140 lines
4.5 KiB
Markdown
140 lines
4.5 KiB
Markdown
---
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title: Averages-Pythagorean means
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id: 594d966a1467eb84194f0086
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localeTitle: 594d966a1467eb84194f0086
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challengeType: 5
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---
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## Description
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<section id='description'>
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<p class='rosetta__paragraph'> Calcule los tres <a class='rosetta__link--wiki' href='https://en.wikipedia.org/wiki/Pythagorean means' title="wp: medios pitagóricos">medios pitagóricos</a> del conjunto de enteros del <big>1</big> al <big>10</big> (inclusive). </p><p class='rosetta__paragraph'> Muestre que <big>$ A (x_1, \ ldots, x_n) \ geq G (x_1, \ ldots, x_n) \ geq H (x_1, \ ldots, x_n) $</big> para este conjunto de enteros positivos. </p> El más común de los tres medios, la <a class='rosetta__link--rosetta' href='http://rosettacode.org/wiki/Averages/Arithmetic mean' title="Medias / media aritmética">media aritmética</a> , es la suma de la lista dividida por su longitud: <big>$ A (x_1, \ ldots, x_n) = \ frac {x_1 + \ cdots + x_n} {n} $</big> La <a class='rosetta__link--wiki' href='https://en.wikipedia.org/wiki/Geometric mean' title="wp: media geométrica">geometría media</a> es la raíz $ n $ th del producto de la lista: <big>$ G (x_1, \ ldots, x_n) = \ sqrt [n] {x_1 \ cdots x_n} $</big> La <a class='rosetta__link--wiki' href='https://en.wikipedia.org/wiki/Harmonic mean' title="wp: media armónica">media armónica</a> es $ n $ dividida por la suma de el recíproco de cada elemento en la lista: <big>$ H (x_1, \ ldots, x_n) = \ frac {n} {\ frac {1} {x_1} + \ cdots + \ frac {1} {x_n}} $</big>
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<p class='rosetta__paragraph'> Suponga que la entrada es una matriz ordenada de todos los números inclusivos. </p>
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<p class='rosetta__paragraph'> Para la respuesta, envíe un objeto en el siguiente formato: </p>
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<pre class='rosetta__pre'>
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{
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valores: {
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Aritmética: 5.5,
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Geométrica: 4.528728688116765,
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Armónica: 3.414171521474055
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},
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prueba: 'es A> = G> = H? si '
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}
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</pre>
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</section>
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## Instructions
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<section id='instructions'>
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</section>
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## Tests
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<section id='tests'>
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```yml
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tests:
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- text: <code>pythagoreanMeans</code> es una función.
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testString: 'assert(typeof pythagoreanMeans === "function", "<code>pythagoreanMeans</code> is a function.");'
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- text: ' <code>pythagoreanMeans([1, 2, ..., 10])</code> debe ser igual a la salida anterior.'
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testString: 'assert.deepEqual(pythagoreanMeans(range1), answer1, "<code>pythagoreanMeans([1, 2, ..., 10])</code> should equal the same output above.");'
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```
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</section>
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## Challenge Seed
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<section id='challengeSeed'>
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<div id='js-seed'>
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```js
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function pythagoreanMeans (rangeArr) {
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// Good luck!
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}
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```
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</div>
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### After Test
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<div id='js-teardown'>
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```js
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console.info('after the test');
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```
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</div>
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</section>
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## Solution
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<section id='solution'>
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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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</section>
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