Just another update

Task/Zig-zag-matrix/00DESCRIPTION

@@ -1,4 +1,7 @@
-Produce a zig-zag array.  A zig-zag array is a square arrangement of the first <tt>N<sup>2</sup></tt> integers, where the numbers increase sequentially as you zig-zag along the anti-diagonals of the array.  For a graphical representation, see [[wp:Image:JPEG_ZigZag.svg|JPG zigzag]] (JPG uses such arrays to encode images).
+Produce a zig-zag array.
+A zig-zag array is a square arrangement of the first <tt>N<sup>2</sup></tt> integers, where the numbers increase sequentially as you zig-zag along the anti-diagonals of the array. <br>
+For a graphical representation, see [[wp:Image:JPEG_ZigZag.svg|JPG zigzag]]
+(JPG uses such arrays to encode images).
 
 For example, given <tt>5</tt>, produce this array:
 <pre>
@@ -8,3 +11,5 @@ For example, given <tt>5</tt>, produce this array:
  9 11 17 20 22
 10 18 19 23 24
 </pre>
+
+;See also [[Spiral matrix]]

Task/Zig-zag-matrix/C/zig-zag-matrix.c

@@ -0,0 +1,23 @@
+#include <stdio.h>
+#include <stdlib.h>
+
+int main(int c, char **v)
+{
+	int i, j, m, n, *s;
+
+	/* default size: 5 */
+	if (c < 2 || ((m = atoi(v[1]))) <= 0) m = 5;
+
+	/* alloc array*/
+	s = malloc(sizeof(int) * m * m);
+
+	for (i = n = 0; i < m * 2; i++)
+		for (j = (i < m) ? 0 : i-m+1; j <= i && j < m; j++)
+			s[(i&1)? j*(m-1)+i : (i-j)*m+j ] = n++;
+
+	for (i = 0; i < m * m; putchar((++i % m) ? ' ':'\n'))
+		printf("%3d", s[i]);
+
+	/* free(s) */
+	return 0;
+}

Task/Zig-zag-matrix/CoffeeScript/zig-zag-matrix.coffee

@@ -0,0 +1,41 @@
+# Calculate a zig-zag pattern of numbers like so:
+#   0 1 5
+#   2 4 6
+#   3 7 8
+#
+# There are many interesting ways to solve this; we
+# try for an algebraic approach, calculating triangle
+# areas, so that me minimize space requirements.
+
+zig_zag_value = (x, y, n) ->
+
+  upper_triangle_zig_zag = (x, y) ->
+    # calculate the area of the triangle from the prior
+    # diagonals
+    diag = x + y
+    triangle_area = diag * (diag+1) / 2
+    # then add the offset along the diagonal
+    if diag % 2 == 0
+      triangle_area + y
+    else
+      triangle_area + x
+
+  if x + y < n
+    upper_triangle_zig_zag x, y
+  else
+    # For the bottom right part of the matrix, we essentially
+    # use reflection to count backward.
+    bottom_right_cell = n * n - 1
+    n -= 1
+    v = upper_triangle_zig_zag(n-x, n-y)
+    bottom_right_cell - v
+
+zig_zag_matrix = (n) ->
+  row = (i) -> (zig_zag_value i, j, n for j in [0...n])
+  (row i for i in [0...n])
+
+do ->
+  for n in [4..6]
+    console.log "---- n=#{n}"
+    console.log zig_zag_matrix(n)
+    console.log "\n"

Task/Zig-zag-matrix/D/zig-zag-matrix-1.d

@@ -1,5 +1,6 @@
-int[][] zigZag(in int n) pure nothrow {
-    static void move(in int n, ref int i, ref int j) pure nothrow {
+int[][] zigZag(in int n) pure nothrow @safe {
+    static void move(in int n, ref int i, ref int j)
+    pure nothrow @safe @nogc {
         if (j < n - 1) {
             if (i > 0) i--;
             j++;
@@ -18,5 +19,6 @@ int[][] zigZag(in int n) pure nothrow {
 
 void main() {
     import std.stdio;
-    writefln("%(%(%2d %)\n%)", zigZag(5));
+
+    writefln("%(%(%2d %)\n%)", 5.zigZag);
 }

Task/Zig-zag-matrix/D/zig-zag-matrix-2.d

@@ -1,15 +1,14 @@
-import std.stdio, std.algorithm, std.typecons, std.range, std.array;
+import std.stdio, std.algorithm, std.range, std.array;
 
-int[][] zigZag(int n) {
-    alias P2 = Tuple!(int,"x", int,"y");
-    auto L = iota(n ^^ 2).map!(i => P2(i % n, i / n)).array;
-
-    L.sort!q{ (a.x + a.y == b.x + b.y) ?
-              ((a.x + a.y) % 2 ? a.y < b.y : a.x < b.x) :
-              (a.x + a.y) < (b.x + b.y) };
+int[][] zigZag(in int n) pure nothrow {
+    static struct P2 { int x, y; }
+    const L = iota(n ^^ 2).map!(i => P2(i % n, i / n)).array
+              .sort!q{ (a.x + a.y == b.x + b.y) ?
+                       ((a.x + a.y) % 2 ? a.y < b.y : a.x < b.x) :
+                       (a.x + a.y) < (b.x + b.y) }.release;
 
     auto result = new typeof(return)(n, n);
-    foreach (i, p; L)
+    foreach (immutable i, immutable p; L)
         result[p.y][p.x] = i;
     return result;
 }

Task/Zig-zag-matrix/MATLAB/zig-zag-matrix.m

@@ -0,0 +1,66 @@
+function matrix = zigZag(n)
+
+    %This is very unintiutive. This algorithm parameterizes the
+    %zig-zagging movement along the matrix indicies. The easiest way to see
+    %what this algorithm does is to go through line-by-line and write out
+    %what the algorithm does on a peace of paper.
+
+    matrix = zeros(n);
+    counter = 1;
+    flipCol = true;
+    flipRow = false;
+
+    %This for loop does the top-diagonal of the matrix
+    for i = (2:n)
+        row = (1:i);
+        column = (1:i);
+
+        %Causes the zig-zagging. Without these conditionals,
+        %you would end up with a diagonal matrix.
+        %To see what happens, comment these conditionals out.
+        if flipCol
+            column = fliplr(column);
+            flipRow = true;
+            flipCol = false;
+        elseif flipRow
+            row = fliplr(row);
+            flipRow = false;
+            flipCol = true;
+        end
+
+        %Selects a diagonal of the zig-zag matrix and places the
+        %correct integer value in each index along that diagonal
+        for j = (1:numel(row))
+            matrix(row(j),column(j)) = counter;
+            counter = counter + 1;
+        end
+    end
+
+    %This for loop does the bottom-diagonal of the matrix
+    for i = (2:n)
+        row = (i:n);
+        column = (i:n);
+
+        %Causes the zig-zagging. Without these conditionals,
+        %you would end up with a diagonal matrix.
+        %To see what happens comment these conditionals out.
+        if flipCol
+            column = fliplr(column);
+            flipRow = true;
+            flipCol = false;
+        elseif flipRow
+            row = fliplr(row);
+            flipRow = false;
+            flipCol = true;
+        end
+
+        %Selects a diagonal of the zig-zag matrix and places the
+        %correct integer value in each index along that diagonal
+        for j = (1:numel(row))
+            matrix(row(j),column(j)) = counter;
+            counter = counter + 1;
+        end
+    end
+
+
+end

Task/Zig-zag-matrix/Prolog/zig-zag-matrix.pro

@@ -69,8 +69,6 @@ compute_next(_NL, NC, Lig, Col, up, Lig1, Col, down) :-
 	Lig1 is Lig + 1.
 
 
-
-
 print_line(L) :-
 	maplist(print_val, L),
 	nl.

Task/Zig-zag-matrix/Python/zig-zag-matrix-4.py

@@ -1,7 +1,3 @@
-#ZigZag
-#
-# Nigel Galloway: June 7th., 2012,
-#
 COLS = 9
 def CX(x, ran):
   while True: