127 lines
2.7 KiB
Markdown
127 lines
2.7 KiB
Markdown
---
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id: 5949b579404977fbaefcd737
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title: Amicable pairs
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challengeType: 5
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forumTopicId: 302225
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dashedName: amicable-pairs
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---
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# --description--
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Two integers $N$ and $M$ are said to be [amicable pairs](https://en.wikipedia.org/wiki/Amicable numbers "wp: Amicable numbers") if $N \\neq M$ and the sum of the [proper divisors](https://rosettacode.org/wiki/Proper divisors "Proper divisors") of $N$ ($\\mathrm{sum}(\\mathrm{propDivs}(N))$) $= M$ as well as $\\mathrm{sum}(\\mathrm{propDivs}(M)) = N$.
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**Example:**
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**1184** and **1210** are an amicable pair, with proper divisors:
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<ul>
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<li>1, 2, 4, 8, 16, 32, 37, 74, 148, 296, 592 and</li>
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<li>1, 2, 5, 10, 11, 22, 55, 110, 121, 242, 605 respectively.</li>
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</ul>
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# --instructions--
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Calculate and show here the Amicable pairs below 20,000 (there are eight).
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# --hints--
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`amicablePairsUpTo` should be a function.
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```js
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assert(typeof amicablePairsUpTo === 'function');
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```
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`amicablePairsUpTo(300)` should return `[[220,284]]`.
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```js
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assert.deepEqual(amicablePairsUpTo(300), answer300);
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```
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`amicablePairsUpTo(3000)` should return `[[220,284],[1184,1210],[2620,2924]]`.
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```js
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assert.deepEqual(amicablePairsUpTo(3000), answer3000);
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```
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`amicablePairsUpTo(20000)` should return `[[220,284],[1184,1210],[2620,2924],[5020,5564],[6232,6368],[10744,10856],[12285,14595],[17296,18416]]`.
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```js
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assert.deepEqual(amicablePairsUpTo(20000), answer20000);
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```
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# --seed--
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## --after-user-code--
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```js
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const answer300 = [[220, 284]];
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const answer3000 = [
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[220, 284],
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[1184, 1210],
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[2620, 2924]
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];
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const answer20000 = [
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[220, 284],
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[1184, 1210],
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[2620, 2924],
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[5020, 5564],
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[6232, 6368],
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[10744, 10856],
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[12285, 14595],
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[17296, 18416]
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];
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```
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## --seed-contents--
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```js
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function amicablePairsUpTo(maxNum) {
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return true;
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}
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```
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# --solutions--
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```js
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// amicablePairsUpTo :: Int -> [(Int, Int)]
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function amicablePairsUpTo(maxNum) {
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return range(1, maxNum)
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.map(x => properDivisors(x)
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.reduce((a, b) => a + b, 0))
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.reduce((a, m, i, lst) => {
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const n = i + 1;
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return (m > n) && lst[m - 1] === n ?
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a.concat([
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[n, m]
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]) : a;
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}, []);
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}
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// properDivisors :: Int -> [Int]
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function properDivisors(n) {
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if (n < 2) return [];
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const rRoot = Math.sqrt(n);
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const intRoot = Math.floor(rRoot);
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const blnPerfectSquare = rRoot === intRoot;
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const lows = range(1, intRoot)
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.filter(x => (n % x) === 0);
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return lows.concat(lows.slice(1)
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.map(x => n / x)
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.reverse()
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.slice(blnPerfectSquare | 0));
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}
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// Int -> Int -> Maybe Int -> [Int]
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function range(m, n, step) {
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const d = (step || 1) * (n >= m ? 1 : -1);
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return Array.from({
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length: Math.floor((n - m) / d) + 1
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}, (_, i) => m + (i * d));
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}
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```
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