ee1e8abd87
* feat(tools): add seed/solution restore script * chore(curriculum): remove empty sections' markers * chore(curriculum): add seed + solution to Chinese * chore: remove old formatter * fix: update getChallenges parse translated challenges separately, without reference to the source * chore(curriculum): add dashedName to English * chore(curriculum): add dashedName to Chinese * refactor: remove unused challenge property 'name' * fix: relax dashedName requirement * fix: stray tag Remove stray `pre` tag from challenge file. Signed-off-by: nhcarrigan <nhcarrigan@gmail.com> Co-authored-by: nhcarrigan <nhcarrigan@gmail.com>
62 lines
1.6 KiB
Markdown
62 lines
1.6 KiB
Markdown
---
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id: 5900f4341000cf542c50ff46
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title: 问题199：迭代圆包装
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challengeType: 5
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videoUrl: ''
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dashedName: problem-199-iterative-circle-packing
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---
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# --description--
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三个相等半径的圆放置在较大的圆内，使得每对圆彼此相切并且内圆不重叠。有四个未覆盖的“间隙”，它们将用更多的切圆迭代地填充。
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在每次迭代中，在每个间隙中放置最大尺寸的圆，这为下一次迭代创建了更多的间隙。经过3次迭代（如图）后，有108个间隙，未被圆圈覆盖的区域部分为0.06790342，四舍五入到小数点后8位。
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10次迭代后，圆圈没有覆盖哪一部分区域？使用格式x.xxxxxxxx将您的答案四舍五入到小数点后八位。
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# --hints--
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`euler199()`应该返回0.00396087。
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```js
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assert.strictEqual(euler199(), 0.00396087);
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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 iterativeCirclePacking(n) {
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return true;
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}
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iterativeCirclePacking(10);
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```
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# --solutions--
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```js
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function iterativeCirclePacking(n) {
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let k1 = 1;
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let k0 = k1 * (3 - 2 * Math.sqrt(3));
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let a0 = 1 / (k0 * k0);
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let a1 = 3 / (k1 * k1);
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a1 += 3 * getArea(k0, k1, k1, n);
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a1 += getArea(k1, k1, k1, n);
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let final = ((a0 - a1) / a0).toFixed(8);
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return parseFloat(final);
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function getArea(k1, k2, k3, depth) {
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if (depth == 0) return 0.0;
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let k4 = k1 + k2 + k3 + 2 * Math.sqrt(k1 * k2 + k2 * k3 + k3 * k1);
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let a = 1 / (k4 * k4);
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a += getArea(k1, k2, k4, depth - 1);
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a += getArea(k2, k3, k4, depth - 1);
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a += getArea(k3, k1, k4, depth - 1);
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return a;
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}
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}
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```
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