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>
78 lines
1.6 KiB
Markdown
78 lines
1.6 KiB
Markdown
---
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id: 5900f3a11000cf542c50feb4
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title: 问题53：组合选择
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challengeType: 5
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videoUrl: ''
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dashedName: problem-53-combinatoric-selections
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---
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# --description--
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有十种方法从五种中选择三种，12345：123,124,125,134,135,145,234,235,245和345在组合学中，我们使用符号，5C3 = 10.一般来说，
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nCr = n！r！（n-r）！ ，其中r≤n，n！ = n×（n-1）×...×3×2×1和0！ = 1。
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直到n = 23，一个值超过一百万：23C10 = 1144066.对于1≤n≤100，nCr的多少，不一定是不同的值大于一百万？
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# --hints--
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`combinatoricSelections(1000)`应返回4626。
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```js
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assert.strictEqual(combinatoricSelections(1000), 4626);
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```
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`combinatoricSelections(10000)`应该返回4431。
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```js
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assert.strictEqual(combinatoricSelections(10000), 4431);
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```
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`combinatoricSelections(100000)`应返回4255。
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```js
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assert.strictEqual(combinatoricSelections(100000), 4255);
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```
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`combinatoricSelections(1000000)`应该返回4075。
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```js
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assert.strictEqual(combinatoricSelections(1000000), 4075);
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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 combinatoricSelections(limit) {
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return 1;
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}
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combinatoricSelections(1000000);
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```
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# --solutions--
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```js
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function combinatoricSelections(limit) {
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const factorial = n =>
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Array.apply(null, { length: n })
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.map((_, i) => i + 1)
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.reduce((p, c) => p * c, 1);
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let result = 0;
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const nMax = 100;
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for (let n = 1; n <= nMax; n++) {
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for (let r = 0; r <= n; r++) {
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if (factorial(n) / (factorial(r) * factorial(n - r)) >= limit)
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result++;
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}
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}
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return result;
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}
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```
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