Fibonacci word: Difference between revisions
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(Created page with "{{task}} The standard Fibonacci Word may be created in a manner analogous to the Fibonacci Sequence: : Define F_Word 1 as 0; : Define F_Word 2 as 01; : Form F_Word 3 as F_Wor...") |
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Instead create a table which for F_Words 1 to 36 shows the [[Rep-string]] and [[Entropy]]. |
Instead create a table which for F_Words 1 to 36 shows the [[Rep-string]] and [[Entropy]]. |
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=={{header|Icon}} and {{header|Unicon}}== |
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The following solution works in both Icon and Unicon. The first 7 Fibonacci |
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words are shown, while the [[Entropy]] is shown for all 36. None of the fibonacci words |
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have rep-strings, by the definition given in the [[Rep-string]] task. |
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<lang unicon>procedure main(A) |
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n := integer(A[1]) | 36 |
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every w := fword(i := 1 to n) do { |
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writes(right(i,4)," ",left(H(w),5)) |
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if i <= 7 then write(": ",w) else write() |
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} |
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end |
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procedure fword(n) |
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static fcache |
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initial fcache := table() |
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/fcache[n] := case n of { |
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1: "0" |
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2: "01" |
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default: fword(n-1)||fword(n-2) |
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} |
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return fcache[n] |
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end |
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procedure H(s) |
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P := table(0.0) |
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every P[!s] +:= 1.0/*s |
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every (h := 0.0) -:= P[c := key(P)] * log(P[c],2) |
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return h |
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end</lang>fw |
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Sample run: |
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<pre> |
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->fw |
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1 0.0 : 0 |
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2 1.0 : 01 |
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3 0.9182958340544: 010 |
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4 0.9709505944546: 01001 |
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5 0.9544340029249: 01001010 |
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6 0.9612366047228: 0100101001001 |
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7 0.9587118829771: 010010100100101001010 |
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8 0.9596868937742 |
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9 0.9593160320543 |
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10 0.9594579158386 |
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11 0.9594037542210 |
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12 0.9594244469559 |
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13 0.9594165437404 |
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14 0.9594195626031 |
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15 0.9594184095152 |
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16 0.9594188499578 |
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17 0.9594186817240 |
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18 0.9594187459836 |
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19 0.9594187214387 |
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20 0.9594187308140 |
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21 0.9594187272330 |
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22 0.9594187286009 |
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23 0.9594187280783 |
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24 0.9594187282781 |
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25 0.9594187282015 |
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26 0.9594187282313 |
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27 0.9594187282195 |
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28 0.9594187282251 |
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29 0.9594187282196 |
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30 0.9594187282169 |
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31 0.9594187282191 |
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32 0.9594187282130 |
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33 0.9594187282322 |
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34 0.9594187281818 |
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35 0.9594187282743 |
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36 0.9594187282928 |
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-> |
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</pre> |
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Revision as of 16:41, 12 July 2013
You are encouraged to solve this task according to the task description, using any language you may know.
The standard Fibonacci Word may be created in a manner analogous to the Fibonacci Sequence:
- Define F_Word 1 as 0;
- Define F_Word 2 as 01;
- Form F_Word 3 as F_Word 2 concatenated with F_Word 1 i.e "010"
- Form F_Word n as F_Word n-1 concatenated with F_word n-2
For this task we shall do this for n = 32. You may display the first few but not the larger values of n, doing so will get me into trouble with them what be (again!).
Instead create a table which for F_Words 1 to 36 shows the Rep-string and Entropy.
Icon and Unicon
The following solution works in both Icon and Unicon. The first 7 Fibonacci words are shown, while the Entropy is shown for all 36. None of the fibonacci words have rep-strings, by the definition given in the Rep-string task.
<lang unicon>procedure main(A)
n := integer(A[1]) | 36
every w := fword(i := 1 to n) do {
writes(right(i,4)," ",left(H(w),5))
if i <= 7 then write(": ",w) else write()
}
end
procedure fword(n)
static fcache
initial fcache := table()
/fcache[n] := case n of {
1: "0"
2: "01"
default: fword(n-1)||fword(n-2)
}
return fcache[n]
end
procedure H(s)
P := table(0.0) every P[!s] +:= 1.0/*s every (h := 0.0) -:= P[c := key(P)] * log(P[c],2) return h
end</lang>fw
Sample run:
->fw 1 0.0 : 0 2 1.0 : 01 3 0.9182958340544: 010 4 0.9709505944546: 01001 5 0.9544340029249: 01001010 6 0.9612366047228: 0100101001001 7 0.9587118829771: 010010100100101001010 8 0.9596868937742 9 0.9593160320543 10 0.9594579158386 11 0.9594037542210 12 0.9594244469559 13 0.9594165437404 14 0.9594195626031 15 0.9594184095152 16 0.9594188499578 17 0.9594186817240 18 0.9594187459836 19 0.9594187214387 20 0.9594187308140 21 0.9594187272330 22 0.9594187286009 23 0.9594187280783 24 0.9594187282781 25 0.9594187282015 26 0.9594187282313 27 0.9594187282195 28 0.9594187282251 29 0.9594187282196 30 0.9594187282169 31 0.9594187282191 32 0.9594187282130 33 0.9594187282322 34 0.9594187281818 35 0.9594187282743 36 0.9594187282928 ->