Initial data commit

2023-07-01 11:58:00 -04:00 · 2023-07-01 11:58:00 -04:00 · f23f22d71c
commit f23f22d71c
parent 72d218235f
199087 changed files with 3378941 additions and 0 deletions
--- a/Task/Catalan-numbers/JavaScript/catalan-numbers-1.js
+++ b/Task/Catalan-numbers/JavaScript/catalan-numbers-1.js
@ -0,0 +1,29 @@
+<html><head><title>Catalan</title></head>
+<body><pre id='x'></pre><script type="application/javascript">
+function disp(x) {
+	var e = document.createTextNode(x + '\n');
+	document.getElementById('x').appendChild(e);
+}
+
+var fc = [], c2 = [], c3 = [];
+function fact(n) { return fc[n] ? fc[n] : fc[n] = (n ? n * fact(n - 1) : 1); }
+function cata1(n) { return Math.floor(fact(2 * n) / fact(n + 1) / fact(n) + .5); }
+function cata2(n) {
+	if (n == 0) return 1;
+	if (!c2[n]) {
+		var s = 0;
+		for (var i = 0; i < n; i++) s += cata2(i) * cata2(n - i - 1);
+		c2[n] = s;
+	}
+	return c2[n];
+}
+function cata3(n) {
+	if (n == 0) return 1;
+	return c3[n] ? c3[n] : c3[n] = (4 * n - 2) * cata3(n - 1) / (n + 1);
+}
+
+disp("       meth1   meth2   meth3");
+for (var i = 0; i <= 15; i++)
+	disp(i + '\t' + cata1(i) + '\t' + cata2(i) + '\t' + cata3(i));
+
+</script></body></html>
--- a/Task/Catalan-numbers/JavaScript/catalan-numbers-2.js
+++ b/Task/Catalan-numbers/JavaScript/catalan-numbers-2.js
@ -0,0 +1,85 @@
+(() => {
+    "use strict";
+
+    // ----------------- CATALAN NUMBERS -----------------
+
+    // catalansDefinitionThree :: [Int]
+    const catalansDefinitionThree = () =>
+        // An infinite sequence of Catalan numbers.
+        scanlGen(
+            c => n => Math.floor(
+                (2 * c * pred(2 * n)) / succ(n)
+            )
+        )(1)(
+            enumFrom(1)
+        );
+
+
+    // ---------------------- TEST -----------------------
+    // main :: IO ()
+    const main = () =>
+        take(15)(
+            catalansDefinitionThree()
+        );
+
+
+    // --------------------- GENERIC ---------------------
+
+    // enumFrom :: Enum a => a -> [a]
+    const enumFrom = function* (n) {
+        // An infinite sequence of integers,
+        // starting with n.
+        let v = n;
+
+        while (true) {
+            yield v;
+            v = 1 + v;
+        }
+    };
+
+
+    // pred :: Int -> Int
+    const pred = x =>
+        x - 1;
+
+
+    // scanlGen :: (b -> a -> b) -> b -> Gen [a] -> [b]
+    const scanlGen = f =>
+        // The series of interim values arising
+        // from a catamorphism over an infinite list.
+        startValue => function* (gen) {
+            let
+                a = startValue,
+                x = gen.next();
+
+            yield a;
+            while (!x.done) {
+                a = f(a)(x.value);
+                yield a;
+                x = gen.next();
+            }
+        };
+
+
+    // succ :: Int -> Int
+    const succ = x =>
+        1 + x;
+
+
+    // take :: Int -> [a] -> [a]
+    // take :: Int -> String -> String
+    const take = n =>
+        // The first n elements of a list,
+        // string of characters, or stream.
+        xs => Array.from({
+            length: n
+        }, () => {
+            const x = xs.next();
+
+            return x.done ? [] : [x.value];
+        }).flat();
+
+
+    // MAIN ---
+    return JSON.stringify(main(), null, 2);
+})();