3.4 KiB
3.4 KiB
title | id | challengeType |
---|---|---|
Amicable pairs | 5949b579404977fbaefcd737 | 5 |
Description
- 1, 2, 4, 8, 16, 32, 37, 74, 148, 296, 592 and
- 1, 2, 5, 10, 11, 22, 55, 110, 121, 242, 605 respectively.
Instructions
Tests
tests:
- text: <code>amicablePairsUpTo</code> is a function.
testString: assert(typeof amicablePairsUpTo === 'function', '<code>amicablePairsUpTo</code> is a function.');
- text: <code>amicablePairsUpTo(300)</code> should return <code>[[220,284]]</code>.
testString: assert.deepEqual(amicablePairsUpTo(300), answer300, '<code>amicablePairsUpTo(300)</code> should return <code>[[220,284]]</code>.');
- text: <code>amicablePairsUpTo(3000)</code> should return <code>[[220,284],[1184,1210],[2620,2924]]</code>.
testString: assert.deepEqual(amicablePairsUpTo(3000), answer3000, '<code>amicablePairsUpTo(3000)</code> should return <code>[[220,284],[1184,1210],[2620,2924]]</code>.');
- text: <code>amicablePairsUpTo(20000)</code> should return <code>[[220,284],[1184,1210],[2620,2924],[5020,5564],[6232,6368],[10744,10856],[12285,14595],[17296,18416]]</code>.
testString: assert.deepEqual(amicablePairsUpTo(20000), answer20000, '<code>amicablePairsUpTo(20000)</code> should return <code>[[220,284],[1184,1210],[2620,2924],[5020,5564],[6232,6368],[10744,10856],[12285,14595],[17296,18416]]</code>.');
Challenge Seed
function amicablePairsUpTo(maxNum) {
// Good luck!
return true;
}
After Test
const answer300 = [[220, 284]];
const answer3000 = [
[220, 284],
[1184, 1210],
[2620, 2924]
];
const answer20000 = [
[220, 284],
[1184, 1210],
[2620, 2924],
[5020, 5564],
[6232, 6368],
[10744, 10856],
[12285, 14595],
[17296, 18416]
];
Solution
// amicablePairsUpTo :: Int -> [(Int, Int)]
function amicablePairsUpTo(maxNum) {
return range(1, maxNum)
.map(x => properDivisors(x)
.reduce((a, b) => a + b, 0))
.reduce((a, m, i, lst) => {
const n = i + 1;
return (m > n) && lst[m - 1] === n ?
a.concat([
[n, m]
]) : a;
}, []);
}
// properDivisors :: Int -> [Int]
function properDivisors(n) {
if (n < 2) return [];
const rRoot = Math.sqrt(n);
const intRoot = Math.floor(rRoot);
const blnPerfectSquare = rRoot === intRoot;
const lows = range(1, intRoot)
.filter(x => (n % x) === 0);
return lows.concat(lows.slice(1)
.map(x => n / x)
.reverse()
.slice(blnPerfectSquare | 0));
}
// Int -> Int -> Maybe Int -> [Int]
function range(m, n, step) {
const d = (step || 1) * (n >= m ? 1 : -1);
return Array.from({
length: Math.floor((n - m) / d) + 1
}, (_, i) => m + (i * d));
}