126 lines
2.5 KiB
Markdown
126 lines
2.5 KiB
Markdown
---
|
|
id: 5900f3951000cf542c50fea8
|
|
challengeType: 5
|
|
title: 'Problem 41: Pandigital prime'
|
|
---
|
|
|
|
## Description
|
|
<section id='description'>
|
|
We shall say that an <i>n</i>-digit number is pandigital if it makes use of all the digits 1 to <i>n</i> exactly once. For example, 2143 is a 4-digit pandigital and is also prime.
|
|
What is the largest <i>n</i>-length digit pandigital prime that exists?
|
|
</section>
|
|
|
|
## Instructions
|
|
<section id='instructions'>
|
|
|
|
</section>
|
|
|
|
## Tests
|
|
<section id='tests'>
|
|
|
|
```yml
|
|
tests:
|
|
- text: <code>pandigitalPrime(4)</code> should return 4231.
|
|
testString: assert(pandigitalPrime(4) == 4231, '<code>pandigitalPrime(4)</code> should return 4231.');
|
|
- text: <code>pandigitalPrime(7)</code> should return 7652413.
|
|
testString: assert(pandigitalPrime(7) == 7652413, '<code>pandigitalPrime(7)</code> should return 7652413.');
|
|
|
|
```
|
|
|
|
</section>
|
|
|
|
## Challenge Seed
|
|
<section id='challengeSeed'>
|
|
|
|
<div id='js-seed'>
|
|
|
|
```js
|
|
function pandigitalPrime(n) {
|
|
// Good luck!
|
|
return n;
|
|
}
|
|
|
|
pandigitalPrime(7);
|
|
```
|
|
|
|
</div>
|
|
|
|
|
|
|
|
</section>
|
|
|
|
## Solution
|
|
<section id='solution'>
|
|
|
|
|
|
```js
|
|
function pandigitalPrime(n) {
|
|
function isPrime(num) {
|
|
for (let i = 2, s = Math.sqrt(num); i <= s; i++) {
|
|
if (num % i === 0) {
|
|
return false;
|
|
}
|
|
}
|
|
return num !== 1;
|
|
}
|
|
|
|
function getPermutations(n) {
|
|
if (n === 1) {
|
|
permutations.push(digitsArr.join(''));
|
|
} else {
|
|
for (let i = 0; i < n - 1; i++) {
|
|
getPermutations(n - 1);
|
|
// swap(n % 2 === 0 ? i : 0, n - 1);
|
|
if (n % 2 === 0) {
|
|
swap(i, n - 1);
|
|
} else {
|
|
swap(0, n - 1);
|
|
}
|
|
}
|
|
getPermutations(n - 1);
|
|
}
|
|
}
|
|
function swap(x, y) {
|
|
let temp = digitsArr[x];
|
|
digitsArr[x] = digitsArr[y];
|
|
digitsArr[y] = temp;
|
|
}
|
|
let max = 0;
|
|
let permutations = [];
|
|
let digitsArr;
|
|
let pandigitalNum = '';
|
|
|
|
for (let max = n; max > 0; max--) {
|
|
pandigitalNum += max;
|
|
}
|
|
|
|
for (let i = 0; i < pandigitalNum.length; i++) {
|
|
if (max > 0) {
|
|
break;
|
|
} else {
|
|
permutations = [];
|
|
const currMax = pandigitalNum.slice(i);
|
|
digitsArr = currMax.split('');
|
|
getPermutations(digitsArr.length);
|
|
|
|
// sort permutations in descending order
|
|
permutations.sort(function(a, b) {
|
|
return b - a;
|
|
});
|
|
|
|
for (let perm of permutations) {
|
|
const thisPerm = parseInt(perm);
|
|
if (isPrime(thisPerm)) {
|
|
max = thisPerm;
|
|
break;
|
|
}
|
|
}
|
|
}
|
|
}
|
|
|
|
return max;
|
|
}
|
|
```
|
|
|
|
</section>
|