weave_method
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weave_method [2023/05/15 15:55] harshec created |
weave_method [2023/05/15 16:33] (current) harshec |
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| The basic idea of the weave method is that you can't have a set of 4 fair dice, unless every 3 dice subset is also fair. You start with a n=0 dice set and doing a depth first search, you add one die at a time. | The basic idea of the weave method is that you can't have a set of 4 fair dice, unless every 3 dice subset is also fair. You start with a n=0 dice set and doing a depth first search, you add one die at a time. | ||
| - | Psuedo Code | ||
| - | ``` depthS(string str, int n, int s, int lastinsert) update_fairness_calc(lastinsert) if(!fair()) return | + | ===Psuedo Code=== |
| - | if(s == MAX_S) | + | depthS(string str, int n, int s, int lastinsert) update_fairness_calc(lastinsert) if(!fair()) return |
| - | depthN(str, n) | + | |
| - | + | depthN(str, n) | |
| - | for(i = lastinsert; i <= MAX_S * (n-1); ++i) | + | for(i = lastinsert; i <= MAX_S * (n-1); ++i) |
| - | depthS(str.insert(' | + | depthS(str.insert(' |
| - | + | depthN(string str, int n) if(n == MAX_N) print(" | |
| - | depthN(string str, int n) if(n == MAX_N) print(" | + | main() depthN("", |
| - | + | ||
| - | main() depthN("", | + | |
| ===Future Work=== | ===Future Work=== | ||
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| Here's an outline of the basic idea of the simple version. 1. First build a list of all n=2 solutions. 1. When going from a n=2 set to a n=3 set, ALL n=2 subsets of the n=3 set must be part of the list generated in step 1. Keep a list of all n=2 subsets of the n=3 solutions. 1. Again, when going from a n=3 set to a n=4 set, all n=2 subsets of the n=4 set must be part of the list generated step 2. | Here's an outline of the basic idea of the simple version. 1. First build a list of all n=2 solutions. 1. When going from a n=2 set to a n=3 set, ALL n=2 subsets of the n=3 set must be part of the list generated in step 1. Keep a list of all n=2 subsets of the n=3 solutions. 1. Again, when going from a n=3 set to a n=4 set, all n=2 subsets of the n=4 set must be part of the list generated step 2. | ||
| - | But we can do even better. There are 3 different n=2 subsets in all n=3 sets, ba, ca, and cb. We can keep separate lists for all n=2 subsets. When building n=4 sets, we use their n=3 subsets and again filter based on the more specific 3 different n=2 lists. For example, the db relationship in dcba is part of 2 n=3 subsets, dcb and dba. In those subsets, db is equivalent to ca and cb in cba. Full relationship chart listed below. http:// | + | But we can do even better. There are 3 different n=2 subsets in all n=3 sets, ba, ca, and cb. We can keep separate lists for all n=2 subsets. When building n=4 sets, we use their n=3 subsets and again filter based on the more specific 3 different n=2 lists. For example, the db relationship in dcba is part of 2 n=3 subsets, dcb and dba. In those subsets, db is equivalent to ca and cb in cba. Full relationship chart listed below. |
| + | |||
| + | {{http:// | ||
| Lists of n=2 subset counts are available on the wiki page Results. | Lists of n=2 subset counts are available on the wiki page Results. | ||
weave_method.1684166115.txt.gz · Last modified: 2023/05/15 15:55 by harshec
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