Knuth's power tree: Difference between revisions
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An example of a small power tree for some low integers: |
An example of a small power tree for some low integers: |
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<pre> |
<pre> |
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1 |
1 |
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\ |
\ |
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2 |
2 |
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___________________________________________/ \ |
___________________________________________/ \ |
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/ \ |
/ \ |
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3 4 |
3 4 |
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/ \____________________________________ \ |
/ \____________________________________ \ |
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/ \ \ |
/ \ \ |
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5 6 8 |
5 6 8 |
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/ \____________ / \ \ |
/ \____________ / \ \ |
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/ \ / \ \ |
/ \ / \ \ |
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7 10 9 12 16 |
7 10 9 12 16 |
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/ //\\ │ │ /\ |
/ //\\ │ │ /\ |
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/ _____// \\________ │ │ / \ |
/ _____// \\________ │ │ / \ |
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14 / / \ \ │ │ / \ |
14 / / \ \ │ │ / \ |
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/│ \ 11 13 15 20 18 24 17 32 |
/│ \ 11 13 15 20 18 24 17 32 |
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/ │ \ │ /\ /\ │ /\ │ /\ │ |
/ │ \ │ /\ /\ │ /\ │ /\ │ |
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/ │ \ │ / \ / \ │ / \ │ / \ │ |
/ │ \ │ / \ / \ │ / \ │ / \ │ |
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19 21 28 22 23 26 25 30 40 27 36 48 33 34 64 |
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│ /\ /│\ │ │ /\ │ /\ /│\ │ /\ /│\ │ │ /\ |
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│ / \ / │ \ │ │ / \ │ / \ / │ \ │ / \ / │ \ │ │ / \ |
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38 35 42 29 31 56 44 46 39 52 50 45 60 41 43 80 54 37 72 49 51 96 66 68 65 128 |
38 35 42 29 31 56 44 46 39 52 50 45 60 41 43 80 54 37 72 49 51 96 66 68 65 128 |
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</pre> |
</pre> |
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Where, for the power <big>43</big>, following the tree "downwards" from <big>1</big>: |
Where, for the power <big>43</big>, following the tree "downwards" from <big>1</big>: |