Railway circuit: Difference between revisions
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'''Railway circuit''' |
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Given n sections of curve tracks, each one being an arc of 30° of radius R, the goal is to build and count all possible different railway circuits. |
Given n sections of curve tracks, each one being an arc of 30° of radius R, the goal is to build and count all possible different railway circuits. |
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Constraints : |
'''Constraints''' : |
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* n = 12 + k*4 (k = 0, 1 , ...) |
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* The circuit must be a closed, connected graph, and the last arc must joint the first one |
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* Duplicates, either by symmetry, translation, reflexion or rotation must be eliminated. |
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* Paths may overlap or cross each other. |
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* All tracks must be used. |
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Illustrations : http://www.echolalie.org/echolisp/duplo.html |
'''Illustrations''' : http://www.echolalie.org/echolisp/duplo.html |
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Task |
'''Task:''' |
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Write a function which counts and displays all possible circuits Cn for n = 12, 16 , 20. Extra credit for n = 24, 28, ... 48 (no display, only counts). A circuit Cn will be displayed as a list, or sequence of n Right=1/Left=-1 turns. |
Write a function which counts and displays all possible circuits Cn for n = 12, 16 , 20. Extra credit for n = 24, 28, ... 48 (no display, only counts). A circuit Cn will be displayed as a list, or sequence of n Right=1/Left=-1 turns. |
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Example |
Example: |
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C12 = (1,1,1,1,1,1,1,1,1,1,1,1) or C12 = (-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1) |
C12 = (1,1,1,1,1,1,1,1,1,1,1,1) or C12 = (-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1) |
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'''Straight tracks (extra-extra credit)''' |
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Extra : |
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Suppose we have m = k*2 sections of straight tracks, each of length L. Such a circuit is denoted Cn,m . A circuit is a sequence of +1,-1, or 0 = straight move. Count the number of circuits Cn,m with n same as above and m = 2 to 8 . |
Revision as of 16:17, 21 January 2016
Railway circuit
Given n sections of curve tracks, each one being an arc of 30° of radius R, the goal is to build and count all possible different railway circuits.
Constraints :
- n = 12 + k*4 (k = 0, 1 , ...)
- The circuit must be a closed, connected graph, and the last arc must joint the first one
- Duplicates, either by symmetry, translation, reflexion or rotation must be eliminated.
- Paths may overlap or cross each other.
- All tracks must be used.
Illustrations : http://www.echolalie.org/echolisp/duplo.html
Task:
Write a function which counts and displays all possible circuits Cn for n = 12, 16 , 20. Extra credit for n = 24, 28, ... 48 (no display, only counts). A circuit Cn will be displayed as a list, or sequence of n Right=1/Left=-1 turns.
Example:
C12 = (1,1,1,1,1,1,1,1,1,1,1,1) or C12 = (-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1)
Straight tracks (extra-extra credit)
Suppose we have m = k*2 sections of straight tracks, each of length L. Such a circuit is denoted Cn,m . A circuit is a sequence of +1,-1, or 0 = straight move. Count the number of circuits Cn,m with n same as above and m = 2 to 8 .