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 \{ (x_0,y_0,z_0), (dx,dy,dz) \}, consists of all points (X,$Y$,$Z$) such that x_0 ≤ X ≤ x_0 + dx, y_0 ≤ Y ≤ y_0 + dy and z_0 ≤ Z ≤ z_0 + 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 C_1, \ldots, C_{50000} be a collection of 50000 axis-aligned cuboids such that C_n has parameters

$$\begin{align} & x_0 = S_{6n - 5} \; \text{modulo} \; 10000 \\ & y_0 = S_{6n - 4} \; \text{modulo} \; 10000 \\ & z_0 = S_{6n - 3} \; \text{modulo} \; 10000 \\ & dx = 1 + (S_{6n - 2} \; \text{modulo} \; 399) \\ & dy = 1 + (S_{6n - 1} \; \text{modulo} \; 399) \\ & dz = 1 + (S_{6n} \; \text{modulo} \; 399) \\ \end{align}$$

where S_1, \ldots, S_{300000} come from the "Lagged Fibonacci Generator":

For 1 ≤ k ≤ 55, S_k = [100003 - 200003k + 300007k^3] \\; (modulo \\; 1000000)

For 56 ≤ k, S_k = [S_{k - 24} + S_{k - 55}] \\; (modulo \\; 1000000)

Thus, C_1 has parameters \{(7,53,183), (94,369,56)\}, C_2 has parameters \{(2383,3563,5079), (42,212,344)\}, and so on.

The combined volume of the first 100 cuboids, C_1, \ldots, C_{100}, is 723581599.

What is the combined volume of all 50000 cuboids, C_1, \ldots, C_{50000}?

--hints--

combinedValueOfCuboids() should return 328968937309.

assert.strictEqual(combinedValueOfCuboids(), 328968937309);

--seed--

--seed-contents--

function combinedValueOfCuboids() {

  return true;
}

combinedValueOfCuboids();

--solutions--

// solution required