* fix: clean-up Project Euler 201-220 * fix: corrections from review Co-authored-by: Tom <20648924+moT01@users.noreply.github.com> Co-authored-by: Tom <20648924+moT01@users.noreply.github.com>
1.9 KiB
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