yaworsw/euler-manager

---
:id: 212
:name: Combined Volume of Cuboids
:url: https://projecteuler.net/problem=212
:content: "An axis-aligned cuboid, specified by parameters { (x<sub>0</sub>,y<sub>0</sub>,z<sub>0</sub>),
  (dx,dy,dz) }, consists of all points (X,Y,Z) such that x<sub>0</sub> ≤ X ≤ x<sub>0</sub>+dx,
  y<sub>0</sub> ≤ Y ≤ y<sub>0</sub>+dy and z<sub>0</sub> ≤ Z ≤ z<sub>0</sub>+dz. The
  volume of the cuboid is the product, dx × dy × dz. The combined volume of a collection
  of cuboids is the volume of their union and will be less than the sum of the individual
  volumes if any cuboids overlap.\n\nLet C<sub>1</sub>,...,C<sub>50000</sub> be a
  collection of 50000 axis-aligned cuboids such that C<sub><var>n</var></sub> has
  parameters\n\nx<sub>0</sub> = S<sub>6<var>n</var>-5</sub> modulo 10000  \ny<sub>0</sub>
  = S<sub>6<var>n</var>-4</sub> modulo 10000  \nz<sub>0</sub> = S<sub>6<var>n</var>-3</sub>
  modulo 10000  \ndx = 1 + (S<sub>6<var>n</var>-2</sub> modulo 399)  \ndy = 1 + (S<sub>6<var>n</var>-1</sub>
  modulo 399)  \ndz = 1 + (S<sub>6<var>n</var></sub> modulo 399)\n\nwhere S<sub>1</sub>,...,S<sub>300000</sub>
  come from the \"Lagged Fibonacci Generator\":\n\nFor 1 ≤ <var>k</var> ≤ 55, S<sub><var>k</var></sub>
  = [100003 - 200003<var>k</var> + 300007<var>k</var><sup>3</sup>] &nbsp; (modulo
  1000000)  \nFor 56 ≤ <var>k</var>, S<sub><var>k</var></sub> = [S<sub><var>k</var>-24</sub>
  + S<sub><var>k</var>-55</sub>] &nbsp; (modulo 1000000)\n\nThus, C<sub>1</sub> has
  parameters {(7,53,183),(94,369,56)}, C<sub>2</sub> has parameters {(2383,3563,5079),(42,212,344)},
  and so on.\n\nThe combined volume of the first 100 cuboids, C<sub>1</sub>,...,C<sub>100</sub>,
  is 723581599.\n\nWhat is the combined volume of all 50000 cuboids, C<sub>1</sub>,...,C<sub>50000</sub>
  ?\n\n"