freeCodeCamp/curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-212-combined-volume-of-cuboids.md

id, title, challengeType, forumTopicId, dashedName

id	title	challengeType	forumTopicId	dashedName
5900f4411000cf542c50ff53	Problem 212: Combined Volume of Cuboids	5	301854	problem-212-combined-volume-of-cuboids

--description--

An axis-aligned cuboid, specified by parameters { (x0,y0,z0), (dx,dy,dz) }, consists of all points (X,Y,Z) such that x0 ≤ X ≤ x0+dx, y0 ≤ Y ≤ y0+dy and z0 ≤ Z ≤ z0+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.

Let C1,...,C50000 be a collection of 50000 axis-aligned cuboids such that Cn has parameters

x0 = S6n-5 modulo 10000y0 = S6n-4 modulo 10000z0 = S6n-3 modulo 10000dx = 1 + (S6n-2 modulo 399)dy = 1 + (S6n-1 modulo 399)dz = 1 + (S6n modulo 399)

where S1,...,S300000 come from the "Lagged Fibonacci Generator":

For 1 ≤ k ≤ 55, Sk = [100003 - 200003k + 300007k3] (modulo 1000000)For 56 ≤ k, Sk = [Sk-24 + Sk-55] (modulo 1000000)

Thus, C1 has parameters {(7,53,183),(94,369,56)}, C2 has parameters {(2383,3563,5079),(42,212,344)}, and so on.

The combined volume of the first 100 cuboids, C1,...,C100, is 723581599.

What is the combined volume of all 50000 cuboids, C1,...,C50000 ?

--hints--

euler212() should return 328968937309.

assert.strictEqual(euler212(), 328968937309);

--seed--

--seed-contents--

function euler212() {

  return true;
}

euler212();

--solutions--

// solution required