16 15 14 13 30 55 88 129')
print('148 103 66 37 36 35 34 33 32 31 56 89 130')
print('147 102 65 64 63 62 61 60 59 58 57 90 131')
print('146 101 100 99 98 97 96 95 94 93 92 91 132')
print('145 144 143 142 141 140 139 138 137 136 135 134 133')
print('211 212 213 214 215 216 217 218 219 220 221 222 223 224 225')
print('210 157 158 159 160 161 162 163 164 165 166 167 168 169 170')
print('209 156 111 112 113 114 115 116 117 118 119 120 121 122 171')
print('208 155 110 73 74 75 76 77 78 79 80 81 82 123 172')
print('207 154 109 72 43 44 45 46 47 48 49 50 83 124 173')
print('206 153 108 71 42 21 22 23 24 25 26 51 84 125 174')
print('205 152 107 70 41 20 7 8 9 10 27 52 85 126 175')
print('204 151 106 69 40 19 6 1 2 11 28 53 86 127 176')
print('203 150 105 68 39 18 5 4 3 12 29 54 87 128 177')
print('202 149 104 67 38 17 16 15 14 13 30 55 88 129 178')
print('201 148 103 66 37 36 35 34 33 32 31 56 89 130 179')
print('200 147 102 65 64 63 62 61 60 59 58 57 90 131 180')
print('199 146 101 100 99 98 97 96 95 94 93 92 91 132 181')
print('198 145 144 143 142 141 140 139 138 137 136 135 134 133 182')
print('197 196 195 194 193 192 191 190 189 188 187 186 185 184 183')
Fun challenge: do this in a spreadsheet. It is actually a nice example of how the functional and imperative approaches can differ radically. The shift to functional is, IMO, the hard part about doing Clojure, not the language syntax.
Hey. I’ve been thinking about this and I can’t figure it out. I have no idea how you would to this in a spreadsheet. I wouldn’t even know where to start. With my program above I started with the maximum number being input by the user. With a spreadsheet I don’t know how I would program in that number. Also, I assume I would have to put the whole program in a cell, and then copy that program into every cell which I might need in the output, which will vary based on the maximum number. So, yeah. No idea about this one. If you could show me how it’s done I would be very interested to know!
I haven’t actually gone through and figured it out in detail (nor am I going to), but I’ve done this sort of thing enough to know the general shape.
Basically, you need a mathematical formula from X and Y to a distance along the spiral. I suspect that is a four-way case statement, one for each side – top, bottom, left, right. I would call the center position 0,0 for simplicity.
Too hard! :)
Another interesting way to do it would be to generate a lazy, infinite sequence of state values (current number, current layer, current direction) by making an function of the prior state and iterating. Then map over the first N values to get an array of numbers. Then print.
Still too hard! :)