2016 Update

Task/Catalan-numbers-Pascals-triangle/JavaScript/catalan-numbers-pascals-triangle-2.js

@@ -0,0 +1,64 @@
+(() => {
+    'use strict';
+
+    // CATALAN
+
+    // catalanSeries :: Int -> [Int]
+    let catalanSeries = n => {
+        let alternate = xs => xs.reduce(
+                (a, x, i) => i % 2 === 0 ? a.concat([x]) : a, []
+            ),
+            diff = xs => xs.length > 1 ? xs[0] - xs[1] : xs[0];
+
+        return alternate(pascal(n * 2))
+            .map((xs, i) => diff(drop(i, xs)));
+    }
+
+    // PASCAL
+
+    // pascal :: Int -> [[Int]]
+    let pascal = n => until(
+            m => m.level <= 1,
+            m => {
+                let nxt = zipWith(
+                    (a, b) => a + b, [0].concat(m.row), m.row.concat(0)
+                );
+                return {
+                    row: nxt,
+                    triangle: m.triangle.concat([nxt]),
+                    level: m.level - 1
+                }
+            }, {
+                level: n,
+                row: [1],
+                triangle: [
+                    [1]
+                ]
+            }
+        )
+        .triangle;
+
+
+    // GENERIC FUNCTIONS
+
+    // zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]
+    let zipWith = (f, xs, ys) =>
+        xs.length === ys.length ? (
+            xs.map((x, i) => f(x, ys[i]))
+        ) : undefined;
+
+    // until :: (a -> Bool) -> (a -> a) -> a -> a
+    let until = (p, f, x) => {
+        let v = x;
+        while (!p(v)) v = f(v);
+        return v;
+    }
+
+    // drop :: Int -> [a] -> [a]
+    let drop = (n, xs) => xs.slice(n);
+
+    // tail :: [a] -> [a]
+    let tail = xs => xs.length ? xs.slice(1) : undefined;
+
+    return tail(catalanSeries(16));
+})();