Another update from ingydotnet^djgoku

Task/Spiral-matrix/00DESCRIPTION

@@ -13,4 +13,4 @@ For example, given 5, produce this array:
 12 11 10  9  8
 </pre>
 
-;See also [[Zig-zag matrix]]
+;See also [[Zig-zag matrix]] and [[Ulam_spiral_(for_primes)]]

Task/Spiral-matrix/DCL/spiral-matrix.dcl

@@ -0,0 +1,56 @@
+$ p1 = f$integer( p1 )
+$ max = p1 * p1
+$
+$ i = 0
+$ r = 1
+$ rd = 0
+$ c = 1
+$ cd = 1
+$ loop:
+$  a'r'_'c' = i
+$  nr = r + rd
+$  nc = c + cd
+$  if nr .eq. 0 .or. nc .eq. 0 .or. nr .gt. p1 .or. nc .gt. p1 .or. f$type( a'nr'_'nc' ) .nes. ""
+$  then
+$   gosub change_directions
+$  endif
+$  r = r + rd
+$  c = c + cd
+$  i = i + 1
+$  if i .lt. max then $ goto loop
+$ length = f$length( f$string( max - 1 ))
+$ r = 1
+$ loop2:
+$  c = 1
+$  output = ""
+$  loop3:
+$   output = output + f$fao( "!#UL ", length, a'r'_'c' )
+$   c = c + 1
+$   if c .le. p1 then $ goto loop3
+$  write sys$output output
+$  r = r + 1
+$  if r .le. p1 then $ goto loop2
+$ exit
+$
+$ change_directions:
+$ if rd .eq. 0 .and cd .eq. 1
+$ then
+$  rd = 1
+$  cd = 0
+$ else
+$  if rd .eq. 1 .and. cd .eq. 0
+$  then
+$   rd = 0
+$   cd = -1
+$  else
+$   if rd .eq. 0 .and. cd .eq. -1
+$   then
+$    rd = -1
+$    cd = 0
+$   else
+$    rd = 0
+$    cd = 1
+$   endif
+$  endif
+$ endif
+$ return

Task/Spiral-matrix/Elixir/spiral-matrix.elixir

@@ -0,0 +1,33 @@
+defmodule RC do
+  def spiral_matrix(n) do
+    right(n,n-1,0,[]) |> Enum.with_index |> Enum.sort |>  Enum.with_index |>
+      Enum.each(fn {{_,x},i} ->
+        :io.format("~2w ", [x])
+        if( rem(i+1,n)==0, do: IO.puts "")
+      end)
+  end
+
+  def right(n,side,i,coordinates) do
+    coord = for j <- 0..side, do: {i, i+j}
+    down(n,side,i,coordinates++coord)
+  end
+
+  def down(_,0,_,coordinates), do: coordinates
+  def down(n,side,i,coordinates) do
+    coord = for j <- 1..side, do: {i+j, n-1-i}
+    left(n,side-1,i,coordinates++coord)
+  end
+
+  def left(n,side,i,coordinates) do
+    coord = for j <- 0..side, do: {n-1-i, i+side-j}
+    up(n,side,i,coordinates++coord)
+  end
+
+  def up(_,0,_,coordinates), do: coordinates
+  def up(n,side,i,coordinates) do
+    coord = for j <- 1..side, do: {i+side-j+1, i}
+    right(n,side-1,i+1,coordinates++coord)
+  end
+end
+
+RC.spiral_matrix(5)

Task/Spiral-matrix/JavaScript/spiral-matrix-2.js

@@ -0,0 +1,67 @@
+(function (n) {
+
+  // Spiral: the first row plus a smaller spiral rotated 90 degrees clockwise
+  function spiral(lngRows, lngCols, nStart) {
+    return lngRows ? [range(nStart, (nStart + lngCols) - 1)].concat(
+      transpose(
+        spiral(lngCols, lngRows - 1, nStart + lngCols)
+      ).map(reverse)
+    ) : [
+      []
+    ];
+  }
+
+  // rows and columns transposed (for 90 degree rotation)
+  function transpose(lst) {
+    return lst.length > 1 ? lst[0].map(function (_, col) {
+      return lst.map(function (row) {
+        return row[col];
+      });
+    }) : lst;
+  }
+
+  // elements in reverse order (for 90 degree rotation)
+  function reverse(lst) {
+    return lst.length > 1 ? lst.reduceRight(function (acc, x) {
+      return acc.concat(x);
+    }, []) : lst;
+  }
+
+  // [m..n]
+  function range(m, n) {
+    return Array.apply(null, Array(n - m + 1)).map(function (x, i) {
+      return m + i;
+    });
+  }
+
+  // TESTING
+
+  var lstSpiral = spiral(n, n, 0);
+
+
+  // OUTPUT FORMATTING - JSON and wikiTable
+  function wikiTable(lstRows, blnHeaderRow, strStyle) {
+    return '{| class="wikitable" ' + (
+      strStyle ? 'style="' + strStyle + '"' : ''
+    ) + lstRows.map(function (lstRow, iRow) {
+      var strDelim = ((blnHeaderRow && !iRow) ? '!' : '|');
+
+      return '\n|-\n' + strDelim + ' ' + lstRow.map(function (v) {
+        return typeof v === 'undefined' ? ' ' : v;
+      }).join(' ' + strDelim + strDelim + ' ');
+    }).join('') + '\n|}';
+  }
+
+  return [
+    wikiTable(
+
+      lstSpiral,
+
+      false,
+      'text-align:center;width:12em;height:12em;table-layout:fixed;'
+    ),
+
+    JSON.stringify(lstSpiral)
+  ].join('\n\n');
+
+})(5);

Task/Spiral-matrix/JavaScript/spiral-matrix-3.js

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

Task/Spiral-matrix/Julia/spiral-matrix-1.julia

@@ -0,0 +1,43 @@
+immutable Spiral
+    m::Int
+    n::Int
+    cmax::Int
+    dir::Array{Array{Int,1},1}
+    bdelta::Array{Array{Int,1},1}
+end
+
+function Spiral(m::Int, n::Int)
+    cmax = m*n
+    dir = Array{Int,1}[[0,1], [1,0], [0,-1], [-1,0]]
+    bdelta = Array{Int,1}[[0,0,0,1], [-1,0,0,0],
+                          [0,-1,0,0], [0,0,1,0]]
+    Spiral(m, n, cmax, dir, bdelta)
+end
+
+function spiral(m::Int, n::Int)
+    0<m&&0<n || error("The matrix dimensions must be positive.")
+    Spiral(m, n)
+end
+spiral(n::Int) = spiral(n, n)
+
+type SpState
+    cnt::Int
+    dirdex::Int
+    cell::Array{Int,1}
+    bounds::Array{Int,1}
+end
+
+Base.length(sp::Spiral) = sp.cmax
+Base.start(sp::Spiral) = SpState(1, 1, [1,1], [sp.n,sp.m,1,1])
+Base.done(sp::Spiral, sps::SpState) = sps.cnt > sp.cmax
+
+function Base.next(sp::Spiral, sps::SpState)
+    s = sub2ind((sp.m, sp.n), sps.cell[1], sps.cell[2])
+    if sps.cell[rem1(sps.dirdex+1, 2)] == sps.bounds[sps.dirdex]
+        sps.bounds += sp.bdelta[sps.dirdex]
+        sps.dirdex = rem1(sps.dirdex+1, 4)
+    end
+    sps.cell += sp.dir[sps.dirdex]
+    sps.cnt += 1
+    return (s, sps)
+end

Task/Spiral-matrix/Julia/spiral-matrix-2.julia

@@ -0,0 +1,24 @@
+using Formatting
+
+function width{T<:Integer}(n::T)
+    w = ndigits(n)
+    n < 0 || return w
+    return w + 1
+end
+
+function pretty{T<:Integer}(a::Array{T,2}, indent::Int=4)
+    lo, hi = extrema(a)
+    w = max(width(lo), width(hi))
+    id = " "^indent
+    fe = FormatExpr(@sprintf(" {:%dd}", w))
+    s = id
+    nrow = size(a)[1]
+    for i in 1:nrow
+        for j in a[i,:]
+            s *= format(fe, j)
+        end
+        i != nrow || continue
+        s *= "\n"*id
+    end
+    return s
+end

Task/Spiral-matrix/Julia/spiral-matrix-3.julia

@@ -0,0 +1,26 @@
+n = 5
+println("The n = ", n, " spiral matrix:")
+a = zeros(Int, (n, n))
+for (i, s) in enumerate(spiral(n))
+    a[s] = i-1
+end
+println(pretty(a))
+
+m = 3
+println()
+println("Generalize to a non-square matrix (", m, "x", n, "):")
+a = zeros(Int, (m, n))
+for (i, s) in enumerate(spiral(m, n))
+    a[s] = i-1
+end
+println(pretty(a))
+
+p = primes(10^3)
+n = 7
+println()
+println("An n = ", n, " prime spiral matrix:")
+a = zeros(Int, (n, n))
+for (i, s) in enumerate(spiral(n))
+    a[s] = p[i]
+end
+println(pretty(a))

Task/Spiral-matrix/Ruby/spiral-matrix-3.rb

@@ -0,0 +1,10 @@
+def spiral_matrix(n)
+  x, y, dx, dy = -1, 0, 0, -1
+  fmt = "%#{(n*n-1).to_s.size}d " * n
+  n.downto(1).flat_map{|x| [x, x-1]}.flat_map{|run|
+    dx, dy = -dy, dx                    # turn 90
+    run.times.map { [y+=dy, x+=dx] }
+  }.each_with_index.sort.map(&:last).each_slice(n){|row| puts fmt % row}
+end
+
+spiral_matrix(5)

Task/Spiral-matrix/VBScript/spiral-matrix.vb

@@ -0,0 +1,47 @@
+Function build_spiral(n)
+	botcol = 0 : topcol = n - 1
+	botrow = 0 : toprow = n - 1
+	'declare a two dimensional array
+	Dim matrix()
+	ReDim matrix(topcol,toprow)
+	dir = 0 : col = 0 : row = 0
+	'populate the array
+	For i = 0 To n*n-1
+		matrix(col,row) = i
+		Select Case dir
+			Case 0
+				If col < topcol Then
+					col = col + 1
+				Else
+					dir = 1 : row = row + 1 : botrow = botrow + 1
+				End If
+			Case 1
+				If row < toprow Then
+					row = row + 1
+				Else
+					dir = 2 : col = col - 1 : topcol = topcol - 1	
+				End If
+			Case 2
+				If col > botcol Then
+					col = col - 1
+				Else
+					dir = 3 : row = row - 1 : toprow = toprow - 1
+				End If
+			Case 3
+				If row > botrow Then
+					row = row - 1
+				Else
+					dir = 0 : col = col + 1 : botcol = botcol + 1
+				End If
+		End Select
+	Next
+	'print the array
+	For y = 0 To n-1
+		For x = 0 To n-1
+			WScript.StdOut.Write matrix(x,y) & vbTab
+		Next
+		WScript.StdOut.WriteLine
+	Next
+End Function
+
+build_spiral(CInt(WScript.Arguments(0)))