September 2017 Update

Task/Maximum-triangle-path-sum/JavaScript/maximum-triangle-path-sum-7.js

@@ -0,0 +1,88 @@
+(() => {
+    'use strict';
+
+    // MAX PATH SUM -----------------------------------------------------------
+
+    // Working from the bottom of the triangle upwards,
+    // summing each number with the larger of the two below
+    // until the maximum emerges at the top.
+
+    // maxPathSum ::[[Int]] -> Int
+    const maxPathSum = xss =>
+
+        // A list of lists folded down to a list of just one remaining integer.
+        // The head function returns that integer from the list.
+
+        head(
+            foldr1(
+
+                // The accumulator, zipped with the tail of the
+                // accumulator, yields pairs of adjacent sums so far.
+                (ys, xs) => zipWith3(
+
+                    // Plus greater of two below
+                    (a, b, c) => a + max(b, c),
+                    xs, ys, tail(ys)
+                ),
+                xss
+            )
+        );
+
+
+    // GENERIC FUNCTIONS ------------------------------------------------------
+
+    // Right fold using final element as initial accumulator
+    // foldr1 :: (a -> a -> a) -> [a] -> a
+    const foldr1 = (f, xs) =>
+        xs.length > 0 ? init(xs)
+        .reduceRight(f, last(xs)) : [];
+
+    // head :: [a] -> a
+    const head = xs => xs.length ? xs[0] : undefined;
+
+    // init :: [a] -> [a]
+    const init = xs => xs.length ? xs.slice(0, -1) : undefined;
+
+    // last :: [a] -> a
+    const last = xs => xs.length ? xs.slice(-1)[0] : undefined;
+
+    // max :: Ord a => a -> a -> a
+    const max = (a, b) => b > a ? b : a;
+
+    // minimum :: [a] -> a
+    const minimum = xs =>
+        xs.reduce((a, x) => (x < a || a === undefined ? x : a), undefined);
+
+    // tail :: [a] -> [a]
+    const tail = xs => xs.length ? xs.slice(1) : undefined;
+
+    // Function of arity 3 mapped over nth items of each of 3 lists
+    // zipWith3 :: (a -> b -> c -> d) -> [a] -> [b] -> [c] -> [d]
+    const zipWith3 = (f, xs, ys, zs) =>
+        Array.from({
+            length: minimum([xs.length, ys.length, zs.length])
+        }, (_, i) => f(xs[i], ys[i], zs[i]));
+
+
+    // TEST -------------------------------------------------------------------
+    return maxPathSum([
+        [55],
+        [94, 48],
+        [95, 30, 96],
+        [77, 71, 26, 67],
+        [97, 13, 76, 38, 45],
+        [7, 36, 79, 16, 37, 68],
+        [48, 7, 9, 18, 70, 26, 6],
+        [18, 72, 79, 46, 59, 79, 29, 90],
+        [20, 76, 87, 11, 32, 7, 7, 49, 18],
+        [27, 83, 58, 35, 71, 11, 25, 57, 29, 85],
+        [14, 64, 36, 96, 27, 11, 58, 56, 92, 18, 55],
+        [2, 90, 3, 60, 48, 49, 41, 46, 33, 36, 47, 23],
+        [92, 50, 48, 2, 36, 59, 42, 79, 72, 20, 82, 77, 42],
+        [56, 78, 38, 80, 39, 75, 2, 71, 66, 66, 1, 3, 55, 72],
+        [44, 25, 67, 84, 71, 67, 11, 61, 40, 57, 58, 89, 40, 56, 36],
+        [85, 32, 25, 85, 57, 48, 84, 35, 47, 62, 17, 1, 1, 99, 89, 52],
+        [6, 71, 28, 75, 94, 48, 37, 10, 23, 51, 6, 48, 53, 18, 74, 98, 15],
+        [27, 2, 92, 23, 8, 71, 76, 84, 15, 52, 92, 63, 81, 10, 44, 10, 69, 93]
+    ]);
+})();