eef1805fe6
* 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>
62 lines
1.9 KiB
Markdown
62 lines
1.9 KiB
Markdown
---
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id: 5900f4411000cf542c50ff53
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title: 'Problem 212: Combined Volume of Cuboids'
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challengeType: 5
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forumTopicId: 301854
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dashedName: problem-212-combined-volume-of-cuboids
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---
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# --description--
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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.
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Let $C_1, \ldots, C_{50000}$ be a collection of 50000 axis-aligned cuboids such that $C_n$ has parameters
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$$\begin{align}
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& x_0 = S_{6n - 5} \\; \text{modulo} \\; 10000 \\\\
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& y_0 = S_{6n - 4} \\; \text{modulo} \\; 10000 \\\\
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& z_0 = S_{6n - 3} \\; \text{modulo} \\; 10000 \\\\
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& dx = 1 + (S_{6n - 2} \\; \text{modulo} \\; 399) \\\\
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& dy = 1 + (S_{6n - 1} \\; \text{modulo} \\; 399) \\\\
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& dz = 1 + (S_{6n} \\; \text{modulo} \\; 399) \\\\
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\end{align}$$
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where $S_1, \ldots, S_{300000}$ come from the "Lagged Fibonacci Generator":
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For $1 ≤ k ≤ 55$, $S_k = [100003 - 200003k + 300007k^3] \\; (modulo \\; 1000000)$
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For $56 ≤ k$, $S_k = [S_{k - 24} + S_{k - 55}] \\; (modulo \\; 1000000)$
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Thus, $C_1$ has parameters $\{(7,53,183), (94,369,56)\}$, $C_2$ has parameters $\{(2383,3563,5079), (42,212,344)\}$, and so on.
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The combined volume of the first 100 cuboids, $C_1, \ldots, C_{100}$, is 723581599.
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What is the combined volume of all 50000 cuboids, $C_1, \ldots, C_{50000}$?
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# --hints--
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`combinedValueOfCuboids()` should return `328968937309`.
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```js
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assert.strictEqual(combinedValueOfCuboids(), 328968937309);
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```
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# --seed--
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## --seed-contents--
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```js
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function combinedValueOfCuboids() {
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return true;
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}
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combinedValueOfCuboids();
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```
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# --solutions--
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```js
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// solution required
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```
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