* 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>
138 lines
2.4 KiB
Markdown
138 lines
2.4 KiB
Markdown
---
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id: 5900f3781000cf542c50fe8b
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title: 问题12:高度可分的三角数
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challengeType: 5
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videoUrl: ''
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dashedName: problem-12-highly-divisible-triangular-number
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---
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# --description--
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通过添加自然数生成三角数的序列。所以第7个三角形数字是1 + 2 + 3 + 4 + 5 + 6 + 7 = 28.前十个术语是:
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1,3,6,10,15,21,28,36,45,55 ......
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让我们列出前七个三角形数字的因子:
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**1:** 1
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**3:** 1,3
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**6:** 1,2,3,6
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**10:** 1,2,5,10
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**15:** 1,3,5,15
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**21:** 1,3,7,21
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**28:** 1,2,4,7,14,28
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我们可以看到28是第一个超过五个除数的三角形数。超过`n`除数的第一个三角形数的值是多少?
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# --hints--
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`divisibleTriangleNumber(5)`应该返回28。
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```js
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assert.strictEqual(divisibleTriangleNumber(5), 28);
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```
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`divisibleTriangleNumber(23)`应该返回630。
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```js
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assert.strictEqual(divisibleTriangleNumber(23), 630);
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```
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divisibleTriangleNumber `divisibleTriangleNumber(167)`应该返回1385280。
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```js
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assert.strictEqual(divisibleTriangleNumber(167), 1385280);
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```
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divisibleTriangleNumber `divisibleTriangleNumber(374)`应该返回17907120。
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```js
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assert.strictEqual(divisibleTriangleNumber(374), 17907120);
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```
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divisibleTriangleNumber `divisibleTriangleNumber(500)`应该返回76576500。
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```js
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assert.strictEqual(divisibleTriangleNumber(500), 76576500);
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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 divisibleTriangleNumber(n) {
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return true;
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}
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divisibleTriangleNumber(500);
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```
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# --solutions--
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```js
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function divisibleTriangleNumber(n) {
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if (n === 1) return 3;
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let counter = 1;
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let triangleNumber = counter++;
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while (noOfFactors(triangleNumber) < n) {
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triangleNumber += counter++;
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}
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return triangleNumber;
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}
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function noOfFactors(num) {
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const primeFactors = getPrimeFactors(num);
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let prod = 1;
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for(let p in primeFactors) {
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prod *= (primeFactors[p] + 1)
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}
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return prod;
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}
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function getPrimeFactors(num) {
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let n = num;
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let primes = {};
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let p = 2;
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let sqrt = Math.sqrt(num);
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function checkAndUpdate(inc) {
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if (n % p === 0) {
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const curr = primes[p];
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if (curr) {
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primes[p]++
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} else {
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primes[p] = 1;
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}
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n /= p;
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} else {
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p += inc;
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}
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}
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while(p === 2 && p <= n) {
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checkAndUpdate(1);
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}
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while (p <= n && p <= sqrt) {
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checkAndUpdate(2);
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}
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if(Object.keys(primes).length === 0) {
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primes[num] = 1;
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} else if(n !== 1) {
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primes[n] = 1;
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}
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return primes;
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}
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```
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