Knuth's power tree: Difference between revisions
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power tree for 191 is: 1 2 3 5 7 14 19 38 57 95 190 191 ═══ 3^191 is: 13494588674281093803728157396523884917402502294030101914066705367021922008906273586058258347 |
power tree for 191 is: 1 2 3 5 7 14 19 38 57 95 190 191 ═══ 3^191 is: 13494588674281093803728157396523884917402502294030101914066705367021922008906273586058258347 |
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power tree for 81 is: 1 2 3 5 10 20 40 41 81 ═══ 1.1^81 is: 2253.240236044012487937308538033349567966729852481170503814810577345406584190098644811 |
power tree for 81 is: 1 2 3 5 10 20 40 41 81 ═══ 1.1^81 is: 2253.240236044012487937308538033349567966729852481170503814810577345406584190098644811 |
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</pre> |
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=={{header|Sidef}}== |
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{{trans|zkl}} |
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<lang ruby>func path(n, p = Hash(1 => 0), lvl=[[1]]) { |
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n || return [] |
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while (n !~ p) { |
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var q = [] |
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for x in lvl[0] { |
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for y in path(x, p, lvl) { |
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break if (x+y ~~ p) |
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y = x+y |
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p{y} = x |
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q << y |
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} |
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} |
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lvl[0] = q |
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} |
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path(p{n}) + [n] |
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} |
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func tree_pow(x, n) { |
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var r = Hash(0 => 1, 1 => x) |
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var p = 0 |
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for i in path(n) { |
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r{i} = (r{i-p} * r{p}) |
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p = i |
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} |
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r{n} |
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} |
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func show_pow(x, n) { |
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var fmt = ("%d: %s\n" + ["%g^%s = %f", "%s^%s = %s"][x.is_int] + "\n") |
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print(fmt % (n, path(n), x, n, tree_pow(x, n))) |
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} |
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for x in ^18 { show_pow(2, x) } |
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show_pow(1.1, 81) |
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show_pow(3, 191)</lang> |
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{{out}} |
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<pre style="height:32ex;overflow:scroll"> |
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0: [] |
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2^0 = 1 |
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1: [1] |
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2^1 = 2 |
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2: [1, 2] |
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2^2 = 4 |
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3: [1, 2, 3] |
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2^3 = 8 |
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4: [1, 2, 4] |
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2^4 = 16 |
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5: [1, 2, 4, 5] |
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2^5 = 32 |
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6: [1, 2, 4, 6] |
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2^6 = 64 |
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7: [1, 2, 4, 6, 7] |
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2^7 = 128 |
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8: [1, 2, 4, 8] |
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2^8 = 256 |
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9: [1, 2, 4, 8, 9] |
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2^9 = 512 |
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10: [1, 2, 4, 8, 10] |
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2^10 = 1024 |
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11: [1, 2, 4, 8, 10, 11] |
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2^11 = 2048 |
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12: [1, 2, 4, 8, 12] |
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2^12 = 4096 |
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13: [1, 2, 4, 8, 12, 13] |
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2^13 = 8192 |
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14: [1, 2, 4, 8, 12, 14] |
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2^14 = 16384 |
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15: [1, 2, 4, 8, 12, 14, 15] |
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2^15 = 32768 |
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16: [1, 2, 4, 8, 16] |
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2^16 = 65536 |
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17: [1, 2, 4, 8, 16, 17] |
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2^17 = 131072 |
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81: [1, 2, 4, 8, 16, 32, 64, 80, 81] |
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1.1^81 = 2253.240236 |
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191: [1, 2, 4, 8, 16, 32, 64, 128, 160, 176, 184, 188, 190, 191] |
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3^191 = 13494588674281093803728157396523884917402502294030101914066705367021922008906273586058258347 |
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</pre> |
</pre> |
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