89 lines
2.9 KiB
JavaScript
89 lines
2.9 KiB
JavaScript
(() => {
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'use strict';
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// MAX PATH SUM -----------------------------------------------------------
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// Working from the bottom of the triangle upwards,
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// summing each number with the larger of the two below
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// until the maximum emerges at the top.
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// maxPathSum ::[[Int]] -> Int
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const maxPathSum = xss =>
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// A list of lists folded down to a list of just one remaining integer.
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// The head function returns that integer from the list.
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head(
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foldr1(
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// The accumulator, zipped with the tail of the
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// accumulator, yields pairs of adjacent sums so far.
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(ys, xs) => zipWith3(
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// Plus greater of two below
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(a, b, c) => a + max(b, c),
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xs, ys, tail(ys)
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),
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xss
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)
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);
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// GENERIC FUNCTIONS ------------------------------------------------------
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// Right fold using final element as initial accumulator
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// foldr1 :: (a -> a -> a) -> [a] -> a
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const foldr1 = (f, xs) =>
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xs.length > 0 ? init(xs)
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.reduceRight(f, last(xs)) : [];
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// head :: [a] -> a
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const head = xs => xs.length ? xs[0] : undefined;
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// init :: [a] -> [a]
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const init = xs => xs.length ? xs.slice(0, -1) : undefined;
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// last :: [a] -> a
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const last = xs => xs.length ? xs.slice(-1)[0] : undefined;
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// max :: Ord a => a -> a -> a
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const max = (a, b) => b > a ? b : a;
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// minimum :: [a] -> a
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const minimum = xs =>
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xs.reduce((a, x) => (x < a || a === undefined ? x : a), undefined);
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// tail :: [a] -> [a]
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const tail = xs => xs.length ? xs.slice(1) : undefined;
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// Function of arity 3 mapped over nth items of each of 3 lists
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// zipWith3 :: (a -> b -> c -> d) -> [a] -> [b] -> [c] -> [d]
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const zipWith3 = (f, xs, ys, zs) =>
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Array.from({
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length: minimum([xs.length, ys.length, zs.length])
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}, (_, i) => f(xs[i], ys[i], zs[i]));
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// TEST -------------------------------------------------------------------
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return maxPathSum([
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[55],
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[94, 48],
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[95, 30, 96],
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[77, 71, 26, 67],
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[97, 13, 76, 38, 45],
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[7, 36, 79, 16, 37, 68],
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[48, 7, 9, 18, 70, 26, 6],
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[18, 72, 79, 46, 59, 79, 29, 90],
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[20, 76, 87, 11, 32, 7, 7, 49, 18],
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[27, 83, 58, 35, 71, 11, 25, 57, 29, 85],
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[14, 64, 36, 96, 27, 11, 58, 56, 92, 18, 55],
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[2, 90, 3, 60, 48, 49, 41, 46, 33, 36, 47, 23],
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[92, 50, 48, 2, 36, 59, 42, 79, 72, 20, 82, 77, 42],
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[56, 78, 38, 80, 39, 75, 2, 71, 66, 66, 1, 3, 55, 72],
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[44, 25, 67, 84, 71, 67, 11, 61, 40, 57, 58, 89, 40, 56, 36],
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[85, 32, 25, 85, 57, 48, 84, 35, 47, 62, 17, 1, 1, 99, 89, 52],
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[6, 71, 28, 75, 94, 48, 37, 10, 23, 51, 6, 48, 53, 18, 74, 98, 15],
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[27, 2, 92, 23, 8, 71, 76, 84, 15, 52, 92, 63, 81, 10, 44, 10, 69, 93]
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]);
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})();
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