Difference between revisions of "User:Zhan"
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==DoA== | ==DoA== | ||
| − | What are the next starts i should choose to reduce | + | What are the next starts i should choose to reduce gemstones type difference, the discrete optimization point of view. |
Let us consider the gemstones as a vector ''y'' = (''y<sub>1</sub>, y<sub>2</sub>, y<sub>3</sub>, y<sub>4</sub>'') in N<sup>4</sup>, where the components respectively respresent the number of '''margonite gemstones''', '''stygian gemstones''', '''torment gemstones''', '''titan gemstones'''. | Let us consider the gemstones as a vector ''y'' = (''y<sub>1</sub>, y<sub>2</sub>, y<sub>3</sub>, y<sub>4</sub>'') in N<sup>4</sup>, where the components respectively respresent the number of '''margonite gemstones''', '''stygian gemstones''', '''torment gemstones''', '''titan gemstones'''. | ||
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Where ''k = 2'' in Hard Mode (HM), and where the functions respectively represent '''start city''', '''start veil''', '''start gloom''', '''start foundry'''. | Where ''k = 2'' in Hard Mode (HM), and where the functions respectively represent '''start city''', '''start veil''', '''start gloom''', '''start foundry'''. | ||
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| + | Now, let ''g'' be a finite number ''n<sub>i</sub>'' of composition of functions ''f<sub>i</sub>'', (''i'' in {1,...,4}). We consider ''g'' to be the minimal number of composition which gives the minimum possible difference of gemstones. This gives the following minimization problem: | ||
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| + | argmin<sub>''g''</sub> (max<sub>(i, j)</sub> |g<sub>i</sub>(y) - g<sub>j</sub>(y)|) such that ''||n||<sub>1</sub>'' is minimal. | ||
==Contact== | ==Contact== | ||
Revision as of 17:03, 8 June 2021
DoA
What are the next starts i should choose to reduce gemstones type difference, the discrete optimization point of view.
Let us consider the gemstones as a vector y = (y1, y2, y3, y4) in N4, where the components respectively respresent the number of margonite gemstones, stygian gemstones, torment gemstones, titan gemstones.
Then, we consider successful runs by the following functions going from N4 to N4:
f1(x) = x + k(1, 2, 3, 4)
f2(x) = x + k(4, 1, 2, 3)
f3(x) = x + k(3, 4, 1, 2)
f4(x) = x + k(2, 3, 4, 1)
Where k = 2 in Hard Mode (HM), and where the functions respectively represent start city, start veil, start gloom, start foundry.
Now, let g be a finite number ni of composition of functions fi, (i in {1,...,4}). We consider g to be the minimal number of composition which gives the minimum possible difference of gemstones. This gives the following minimization problem:
argming (max(i, j) |gi(y) - gj(y)|) such that ||n||1 is minimal.
Contact
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In game character name Kunvie Zhan
