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title	id	challengeType
Averages-Pythagorean means	594d966a1467eb84194f0086	5

Description

Compute all three of the Pythagorean means of the set of integers 1 through 10 (inclusive).

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.

The most common of the three means, the arithmetic mean, is the sum of the list divided by its length: $ A(x_1, \ldots, x_n) = \frac{x_1 + \cdots + x_n}{n}$The geometric mean is the $n$th root of the product of the list: $ G(x_1, \ldots, x_n) = \sqrt[n]{x_1 \cdots x_n} $The harmonic mean is $n$ divided by the sum of the reciprocal of each item in the list: $ H(x_1, \ldots, x_n) = \frac{n}{\frac{1}{x_1} + \cdots + \frac{1}{x_n}} $

Assume the input is an ordered array of all inclusive numbers.

For the answer, please output an object in the following format:

{
  values: {
    Arithmetic: 5.5,
    Geometric: 4.528728688116765,
    Harmonic: 3.414171521474055
  },
  test: 'is A >= G >= H ? yes'
}

Instructions

Tests

tests:
  - text: <code>pythagoreanMeans</code> is a function.
    testString: assert(typeof pythagoreanMeans === 'function', '<code>pythagoreanMeans</code> is a function.');
  - text: <code>pythagoreanMeans([1, 2, ..., 10])</code> should equal the same output above.
    testString: assert.deepEqual(pythagoreanMeans(range1), answer1, '<code>pythagoreanMeans([1, 2, ..., 10])</code> should equal the same output above.');

Challenge Seed

function pythagoreanMeans (rangeArr) {
  // Good luck!
}

After Test

const range1 = [1, 2, 3, 4, 5, 6, 7, 8, 9, 10];
const answer1 = {
  values: {
    Arithmetic: 5.5,
    Geometric: 4.528728688116765,
    Harmonic: 3.414171521474055
  },
  test: 'is A >= G >= H ? yes'
};

Solution

function pythagoreanMeans (rangeArr) {
  // arithmeticMean :: [Number] -> Number
  const arithmeticMean = xs =>
    foldl((sum, n) => sum + n, 0, xs) / length(xs);

  // geometricMean :: [Number] -> Number
  const geometricMean = xs =>
    raise(foldl((product, x) => product * x, 1, xs), 1 / length(xs));

  // harmonicMean :: [Number] -> Number
  const harmonicMean = xs =>
    length(xs) / foldl((invSum, n) => invSum + (1 / n), 0, xs);

  // GENERIC FUNCTIONS ------------------------------------------------------

  // A list of functions applied to a list of arguments
  // <*> :: [(a -> b)] -> [a] -> [b]
  const ap = (fs, xs) => //
    Array.prototype.concat(...fs.map(f => //
      Array.prototype.concat(...xs.map(x => [f(x)]))));

  // foldl :: (b -> a -> b) -> b -> [a] -> b
  const foldl = (f, a, xs) => xs.reduce(f, a);

  // length :: [a] -> Int
  const length = xs => xs.length;

  // mapFromList :: [(k, v)] -> Dictionary
  const mapFromList = kvs =>
    foldl((a, [k, v]) =>
      (a[(typeof k === 'string' && k)] = v, a), {}, kvs);

  // raise :: Num -> Int -> Num
  const raise = (n, e) => Math.pow(n, e);
/*
  // show :: a -> String
  // show :: a -> Int -> String
  const show = (...x) =>
    JSON.stringify.apply(
      null, x.length > 1 ? [x[0], null, x[1]] : x
    );
*/
  // zip :: [a] -> [b] -> [(a,b)]
  const zip = (xs, ys) =>
    xs.slice(0, Math.min(xs.length, ys.length))
      .map((x, i) => [x, ys[i]]);

  // TEST -------------------------------------------------------------------
  // mean :: Dictionary
  const mean = mapFromList(zip(
    ['Arithmetic', 'Geometric', 'Harmonic'],
    ap([arithmeticMean, geometricMean, harmonicMean], [
      rangeArr
    ])
  ));

  return {
    values: mean,
    test: `is A >= G >= H ? ${mean.Arithmetic >= mean.Geometric &&
      mean.Geometric >= mean.Harmonic ? 'yes' : 'no'}`
  };
}

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