139 lines
3.2 KiB
Markdown
139 lines
3.2 KiB
Markdown
---
|
|
id: 5900f3781000cf542c50fe8b
|
|
challengeType: 5
|
|
title: 'Problem 12: Highly divisible triangular number'
|
|
forumTopicId: 301746
|
|
---
|
|
|
|
## Description
|
|
<section id='description'>
|
|
|
|
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:
|
|
|
|
<div style='text-align: center;'>1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...</div>
|
|
|
|
Let us list the factors of the first seven triangle numbers:
|
|
|
|
<div style='padding-left: 4em;'><b>1:</b> 1</div>
|
|
<div style='padding-left: 4em;'><b>3:</b> 1, 3</div>
|
|
<div style='padding-left: 4em;'><b>6:</b> 1, 2, 3, 6</div>
|
|
<div style='padding-left: 4em;'><b>10:</b> 1, 2, 5, 10</div>
|
|
<div style='padding-left: 4em;'><b>15:</b> 1, 3, 5, 15</div>
|
|
<div style='padding-left: 4em;'><b>21:</b> 1, 3, 7, 21</div>
|
|
<div style='padding-left: 4em;'><b>28:</b> 1, 2, 4, 7, 14, 28</div>
|
|
|
|
We can see that 28 is the first triangle number to have over five divisors.
|
|
|
|
What is the value of the first triangle number to have over `n` divisors?
|
|
|
|
</section>
|
|
|
|
## Instructions
|
|
<section id='instructions'>
|
|
|
|
</section>
|
|
|
|
## Tests
|
|
<section id='tests'>
|
|
|
|
```yml
|
|
tests:
|
|
- text: <code>divisibleTriangleNumber(5)</code> should return a number.
|
|
testString: assert(typeof divisibleTriangleNumber(5) === 'number');
|
|
- text: <code>divisibleTriangleNumber(5)</code> should return 28.
|
|
testString: assert.strictEqual(divisibleTriangleNumber(5), 28);
|
|
- text: <code>divisibleTriangleNumber(23)</code> should return 630.
|
|
testString: assert.strictEqual(divisibleTriangleNumber(23), 630);
|
|
- text: <code>divisibleTriangleNumber(167)</code> should return 1385280.
|
|
testString: assert.strictEqual(divisibleTriangleNumber(167), 1385280);
|
|
- text: <code>divisibleTriangleNumber(374)</code> should return 17907120.
|
|
testString: assert.strictEqual(divisibleTriangleNumber(374), 17907120);
|
|
- text: <code>divisibleTriangleNumber(500)</code> should return 76576500.
|
|
testString: assert.strictEqual(divisibleTriangleNumber(500), 76576500);
|
|
|
|
```
|
|
|
|
</section>
|
|
|
|
## Challenge Seed
|
|
<section id='challengeSeed'>
|
|
|
|
<div id='js-seed'>
|
|
|
|
```js
|
|
function divisibleTriangleNumber(n) {
|
|
|
|
return true;
|
|
}
|
|
|
|
divisibleTriangleNumber(500);
|
|
```
|
|
|
|
</div>
|
|
|
|
</section>
|
|
|
|
## Solution
|
|
<section id='solution'>
|
|
|
|
```js
|
|
function divisibleTriangleNumber(n) {
|
|
if (n === 1) return 3;
|
|
let counter = 1;
|
|
let triangleNumber = counter++;
|
|
|
|
|
|
while (noOfFactors(triangleNumber) < n) {
|
|
triangleNumber += counter++;
|
|
}
|
|
return triangleNumber;
|
|
}
|
|
|
|
function noOfFactors(num) {
|
|
const primeFactors = getPrimeFactors(num);
|
|
let prod = 1;
|
|
for(let p in primeFactors) {
|
|
prod *= (primeFactors[p] + 1)
|
|
}
|
|
return prod;
|
|
}
|
|
|
|
function getPrimeFactors(num) {
|
|
let n = num;
|
|
let primes = {};
|
|
|
|
let p = 2;
|
|
let sqrt = Math.sqrt(num);
|
|
|
|
function checkAndUpdate(inc) {
|
|
if (n % p === 0) {
|
|
const curr = primes[p];
|
|
if (curr) {
|
|
primes[p]++
|
|
} else {
|
|
primes[p] = 1;
|
|
}
|
|
n /= p;
|
|
} else {
|
|
p += inc;
|
|
}
|
|
}
|
|
|
|
while(p === 2 && p <= n) {
|
|
checkAndUpdate(1);
|
|
}
|
|
|
|
while (p <= n && p <= sqrt) {
|
|
checkAndUpdate(2);
|
|
}
|
|
if(Object.keys(primes).length === 0) {
|
|
primes[num] = 1;
|
|
} else if(n !== 1) {
|
|
primes[n] = 1;
|
|
}
|
|
return primes;
|
|
}
|
|
```
|
|
|
|
</section>
|