June 2018 Update

Task/Zig-zag-matrix/Octave/zig-zag-matrix-1.octave

@@ -0,0 +1,28 @@
+function a = zigzag1(n)
+  j = 1:n;
+  u = repmat([-1; 1], n, 1);
+  v = j.*(2*j-3);
+  v = reshape([v; v+1], 2*n, 1);
+  a = zeros(n, n);
+  for i = 1:n
+    a(:, i) = v(i+j);
+    v += u;
+  endfor
+endfunction
+
+function a = zigzag2(n)
+  a = zigzag1(n);
+  v = (1:n-1)'.^2;
+  for i = 2:n
+    a(n+2-i:n, i) -= v(1:i-1);
+  endfor
+endfunction
+
+>> zigzag2(5)
+ans =
+
+    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/Octave/zig-zag-matrix-2.octave

@@ -0,0 +1,18 @@
+function a = zigzag3(n)
+  a = zeros(n, n);
+  for k=1:n
+    d = (2*(j = mod(k, 2))-1)*(n-1);
+    m = (n-1)*(k-1);
+    a(k+(1-j)*m:d:k+j*m) = k*(k-1)/2:k*(k+1)/2-1;
+    a(n*(n+1-k)+(1-j)*m:d:n*(n+1-k)+j*m) = n*n-k*(k+1)/2:n*n-k*(k-1)/2-1;
+  endfor
+endfunction
+
+>> zigzag3(5)
+ans =
+
+    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/Perl-6/zig-zag-matrix.pl6

@@ -1,4 +1,45 @@
-sub MAIN($size as Int) {
+class Turtle {
+    my @dv =  [0,-1], [1,-1], [1,0], [1,1], [0,1], [-1,1], [-1,0], [-1,-1];
+    my $points = 8; # 'compass' points of neighbors on grid: north=0, northeast=1, east=2, etc.
+
+    has @.loc = 0,0;
+    has $.dir = 0;
+    has %.world;
+    has $.maxegg;
+    has $.range-x;
+    has $.range-y;
+
+    method turn-left ($angle = 90) { $!dir -= $angle / 45; $!dir %= $points; }
+    method turn-right($angle = 90) { $!dir += $angle / 45; $!dir %= $points; }
+
+    method lay-egg($egg) {
+    %!world{~@!loc} = $egg;
+    $!maxegg max= $egg;
+    $!range-x minmax= @!loc[0];
+    $!range-y minmax= @!loc[1];
+    }
+
+    method look($ahead = 1) {
+    my $there = @!loc »+« @dv[$!dir] »*» $ahead;
+    %!world{~$there};
+    }
+
+    method forward($ahead = 1) {
+    my $there = @!loc »+« @dv[$!dir] »*» $ahead;
+    @!loc = @($there);
+    }
+
+    method showmap() {
+    my $form = "%{$!maxegg.chars}s";
+    my $endx = $!range-x.max;
+        for $!range-y.list X $!range-x.list -> ($y, $x) {
+        print (%!world{"$x $y"} // '').fmt($form);
+        print $x == $endx ?? "\n" !! ' ';
+    }
+    }
+}
+
+sub MAIN(Int $size = 5) {
     my $t = Turtle.new(dir => 1);
     my $counter = 0;
     for 1 ..^ $size -> $run {

Task/Zig-zag-matrix/Ring/zig-zag-matrix.ring

@@ -0,0 +1,56 @@
+# Project : Zig-zag matrix
+# Date    : 2018/03/24
+# Author : Gal Zsolt [~ CalmoSoft ~]
+# Email   : <calmosoft@gmail.com>
+
+load "stdlib.ring"
+n = 5
+a = newlist(n,n)
+for j = 1 to n
+     for i = 1 to n
+          a[j][i] = 0
+     next
+next
+i = 1
+j = 1
+k = 1
+while k < n * n
+        a[j][i] = k
+        k = k + 1
+        if i = n
+           j = j + 1
+           a[j][i] = k
+           k = k + 1
+           di = -1
+           dj = 1
+        ok
+        if j = 1
+           i = i + 1
+           a[j][i] = k
+           k = k + 1
+           di = -1
+           dj = 1
+        ok
+        if j = n
+           i = i + 1
+           a[j][i] = k
+           k = k + 1
+           di = 1
+           dj = -1
+        ok
+        if i = 1
+           j = j + 1
+           a[j][i] = k
+           k = k + 1
+           di = 1
+           dj = -1
+        ok
+           i = i + di
+           j = j + dj
+end
+for p = 1 to n
+     for m = 1 to n
+          see "" + a[p][m] + " "
+     next
+     see nl
+next

Task/Zig-zag-matrix/Scilab/zig-zag-matrix.scilab

@@ -0,0 +1,19 @@
+function a = zigzag3(n)
+  a = zeros(n, n)
+  for k=1:n
+    j = modulo(k, 2)
+    d = (2*j-1)*(n-1)
+    m = (n-1)*(k-1)
+    a(k+(1-j)*m:d:k+j*m) = k*(k-1)/2:k*(k+1)/2-1
+    a(n*(n+1-k)+(1-j)*m:d:n*(n+1-k)+j*m) = n*n-k*(k+1)/2:n*n-k*(k-1)/2-1
+  end
+endfunction
+
+-->zigzag3(5)
+ ans  =
+
+    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/Stata/zig-zag-matrix-1.stata

@@ -0,0 +1,22 @@
+function zigzag1(n) {
+	j = 0::n-1
+	u = J(1, n, (-1, 1))
+	v = (j:*(2:*j:+3))
+	v = rowshape((v,v:+1), 1)
+	a = J(n, n, .)
+	for (i=1; i<=n; i++) {
+		a[i, .] = v[j:+i]
+		v = v+u
+	}
+	return(a)
+}
+
+zigzag1(5)
+        1    2    3    4    5
+    +--------------------------+
+  1 |   0    1    5    6   14  |
+  2 |   2    4    7   13   16  |
+  3 |   3    8   12   17   25  |
+  4 |   9   11   18   24   31  |
+  5 |  10   19   23   32   40  |
+    +--------------------------+

Task/Zig-zag-matrix/Stata/zig-zag-matrix-2.stata

@@ -0,0 +1,18 @@
+function zigzag2(n) {
+	a = zigzag1(n)
+	v = (1..n-1):^2
+	for (i=1; i<n; i++) {
+		a[n-i+1, i+1..n] = a[n-i+1, i+1..n] - v[1..n-i]
+	}
+	return(a)
+}
+
+zigzag2(5)
+        1    2    3    4    5
+    +--------------------------+
+  1 |   0    1    5    6   14  |
+  2 |   2    4    7   13   15  |
+  3 |   3    8   12   16   21  |
+  4 |   9   11   17   20   22  |
+  5 |  10   18   19   23   24  |
+    +--------------------------+

Task/Zig-zag-matrix/Stata/zig-zag-matrix-3.stata

@@ -0,0 +1,10 @@
+zigzag1(5)-zigzag2(5)
+[symmetric]
+        1    2    3    4    5
+    +--------------------------+
+  1 |   0                      |
+  2 |   0    0                 |
+  3 |   0    0    0            |
+  4 |   0    0    1    4       |
+  5 |   0    1    4    9   16  |
+    +--------------------------+