计算整数1到10 （包括）的所有三个毕达哥拉斯方法 。
为这组正整数显示$ A（x_1，\ ldots，x_n）\ geq G（x_1，\ ldots，x_n）\ geq H（x_1，\ ldots，x_n）$ 。
这三种方法中最常见的算术平均值是列表的总和除以其长度： $ A（x_1，\\ ldots，x_n）= \\ frac {x_1 + \\ cdots + x_n} {n} $ 几何mean是列表产品的$ n $ th根： $ G（x_1，\\ ldots，x_n）= \\ sqrt \[n] {x_1 \\ cdots x_n} $ 调和平均值是$ n $除以总和列表中每个项目的倒数： $ H（x_1，\\ ldots，x_n）= \\ frac {n} {\\ frac {1} {x_1} + \\ cdots + \\ frac {1} {x_n}} $假设输入是包含所有数字的有序数组。
要获得答案，请按以下格式输出对象：
{
值：{
算术：5.5，
几何：4.528728688116765，
谐波：3.414171521474055
}，
测试：'是A> = G> = H？是'
}
# --hints--
`pythagoreanMeans`是一种功能。
```js
assert(typeof pythagoreanMeans === 'function');
```
`pythagoreanMeans([1, 2, ..., 10])`应该等于上面相同的输出。
```js
assert.deepEqual(pythagoreanMeans(range1), answer1);
```
# --seed--
## --after-user-code--
```js
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'
};
```
## --seed-contents--
```js
function pythagoreanMeans(rangeArr) {
}
```
# --solutions--
```js
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'}`
};
}
```