2016 Update

Task/Zig-zag-matrix/JavaScript/zig-zag-matrix-2.js

@@ -0,0 +1,97 @@
+(function (n) {
+
+    // Read range of values into a series of 'diagonal rows'
+    // for a square of given dimension,
+    // starting at diagonal row i.
+    //  [
+    //   [0],
+    //   [1, 2],
+    //   [3, 4, 5],
+    //   [6, 7, 8, 9],
+    //   [10, 11, 12, 13, 14],
+    //   [15, 16, 17, 18],
+    //   [19, 20, 21],
+    //   [22, 23],
+    //   [24]
+    //  ]
+
+    // diagonals :: n -> [[n]]
+      function diagonals(n) {
+          function diags(xs, iCol, iRow) {
+              if (iCol < xs.length) {
+                  var xxs = splitAt(iCol, xs);
+
+                  return [xxs[0]].concat(diags(
+                      xxs[1],
+                      (iCol + (iRow < n ? 1 : -1)),
+                      iRow + 1
+                  ));
+              } else return [xs];
+          }
+
+          return diags(range(0, n * n - 1), 1, 1);
+      }
+
+
+
+    // Recursively read off n heads from the diagonals (as rows)
+    // n -> [[n]] -> [[n]]
+    function nHeads(n, lst) {
+        var zipEdge = lst.slice(0, n);
+
+        return lst.length ? [zipEdge.map(function (x) {
+            return x[0];
+        })].concat(nHeads(n, [].concat.apply([], zipEdge.map(function (
+                x) {
+                return x.length > 1 ? [x.slice(1)] : [];
+            }))
+            .concat(lst.slice(n)))) : [];
+    }
+
+    // range(intFrom, intTo, optional intStep)
+    // Int -> Int -> Maybe Int -> [Int]
+    function range(m, n, delta) {
+        var d = delta || 1,
+            blnUp = n > m,
+            lng = Math.floor((blnUp ? n - m : m - n) / d) + 1,
+            a = Array(lng),
+            i = lng;
+
+        if (blnUp)
+            while (i--) a[i] = (d * i) + m;
+        else
+            while (i--) a[i] = m - (d * i);
+        return a;
+    }
+
+    // splitAt :: Int -> [a] -> ([a],[a])
+    function splitAt(n, xs) {
+        return [xs.slice(0, n), xs.slice(n)];
+    }
+
+    // Recursively take n heads from the alternately reversed diagonals
+
+    //  [                                            [
+    //   [0],           ->    [0, 1, 5, 6, 14] and:
+    //   [1, 2],                                       [2],
+    //   [5, 4, 3],                                    [4, 3],
+    //   [6, 7, 8, 9],                                 [7, 8, 9],
+    //   [14, 13, 12, 11, 10],                         [13, 12, 11, 10],
+    //   [15, 16, 17, 18],                             [15, 16, 17, 18],
+    //   [21, 20, 19],                                 [21, 20, 19],
+    //   [22, 23],                                     [22, 23],
+    //   [24]                                          [24]
+    // ]                                             ]
+    //
+    //    In the next recursion with the remnant on the right, the next
+    //    5 heads will be [2, 4, 7, 13, 15] - the second row of our zig zag matrix.
+    //    (and so forth)
+
+
+    return nHeads(n, diagonals(n)
+        .map(function (x, i) {
+            i % 2 || x.reverse();
+            return x;
+        }));
+
+})(5);

Task/Zig-zag-matrix/JavaScript/zig-zag-matrix-3.js

@@ -0,0 +1,5 @@
+[[0, 1, 5, 6, 14],
+ [2, 4, 7, 13, 15],
+ [3, 8, 12, 16, 21],
+ [9, 11, 17, 20, 22],
+ [10, 18, 19, 23, 24]]

Task/Zig-zag-matrix/JavaScript/zig-zag-matrix-4.js

@@ -0,0 +1,60 @@
+(n => {
+
+    // diagonals :: n -> [[n]]
+    function diagonals(n) {
+        let diags = (xs, iCol, iRow) => {
+            if (iCol < xs.length) {
+                let xxs = splitAt(iCol, xs);
+
+                return [xxs[0]].concat(diags(
+                    xxs[1],
+                    iCol + (iRow < n ? 1 : -1),
+                    iRow + 1
+                ));
+            } else return [xs];
+        }
+
+        return diags(range(0, n * n - 1), 1, 1);
+    }
+
+
+    // Recursively read off n heads of diagonal lists
+    // rowsFromDiagonals :: n -> [[n]] -> [[n]]
+    function rowsFromDiagonals(n, lst) {
+        if (lst.length) {
+            let [edge, rest] = splitAt(n, lst);
+
+            return [edge.map(x => x[0])]
+                .concat(rowsFromDiagonals(n,
+                    edge.filter(x => x.length > 1)
+                    .map(x => x.slice(1))
+                    .concat(rest)
+                ));
+        } else return [];
+    }
+
+    // GENERIC FUNCTIONS
+
+    // splitAt :: Int -> [a] -> ([a],[a])
+    function splitAt(n, xs) {
+        return [xs.slice(0, n), xs.slice(n)];
+    }
+
+    // range :: From -> To -> Maybe Step -> [Int]
+    // range :: Int -> Int -> Maybe Int -> [Int]
+    function range(m, n, step) {
+        let d = (step || 1) * (n >= m ? 1 : -1);
+
+        return Array.from({
+            length: Math.floor((n - m) / d) + 1
+        }, (_, i) => m + (i * d));
+    }
+
+    // ZIG-ZAG MATRIX
+
+    return rowsFromDiagonals(n,
+        diagonals(n)
+        .map((x, i) => (i % 2 || x.reverse()) && x)
+    );
+
+})(5);

Task/Zig-zag-matrix/JavaScript/zig-zag-matrix-5.js

@@ -0,0 +1,5 @@
+[[0, 1, 5, 6, 14],
+ [2, 4, 7, 13, 15],
+ [3, 8, 12, 16, 21],
+ [9, 11, 17, 20, 22],
+ [10, 18, 19, 23, 24]]