2016 Update

Task/Ordered-Partitions/JavaScript/ordered-partitions-1.js

@@ -0,0 +1,61 @@
+(function () {
+  'use strict';
+
+  // [n] -> [[[n]]]
+  function partitions(a1, a2, a3) {
+    var n = a1 + a2 + a3;
+
+    return combos(range(1, n), n, [a1, a2, a3]);
+  }
+
+  function combos(s, n, xxs) {
+    if (!xxs.length) return [[]];
+
+    var x = xxs[0],
+        xs = xxs.slice(1);
+
+    return mb( choose(s, n, x),                 function (l_rest) {
+    return mb( combos(l_rest[1], (n - x), xs),  function (r) {
+      // monadic return/injection requires 1 additional
+      // layer of list nesting:
+      return [ [l_rest[0]].concat(r) ];
+
+    })});
+  }
+
+  function choose(aa, n, m) {
+    if (!m) return [[[], aa]];
+
+    var a = aa[0],
+        as = aa.slice(1);
+
+    return n === m ? (
+      [[aa, []]]
+    ) : (
+      choose(as, n - 1, m - 1).map(function (xy) {
+        return [[a].concat(xy[0]), xy[1]];
+      }).concat(choose(as, n - 1, m).map(function (xy) {
+        return [xy[0], [a].concat(xy[1])];
+      }))
+    );
+  }
+
+  // GENERIC
+
+  // Monadic bind (chain) for lists
+  function mb(xs, f) {
+    return [].concat.apply([], xs.map(f));
+  }
+
+  // [m..n]
+  function range(m, n) {
+    return Array.apply(null, Array(n - m + 1)).map(function (x, i) {
+      return m + i;
+    });
+  }
+
+  // EXAMPLE
+
+  return partitions(2, 0, 2);
+
+})();

Task/Ordered-Partitions/JavaScript/ordered-partitions-2.js

@@ -0,0 +1,6 @@
+[[[1, 2], [], [3, 4]],
+ [[1, 3], [], [2, 4]],
+ [[1, 4], [], [2, 3]],
+ [[2, 3], [], [1, 4]],
+ [[2, 4], [], [1, 3]],
+ [[3, 4], [], [1, 2]]]