July to September and http://findingmichael.com/members/Better-Flower-Delivery-Your-Flower-Delivery-m-nw.aspx central oregon perennial flower and  xbignz and http://skinnerfamily.biz/members/Better-Adult-Dating-Sites-Your-Adult-Dating-Sites-l-sy.aspx dating jewish guys and  10412 and http://phibetafit.com/members/Better-Life-Insurance-Your-Life-Insurance-u-yc.aspx colonial life group insurance and  575 and http://pursuit.org/pursuitusers/cs/members/Better+Bankruptcy+Services+Your+Bankruptcy+Services+e+uy.aspx usc trustee in bankruptcy and  8-( and http://winecountrywashington.org/cs/members/Better+Cosmetic+Surgery+Your+Cosmetic+Surgery+c+wm.aspx bloodless medicine and surgery power point and  xcug and http://pursuit.org/pursuitusers/cs/members/Better+Bankruptcy+Services+Your+Bankruptcy+Services+e+uy.aspx bankruptcies pittsburgh tribune review and  cbys and http://blog.chriscap.net/members/Better-Vacation-Deals-Your-Vacation-Deals-r-vy.aspx wisconsin dells wildernesss resort and  31385 and http://jetlounge.net/members/Better-Debt-Settlement-Your-Debt-Settlement-o-lc.aspx credit solutions debt settlement and  4542 and http://uat.manpowerprofessional.com.au:81/members/Better-Home-Loans-Your-Home-Loans-c-bt.aspx maine long form mortgage and  :-))) and
*[[Problem 212:http://projecteuler.net/problem=212]] 「結合直方体の体積」 [#o334d683]

座標軸に平行な直方体 (axis-aligned cuboid) は {&tex{(x_{0}, y_{0}, z_{0}), (dx, dy, dz)};} で与えられ, &tex{x_{0}}; ≤ X ≤ &tex{x_{0} + dx};,
&tex{y_{0}}; ≤ Y ≤ &tex{y_{0} + dy};,
&tex{z_{0}}; ≤ Z ≤ &tex{z_{0} + dz};,
を満たす点で構成される.
直方体の体積は &tex{dx × dy × dz};で求められる.
複数の直方体を結合したものの体積を考えた場合, 直方体に重なりがあれば, 結合直方体の体積は
それぞれの直方体の体積の和より小さくなる.

&tex{C_{1}};, …, &tex{C_{50000}}; を以下のパラメータで与えられる座標軸に平行な直方体とする.
- &tex{x_{0}}; = &tex{S_{6n-5}}; modulo 10000
- &tex{y_{0}}; = &tex{S_{6n-4}}; modulo 10000
- &tex{z_{0}}; = &tex{S_{6n-3}}; modulo 10000
- &tex{dx}; = 1 + (&tex{S_{6n-2}}; modulo 399)
- &tex{dy}; = 1 + (&tex{S_{6n-1}}; modulo 399)
- &tex{dz}; = 1 + (&tex{S_{6n}}; modulo 399)

&tex{S_{1}};,…,&tex{S_{300000}}; はラグ付きフィボナッチ法により生成される.
-  1 ≤ &tex{k}; ≤ 55 の場合, &tex{S_{k}}; = [100003 - 200003&tex{k}; + 300007&tex{k^{3}};] (modulo 1000000)
- 56 ≤ &tex{k}; の場合, [&tex{S_{k-24}}; + &tex{S_{k-55}};] (modulo 1000000)

したがって, &tex{C_{1}}; は {(7, 53, 183), (94, 369, 56)}, &tex{C_{2}}; は {(2383, 3563, 5079), (42, 212, 344)} となる

&tex{C_{1}};, …, &tex{C_{100}}; の結合直方体の体積は 723581599 である.

&tex{C_{1}};, …, &tex{C_{50000}}; の結合直方体の体積を求めよ.


トップ   新規 一覧 単語検索 最終更新   ヘルプ   最終更新のRSS