145 lines
4.1 KiB
Markdown
145 lines
4.1 KiB
Markdown
---
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id: 594d966a1467eb84194f0086
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title: Averages/Pythagorean means
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challengeType: 5
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forumTopicId: 302227
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dashedName: averagespythagorean-means
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---
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# --description--
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Compute all three of the [Pythagorean means](https://en.wikipedia.org/wiki/Pythagorean means "wp: Pythagorean means") of the set of integers $1$ through $10$ (inclusive).
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Show that $A(x_1,\\ldots,x_n) \\geq G(x_1,\\ldots,x_n) \\geq H(x_1,\\ldots,x_n)$ for this set of positive integers.
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<ul>
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<li>The most common of the three means, the <a class='rosetta__link--rosetta' href='https://rosettacode.org/wiki/Averages/Arithmetic mean' title='Averages/Arithmetic mean' target='_blank'>arithmetic mean</a>, is the sum of the list divided by its length:<br>
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<big>$ A(x_1, \ldots, x_n) = \frac{x_1 + \cdots + x_n}{n}$</big></li>
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<li>The <a class='rosetta__link--wiki' href='https://en.wikipedia.org/wiki/Geometric mean' title='wp: Geometric mean' target='_blank'>geometric mean</a> is the $n$th root of the product of the list:<br>
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<big>$ G(x_1, \ldots, x_n) = \sqrt[n]{x_1 \cdots x_n} $</big></li>
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<li>The <a class='rosetta__link--wiki' href='https://en.wikipedia.org/wiki/Harmonic mean' title='wp: Harmonic mean' target='_blank'>harmonic mean</a> is $n$ divided by the sum of the reciprocal of each item in the list:<br>
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<big>$ H(x_1, \ldots, x_n) = \frac{n}{\frac{1}{x_1} + \cdots + \frac{1}{x_n}} $</big></li>
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</ul>
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# --instructions--
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When writing your function, assume the input is an ordered array of all inclusive numbers.
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For the answer, please output an object in the following format:
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```js
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{
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values: {
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Arithmetic: 5.5,
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Geometric: 4.528728688116765,
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Harmonic: 3.414171521474055
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},
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test: 'is A >= G >= H ? yes'
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}
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```
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# --hints--
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`pythagoreanMeans` should be a function.
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```js
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assert(typeof pythagoreanMeans === 'function');
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```
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`pythagoreanMeans([1, 2, ..., 10])` should equal the same output above.
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```js
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assert.deepEqual(pythagoreanMeans(range1), answer1);
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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 range1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10];
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const answer1 = {
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values: {
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Arithmetic: 5.5,
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Geometric: 4.528728688116765,
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Harmonic: 3.414171521474055
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},
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test: 'is A >= G >= H ? yes'
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};
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```
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## --seed-contents--
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```js
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function pythagoreanMeans(rangeArr) {
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}
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```
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# --solutions--
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```js
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function pythagoreanMeans(rangeArr) {
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// arithmeticMean :: [Number] -> Number
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const arithmeticMean = xs =>
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foldl((sum, n) => sum + n, 0, xs) / length(xs);
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// geometricMean :: [Number] -> Number
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const geometricMean = xs =>
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raise(foldl((product, x) => product * x, 1, xs), 1 / length(xs));
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// harmonicMean :: [Number] -> Number
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const harmonicMean = xs =>
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length(xs) / foldl((invSum, n) => invSum + (1 / n), 0, xs);
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// GENERIC FUNCTIONS ------------------------------------------------------
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// A list of functions applied to a list of arguments
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// <*> :: [(a -> b)] -> [a] -> [b]
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const ap = (fs, xs) => //
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Array.prototype.concat(...fs.map(f => //
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Array.prototype.concat(...xs.map(x => [f(x)]))));
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// foldl :: (b -> a -> b) -> b -> [a] -> b
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const foldl = (f, a, xs) => xs.reduce(f, a);
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// length :: [a] -> Int
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const length = xs => xs.length;
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// mapFromList :: [(k, v)] -> Dictionary
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const mapFromList = kvs =>
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foldl((a, [k, v]) =>
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(a[(typeof k === 'string' && k)] = v, a), {}, kvs);
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// raise :: Num -> Int -> Num
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const raise = (n, e) => Math.pow(n, e);
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/*
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// show :: a -> String
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// show :: a -> Int -> String
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const show = (...x) =>
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JSON.stringify.apply(
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null, x.length > 1 ? [x[0], null, x[1]] : x
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);
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*/
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// zip :: [a] -> [b] -> [(a,b)]
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const zip = (xs, ys) =>
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xs.slice(0, Math.min(xs.length, ys.length))
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.map((x, i) => [x, ys[i]]);
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// TEST -------------------------------------------------------------------
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// mean :: Dictionary
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const mean = mapFromList(zip(
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['Arithmetic', 'Geometric', 'Harmonic'],
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ap([arithmeticMean, geometricMean, harmonicMean], [
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rangeArr
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])
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));
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return {
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values: mean,
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test: `is A >= G >= H ? ${mean.Arithmetic >= mean.Geometric &&
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mean.Geometric >= mean.Harmonic ? 'yes' : 'no'}`
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};
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}
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```
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