65 lines
1.5 KiB
JavaScript
65 lines
1.5 KiB
JavaScript
(() => {
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'use strict';
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// CATALAN
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// catalanSeries :: Int -> [Int]
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let catalanSeries = n => {
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let alternate = xs => xs.reduce(
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(a, x, i) => i % 2 === 0 ? a.concat([x]) : a, []
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),
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diff = xs => xs.length > 1 ? xs[0] - xs[1] : xs[0];
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return alternate(pascal(n * 2))
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.map((xs, i) => diff(drop(i, xs)));
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}
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// PASCAL
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// pascal :: Int -> [[Int]]
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let pascal = n => until(
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m => m.level <= 1,
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m => {
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let nxt = zipWith(
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(a, b) => a + b, [0].concat(m.row), m.row.concat(0)
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);
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return {
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row: nxt,
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triangle: m.triangle.concat([nxt]),
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level: m.level - 1
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}
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}, {
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level: n,
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row: [1],
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triangle: [
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[1]
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]
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}
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)
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.triangle;
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// GENERIC FUNCTIONS
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// zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]
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let zipWith = (f, xs, ys) =>
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xs.length === ys.length ? (
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xs.map((x, i) => f(x, ys[i]))
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) : undefined;
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// until :: (a -> Bool) -> (a -> a) -> a -> a
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let until = (p, f, x) => {
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let v = x;
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while (!p(v)) v = f(v);
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return v;
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}
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// drop :: Int -> [a] -> [a]
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let drop = (n, xs) => xs.slice(n);
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// tail :: [a] -> [a]
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let tail = xs => xs.length ? xs.slice(1) : undefined;
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return tail(catalanSeries(16));
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})();
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