140 lines
2.9 KiB
Markdown
140 lines
2.9 KiB
Markdown
---
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id: 5900f3781000cf542c50fe8b
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title: 'Problem 12: Highly divisible triangular number'
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challengeType: 5
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forumTopicId: 301746
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dashedName: problem-12-highly-divisible-triangular-number
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---
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# --description--
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The sequence of triangle numbers is generated by adding the natural numbers. So the 7th triangle number would be 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28. The first ten terms would be:
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<div style='text-align: center;'>1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...</div>
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Let us list the factors of the first seven triangle numbers:
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<div style='padding-left: 4em;'><b>1:</b> 1</div>
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<div style='padding-left: 4em;'><b>3:</b> 1, 3</div>
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<div style='padding-left: 4em;'><b>6:</b> 1, 2, 3, 6</div>
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<div style='padding-left: 4em;'><b>10:</b> 1, 2, 5, 10</div>
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<div style='padding-left: 4em;'><b>15:</b> 1, 3, 5, 15</div>
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<div style='padding-left: 4em;'><b>21:</b> 1, 3, 7, 21</div>
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<div style='padding-left: 4em;'><b>28:</b> 1, 2, 4, 7, 14, 28</div>
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We can see that 28 is the first triangle number to have over five divisors.
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What is the value of the first triangle number to have over `n` divisors?
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# --hints--
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`divisibleTriangleNumber(5)` should return a number.
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```js
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assert(typeof divisibleTriangleNumber(5) === 'number');
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```
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`divisibleTriangleNumber(5)` should return 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)` should return 630.
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```js
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assert.strictEqual(divisibleTriangleNumber(23), 630);
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```
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`divisibleTriangleNumber(167)` should return 1385280.
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```js
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assert.strictEqual(divisibleTriangleNumber(167), 1385280);
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```
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`divisibleTriangleNumber(374)` should return 17907120.
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```js
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assert.strictEqual(divisibleTriangleNumber(374), 17907120);
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```
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`divisibleTriangleNumber(500)` should return 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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