1.9 KiB
1.9 KiB
| 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`.
```js
assert.strictEqual(combinedValueOfCuboids(), 328968937309);
```
# --seed--
## --seed-contents--
```js
function combinedValueOfCuboids() {
return true;
}
combinedValueOfCuboids();
```
# --solutions--
```js
// solution required
```