Merge pull request #6182 from Firedrake/rogerbw-challenge-167

Solutions for challenge #167

14 files changed, 1325 insertions, 0 deletions

diff --git a/challenge-167/roger-bell-west/javascript/ch-1.js b/challenge-167/roger-bell-west/javascript/ch-1.js
new file mode 100755
index 0000000000..90c70da995
--- /dev/null
+++ b/challenge-167/roger-bell-west/javascript/ch-1.js
@@ -0,0 +1,117 @@
+#! /usr/bin/node
+function deepEqual(a,b)
+{
+    if( (typeof a == 'object' && a != null) &&
+        (typeof b == 'object' && b != null) )
+    {
+        var count = [0,0]
+        for( var key in a) count[0]++
+        for( var key in b) count[1]++
+        if( count[0]-count[1] != 0) {return false}
+        for( var key in a)
+        {
+            if(!(key in b) || !deepEqual(a[key],b[key])) {return false}
+        }
+        for( var key in b)
+        {
+            if(!(key in a) || !deepEqual(b[key],a[key])) {return false}
+        }
+        return true
+    }
+    else
+    {
+        return a === b
+    }
+}
+
+function genprimes(mx) {
+    let primesh=new Set([2,3])
+    for (let i = 6; i <= mx; i += 6) {
+        for (let j = i-1; j <= i+1; j += 2) {
+            if (j <= mx) {
+                primesh.add(j);
+            }
+        }
+    }
+    let q=[2,3,5,7];
+    let p=q.shift();
+    let mr=Math.floor(Math.sqrt(mx));
+    while (p <= mr) {
+        if (primesh.has(p)) {
+            let i=p*p
+            for (let i=p*p; i <= mx; i += p) {
+                primesh.delete(i);
+            }
+        }
+        if (q.length < 2) {
+            q.push(q[q.length-1]+4);
+            q.push(q[q.length-1]+2);
+        }
+        p=q.shift();
+    }
+    let primes=[...primesh];
+    primes.sort(function(a,b) {
+        return a-b;
+    });
+    return primes;
+}
+
+function cyclicpermute(n) {
+    let ss = n.toString();
+    let o = [];
+    for (let p = 0; p < ss.length; p++) {
+        ss = ss.slice(1,ss.length) + ss.slice(0,1)
+        o.push(parseInt(ss));
+    }
+    return o;
+}
+
+function circular(mindigits,ct) {
+    let o = [];
+    let base = 1;
+    for (let p = 2; p <= mindigits; p++) {
+        base *= 10;
+    }
+    while (o.length < ct) {
+        let pr = genprimes(base * 10);
+        let prs = new Set(pr);
+        for (let cp of pr) {
+            if (cp >= base) {
+                let v = true;
+                let cpp = cyclicpermute(cp);
+                for (let cpc of cpp) {
+                    if (!prs.has(cpc)) {
+                        v = false;
+                        break;
+                    }
+                }
+                if (v) {
+                    o.push(cp);
+                    if (o.size >= ct) {
+                        break;
+                    }
+                    for (let cpc of cpp) {
+                        prs.delete(cpc);
+                    }
+                }
+            }
+        }
+        base *= 10;
+    }
+    return o;
+}
+
+if (deepEqual(cyclicpermute(123),[231, 312, 123])) {
+    process.stdout.write("Pass");
+} else {
+    process.stdout.write("FAIL");
+}
+process.stdout.write(" ");
+
+if (deepEqual(circular(3,10),[113, 197, 199, 337, 1193, 3779, 11939,
+                              19937, 193939, 199933])) {
+    process.stdout.write("Pass");
+} else {
+    process.stdout.write("FAIL");
+}
+process.stdout.write("\n");
diff --git a/challenge-167/roger-bell-west/kotlin/ch-1.kt b/challenge-167/roger-bell-west/kotlin/ch-1.kt
new file mode 100644
index 0000000000..f598869bb6
--- /dev/null
+++ b/challenge-167/roger-bell-west/kotlin/ch-1.kt
@@ -0,0 +1,95 @@
+import kotlin.math.*
+
+fun genprimes(mx: Int): ArrayList<Int> {
+    var primesh=mutableSetOf<Int>()
+    for (i in 2..3) {
+        primesh.add(i)
+    }
+    for (i in 6..mx+1 step 6) {
+        for (j in i-1..i+1 step 2) {
+            if (j <= mx) {
+                primesh.add(j)
+            }
+        }
+    }
+    var q=ArrayDeque(listOf(2,3,5,7))
+    var p=q.removeFirst()
+    val mr=sqrt(mx.toDouble()).toInt()
+    while (p <= mr) {
+        if (primesh.contains(p)) {
+            for (i in p*p..mx step p) {
+                primesh.remove(i)
+            }
+        }
+        if (q.size < 2) {
+            q.add(q.last()+4)
+            q.add(q.last()+2)
+        }
+        p=q.removeFirst()
+    }
+    var primes=ArrayList(primesh.distinct())
+    primes.sort()
+    return primes
+}
+
+fun cyclicpermute(n: Int): ArrayList<Int> {
+    var ss = n.toString()
+    var o = ArrayList<Int>()
+    for (p in 1..ss.length) {
+        ss = ss.slice(1..ss.length-1) + ss.slice(0..0)
+        o.add(ss.toInt())
+    }
+    return o
+}
+
+fun circular(mindigits: Int, ct: Int): ArrayList<Int> {
+    var o = ArrayList<Int>()
+    var base = 1
+    for (p in 2..mindigits) {
+        base *= 10
+    }
+    while (o.size < ct) {
+        val pr = genprimes(base * 10)
+        var prs = pr.toMutableSet()
+        for (cp in pr) {
+            if (cp >= base) {
+                var v = true
+                val cpp = cyclicpermute(cp)
+                for (cpc in cpp) {
+                    if (!prs.contains(cpc)) {
+                        v = false
+                        break
+                    }
+                }
+                if (v) {
+                    o.add(cp)
+                    if (o.size >= ct) {
+                        break
+                    }
+                    for (cpc in cpp) {
+                        prs.remove(cpc)
+                    }
+                }
+            }
+        }
+        base *= 10
+    }
+    return o
+}
+
+fun main() {
+    if (cyclicpermute(123) == listOf(231, 312, 123)) {
+        print("Pass")
+    } else {
+        print("FAIL")
+    }
+    print(" ")
+    
+    if (circular(3,10) == listOf(113, 197, 199, 337, 1193, 3779,
+                                 11939, 19937, 193939, 199933)) {
+        print("Pass")
+    } else {
+        print("FAIL")
+    }
+    println("")
+}
diff --git a/challenge-167/roger-bell-west/lua/ch-1.lua b/challenge-167/roger-bell-west/lua/ch-1.lua
new file mode 100755
index 0000000000..f7ff8a8b1e
--- /dev/null
+++ b/challenge-167/roger-bell-west/lua/ch-1.lua
@@ -0,0 +1,141 @@
+#! /usr/bin/lua
+
+function dump(o)
+   if type(o) == 'table' then
+      local s = '{ '
+      for k,v in pairs(o) do
+         if type(k) ~= 'number' then k = '"'..k..'"' end
+         s = s .. '['..k..'] = ' .. dump(v) .. ','
+      end
+      return s .. '} '
+   else
+      return tostring(o)
+   end
+end
+
+-- by Michael Anderson at
+-- https://stackoverflow.com/questions/8722620/comparing-two-index-tables-by-index-value-in-lua
+function recursive_compare(t1,t2)
+  -- Use usual comparison first.
+  if t1==t2 then return true end
+  -- We only support non-default behavior for tables
+  if (type(t1)~="table") then return false end
+  -- They better have the same metatables
+  local mt1 = getmetatable(t1)
+  local mt2 = getmetatable(t2)
+  if( not recursive_compare(mt1,mt2) ) then return false end
+
+  -- Check each key-value pair
+  -- We have to do this both ways in case we miss some.
+  -- TODO: Could probably be smarter and not check those we've 
+  -- already checked though!
+  for k1,v1 in pairs(t1) do
+    local v2 = t2[k1]
+    if( not recursive_compare(v1,v2) ) then return false end
+  end
+  for k2,v2 in pairs(t2) do
+    local v1 = t1[k2]
+    if( not recursive_compare(v1,v2) ) then return false end
+  end
+
+  return true  
+end
+
+function genprimes(mx)
+   local primesh = {}
+   for i = 2, 3 do
+      primesh[i] = true
+   end
+   for i = 6, mx, 6 do
+      for j = i-1, i+1, 2 do
+         if j <= mx then
+            primesh[j]=true
+         end
+      end
+   end
+   local q={2,3,5,7}
+   local p=table.remove(q,1)
+   local mr=math.floor(math.sqrt(mx))
+   while p <= mr do
+      if primesh[p] ~= nil then
+         for i = p*p,mx,p do
+            primesh[i] = nil
+         end
+      end
+      if #q < 2 then
+         table.insert(q,q[#q]+4)
+         table.insert(q,q[#q]+2)
+      end
+      p=table.remove(q,1)
+   end
+   local primes = {}
+   for k,v in pairs(primesh) do
+      table.insert(primes,k)
+   end
+   table.sort(primes)
+   return primes
+end
+
+function cyclicpermute(n)
+   local ss = n
+   local o = {}
+   for p = 1,string.len(ss) do
+      ss = string.sub(ss,2) .. string.sub(ss,1,1)
+      table.insert(o,ss+0)
+   end
+   return o
+end
+
+function circular(mindigits,ct)
+   local o = {}
+   local base = 1
+   for p = 2,mindigits do
+      base = base * 10
+   end
+   while #o < ct do
+      local pr = genprimes(base * 10)
+      local prs = {}
+      for k,q in pairs(pr) do
+         prs[q] = true
+      end
+      for k,cp in pairs(pr) do
+         if cp >= base then
+            local v = true
+            local cpp = cyclicpermute(cp)
+            for k2,cpc in pairs(cpp) do
+               if prs[cpc] == nil then
+                  v = false
+                  break
+               end
+            end
+            if v then
+               table.insert(o,cp)
+               if #o >= ct then
+                  break
+               end
+               for k2,cpc in pairs(cpp) do
+                  prs[cpc] = nil
+               end               
+            end
+         end
+      end
+      base = base * 10
+   end
+   return o
+end
+
+if recursive_compare(cyclicpermute(123), {231, 312, 123}) then
+   io.write("Pass")
+else
+   io.write("FAIL")
+end
+io.write(" ")
+
+if recursive_compare(circular(3,10), {113, 197, 199, 337, 1193, 3779,
+                                      11939, 19937, 193939, 199933})
+then
+   io.write("Pass")
+else
+   io.write("FAIL")
+end
+print("")
diff --git a/challenge-167/roger-bell-west/perl/ch-1.pl b/challenge-167/roger-bell-west/perl/ch-1.pl
new file mode 100755
index 0000000000..33b040a0c4
--- /dev/null
+++ b/challenge-167/roger-bell-west/perl/ch-1.pl
@@ -0,0 +1,96 @@
+#! /usr/bin/perl
+
+use strict;
+use warnings;
+
+use experimental 'signatures';
+use List::Util qw(max);
+
+use Test::More tests => 2;
+
+is_deeply(cyclicpermute(123),
+          [231, 312, 123],
+          'example 1');
+
+is_deeply(circular(3,10),
+          [113, 197, 199, 337, 1193, 3779, 11939, 19937, 193939,
+           199933],
+          'example 2');
+
+sub genprimes($mx) {
+  my @primes;
+  {
+    my %primesh=map {$_ => 1} (2,3);
+    for (my $i=6;$i <= $mx+1; $i += 6) {
+      foreach my $j ($i-1,$i+1) {
+        if ($j <= $mx) {
+          $primesh{$j}=1;
+        }
+      }
+    }
+    my @q=(2,3,5,7);
+    my $p=shift @q;
+    my $mr=int(sqrt($mx));
+    while ($p <= $mr) {
+      if ($primesh{$p}) {
+        my $i=$p*$p;
+        while ($i <= $mx) {
+          delete $primesh{$i};
+          $i += $p;
+        }
+      }
+      if (scalar @q < 2) {
+        push @q,$q[-1]+4;
+        push @q,$q[-1]+2;
+      }
+      $p=shift @q;
+    }
+    @primes=sort {$a <=> $b} keys %primesh;
+  }
+  return \@primes;
+}
+
+sub cyclicpermute($n) {
+  my $ss = $n;
+  my @o;
+  foreach my $p (1..length($ss)) {
+    $ss = substr($ss,1) . substr($ss,0,1);
+    push @o,0+$ss;
+  }
+  return \@o;
+}
+
+sub circular($mindigits, $ct) {
+  my @o;
+  my $base = 1;
+  foreach my $p (2..$mindigits) {
+    $base *= 10;
+  }
+  while (scalar @o < $ct) {
+    my $pr = genprimes($base * 10);
+    my %prs = map {$_ => 1} @{$pr};
+    foreach my $cp (@{$pr}) {
+      if ($cp >= $base) {
+        my $v = 1;
+        my $cpp = cyclicpermute($cp);
+        foreach my $cpc (@{$cpp}) {
+          if (!exists $prs{$cpc}) {
+            $v = 0;
+            last;
+          }
+        }
+        if ($v) {
+          push @o,$cp;
+          if (scalar @o >= $ct) {
+            last;
+          }
+          foreach my $cpc (@{$cpp}) {
+            delete $prs{$cpc};
+          }
+        }
+      }
+    }
+    $base *= 10;
+  }
+  return \@o;
+}
diff --git a/challenge-167/roger-bell-west/perl/ch-2.pl b/challenge-167/roger-bell-west/perl/ch-2.pl
new file mode 100755
index 0000000000..adcb42df88
--- /dev/null
+++ b/challenge-167/roger-bell-west/perl/ch-2.pl
@@ -0,0 +1,50 @@
+#! /usr/bin/perl
+
+use strict;
+use warnings;
+
+use experimental 'signatures';
+
+use Math::Complex;
+
+use Test::More tests => 3;
+
+my $EPSILON = 1e-7;
+
+my @p = (676.5203681218851,
+        -1259.1392167224028,
+        771.32342877765313,
+        -176.61502916214059,
+        12.507343278686905,
+        -0.13857109526572012,
+        9.9843695780195716e-6,
+        1.5056327351493116e-7);
+
+cmp_ok(abs(gamma(3)-2), '<=', $EPSILON,'example 1');
+cmp_ok(abs(gamma(5)-24), '<=', $EPSILON,'example 2');
+cmp_ok(abs(gamma(7)-720), '<=', $EPSILON,'example 3');
+
+sub drop_imag($z0) {
+  my $z = $z0;
+  if (abs(Im($z0)) <= $EPSILON) {
+    $z = Math::Complex->make(Re($z),0);
+  }
+  return $z;
+}
+
+sub gamma($z0) {
+  my $z = Math::Complex->make($z0,0);
+  my $y;
+  if (Re($z) < 0.5) {
+    $y = pi / (sin(pi * $z) * gamma(1-$z));
+  } else {
+    $z--;
+    my $x = 0.99999999999980993;
+    foreach my $i (0..$#p) {
+      $x += $p[$i] / ($z + $i + 1);
+    }
+    my $t = $z + scalar(@p) - 0.5;
+    $y = sqrt(2 * pi) * $t ** ($z + 0.5) * exp(-$t) * $x;
+  }
+  return drop_imag($y);
+}
diff --git a/challenge-167/roger-bell-west/postscript/ch-1.ps b/challenge-167/roger-bell-west/postscript/ch-1.ps
new file mode 100644
index 0000000000..4b554f0148
--- /dev/null
+++ b/challenge-167/roger-bell-west/postscript/ch-1.ps
@@ -0,0 +1,281 @@
+%!PS
+
+% begin library code
+
+/test {
+    /test.count test.count 1 add def
+    {
+        /test.pass test.pass 1 add def
+    } {
+        ( ) print
+        test.count (....) cvs print
+        (-fail) print
+    } ifelse
+} bind def
+
+/test.start {
+    print (:) print
+    /test.pass 0 def
+    /test.count 0 def
+} bind def
+
+/test.end {
+    ( ) print
+    test.count 0 gt {
+        (Passed ) print
+        test.pass (...) cvs print
+        (/) print
+        test.count (...) cvs print
+        ( \() print
+        test.pass 100 mul test.count idiv (...) cvs print
+        (%\)) print
+        (\r\n) print
+    } if
+} bind def
+
+/deepeq {
+    2 dict begin
+    /a exch def
+    /b exch def
+    a type b type eq {
+        a type /dicttype eq {
+            a length b length eq {
+                <<
+                    a {
+                        pop
+                        true
+                    } forall
+                    b {
+                        pop
+                        true
+                    } forall
+                >>
+                true exch
+                {
+                    pop
+                    dup a exch known {
+                        dup b exch known {
+                            dup a exch get exch b exch get deepeq not {
+                                pop false
+                            } if
+                        } {
+                            false
+                        } ifelse
+                    } {
+                        false
+                    } ifelse
+                } forall
+            } {
+                false
+            } ifelse
+        } {
+            a type dup /arraytype eq exch /stringtype eq or {
+                a length b length eq {
+                    true
+                    0 1 a length 1 sub {
+                        dup a exch get exch b exch get deepeq not {
+                            pop false
+                            exit
+                        } if
+                    } for
+                } {
+                    false
+                } ifelse
+            } {
+                a b eq
+            } ifelse
+        } ifelse
+    } {
+        false
+    } ifelse
+    end
+} bind def
+
+/quicksort { % [ a c b ] -> [ a b c ]
+    1 dict begin
+    /arr exch def
+    0 arr length 1 sub quicksort.main
+    arr
+    end
+} bind def
+
+/quicksort.main { % lo hi -> (null)
+    3 dict begin
+    /hi exch def
+    /lo exch def
+    /xit false def
+    lo 0 lt {
+        /xit true def
+    } if
+    hi 0 lt {
+        /xit true def
+    } if
+    lo hi ge {
+        /xit true def
+    } if
+    xit not {
+        /p quicksort.partition def
+        lo p quicksort.main
+        p 1 add hi quicksort.main
+    } if
+    end
+} bind def
+
+/quicksort.partition {
+    3 dict begin
+    /pivot arr hi lo add 2 idiv get def
+    /i lo 1 sub def
+    /j hi 1 add def
+    {
+        {
+            /i i 1 add def
+            arr i get pivot ge {
+                exit
+            } if
+        } loop
+        {
+            /j j 1 sub def
+            arr j get pivot le {
+                exit
+            } if
+        } loop
+        i j ge {
+            j
+            exit
+        } if
+        i j quicksort.swap
+    } loop
+    end
+} bind def
+
+/quicksort.swap {
+    2 dict begin
+    /bi exch def
+    /ai exch def
+    arr ai get
+    arr bi get
+    arr exch ai exch put
+    arr exch bi exch put
+    end
+} bind def
+
+/apush { % [a b] c -> [a b c]
+    exch
+    [ exch aload length 2 add -1 roll ]
+} bind def
+
+/genprimes {
+    /mx exch def
+    /primesh mx dict def
+    2 1 3 {
+        primesh exch true put
+    } for
+    6 6 mx 1 add {
+        dup 1 sub exch 1 add 2 exch {
+            dup mx le {
+                primesh exch true put
+            } {
+                pop
+            } ifelse
+        } for
+    } for
+    /q [ 3 5 7 ] def
+    /qi 0 def
+    /p 2 def
+    /mr mx sqrt cvi def
+    {
+        p mr le not {
+            exit
+        } if
+        primesh p known {
+            p dup mul p mx {
+                primesh exch undef
+            } for
+        } if
+        q length qi sub 2 le {
+            /q q q q length 1 sub get 4 add apush def
+            /q q q q length 1 sub get 2 add apush def
+        } if
+        /p q qi get def
+        /qi qi 1 add def
+    } loop
+    [ primesh { pop } forall ] quicksort
+} bind def
+
+/toset { % array -> dict of (array, true)
+    << exch
+       {
+           true
+       } forall
+    >>
+} bind def
+
+% end library code
+
+/cyclicpermute {
+    3 dict begin
+    /n exch def
+    [
+        /ss n 1 sub log cvi 1 add string n exch cvs def
+        ss length {
+            /ss2 ss length string def
+            ss2 0 ss 1 ss length 1 sub getinterval putinterval
+            ss2 ss2 length 1 sub ss 0 get put
+            ss2 cvi
+            /ss ss2 def
+        } repeat
+    ]
+    end
+} bind def
+
+/circular {
+    8 dict begin
+    /ct exch def
+    /mindigits exch def
+    /o 0 array def
+    /base 1 def
+    mindigits 1 sub {
+        /base base 10 mul def
+    } repeat
+    {
+        o length ct ge {
+            exit
+        } if
+        /pr base 10 mul genprimes def
+        /prs pr toset def
+        pr {
+            /cp exch def
+            cp base ge {
+                /v true def
+                /cpp cp cyclicpermute def
+                cpp {
+                    prs exch known not {
+                        /v false def
+                        exit
+                    } if
+                } forall
+                v {
+                    /o o cp apush def
+                    o length ct ge {
+                        exit
+                    } if
+                    cpp {
+                        prs exch undef
+                    } forall
+                } if
+            } if
+        } forall
+        /base base 10 mul def
+    } loop
+    o
+    end
+} bind def
+
+(circular) test.start
+123 cyclicpermute [ 231 312 123 ] deepeq test
+
+3 10 circular
+[ 113 197 199 337 1193 3779 11939 19937 193939 199933 ]
+deepeq test
+
+test.end
diff --git a/challenge-167/roger-bell-west/python/ch-1.py b/challenge-167/roger-bell-west/python/ch-1.py
new file mode 100755
index 0000000000..5e6cb67ce6
--- /dev/null
+++ b/challenge-167/roger-bell-west/python/ch-1.py
@@ -0,0 +1,73 @@
+#! /usr/bin/python3
+
+import unittest
+
+from math import sqrt,floor
+from collections import deque
+
+def genprimes(mx):
+  primesh=set(range(2,4))
+  for i in range(6,mx+2,6):
+    for j in range(i-1,i+2,2):
+      if j <= mx:
+        primesh.add(j)
+  q=deque([2,3,5,7])
+  p=q.popleft()
+  mr=floor(sqrt(mx))
+  while p <= mr:
+    if p in primesh:
+      for i in range(p*p,mx+1,p):
+        primesh.discard(i)
+    if len(q) < 2:
+      q.append(q[-1]+4)
+      q.append(q[-1]+2)
+    p=q.popleft()
+  primes=list(primesh)
+  primes.sort()
+  return primes
+
+def cyclicpermute(n):
+  ss = str(n)
+  o = []
+  for p in range(len(ss)):
+    ss = ss[1:] + ss[0]
+    o.append(int(ss))
+  return o
+
+def circular(mindigits,ct):
+  o = []
+  base = 1
+  for p in range(mindigits-1):
+    base = base * 10
+  while len(o) < ct:
+    pr = genprimes(base * 10)
+    prs = set(pr)
+    for cp in pr:
+      if cp >= base:
+        v = True
+        cpp = cyclicpermute(cp)
+        for cpc in cpp:
+          if cpc not in prs:
+            v = False
+            break
+        if v:
+          o.append(cp)
+          if len(o) >= ct:
+            break
+          for cpc in cpp:
+            prs.discard(cpc)
+    base = base * 10
+  return o
+
+class TestCircular(unittest.TestCase):
+
+        def test_ex1(self):
+          self.assertEqual(cyclicpermute(123),
+                           [231,312,123],'example 1')
+
+        def test_ex2(self):
+          self.assertEqual(circular(3,10),
+                           [113, 197, 199, 337, 1193, 3779, 11939,
+                            19937, 193939, 199933],'example 2')
+
+unittest.main()
diff --git a/challenge-167/roger-bell-west/python/ch-2.py b/challenge-167/roger-bell-west/python/ch-2.py
new file mode 100755
index 0000000000..881a94bec9
--- /dev/null
+++ b/challenge-167/roger-bell-west/python/ch-2.py
@@ -0,0 +1,49 @@
+#! /usr/bin/python3
+
+# taken from https://en.wikipedia.org/wiki/Lanczos_approximation
+
+import unittest
+
+from cmath import sin, sqrt, pi, exp
+
+p = [676.5203681218851
+    ,-1259.1392167224028
+    ,771.32342877765313
+    ,-176.61502916214059
+    ,12.507343278686905
+    ,-0.13857109526572012
+    ,9.9843695780195716e-6
+    ,1.5056327351493116e-7
+    ]
+
+EPSILON = 1e-07
+def drop_imag(z):
+    if abs(z.imag) <= EPSILON:
+        z = z.real
+    return z
+
+def gamma(z):
+    z = complex(z)
+    if z.real < 0.5:
+        y = pi / (sin(pi * z) * gamma(1 - z))
+    else:
+        z -= 1
+        x = 0.99999999999980993
+        for (i, pval) in enumerate(p):
+            x += pval / (z + i + 1)
+        t = z + len(p) - 0.5
+        y = sqrt(2 * pi) * t ** (z + 0.5) * exp(-t) * x
+    return drop_imag(y)
+
+class TestGamma(unittest.TestCase):
+
+        def test_ex1(self):
+          self.assertTrue(abs(gamma(3)-2) < EPSILON,'example 1')
+
+        def test_ex2(self):
+          self.assertTrue(abs(gamma(5)-24) < EPSILON,'example 2')
+
+        def test_ex3(self):
+          self.assertTrue(abs(gamma(7)-720) < EPSILON,'example 3')
+
+unittest.main()
diff --git a/challenge-167/roger-bell-west/raku/ch-1.p6 b/challenge-167/roger-bell-west/raku/ch-1.p6
new file mode 100755
index 0000000000..ebbba9b244
--- /dev/null
+++ b/challenge-167/roger-bell-west/raku/ch-1.p6
@@ -0,0 +1,91 @@
+#! /usr/bin/perl6
+
+use Test;
+plan 2;
+
+is-deeply(cyclicpermute(123),
+          [231, 312, 123],
+          'example 1');
+
+is-deeply(circular(3,10),
+          [113, 197, 199, 337, 1193, 3779, 11939, 19937, 193939,
+           199933],
+          'example 2');
+
+sub genprimes($mx) {
+    my @primes;
+    {
+        my $primesh=(2,3).SetHash;
+        loop (my $i=6;$i <= $mx+1; $i += 6) {
+            for ($i-1,$i+1) -> $j {
+                if ($j <= $mx) {
+                    $primesh{$j}=True;
+                }
+            }
+        }
+        my $p=2;
+        my @q=[2,3,5,7];
+        my $mr=floor(sqrt($mx));
+        while ($p <= $mr) {
+            if ($primesh{$p}:exists) {
+                my $i=$p*$p;
+                while ($i <= $mx) {
+                    $primesh{$i}:delete;
+                    $i += $p;
+                }
+            }
+            if (@q.elems < 2) {
+                @q.push(@q[*-1]+4);
+                @q.push(@q[*-1]+2);
+            }
+            $p=@q.shift;
+        }
+        @primes=$primesh.keys.sort;
+    }
+    return @primes;
+}
+
+sub cyclicpermute($n) {
+    my $ss = $n;
+    my @o;
+    for (1..$ss.chars) {
+        $ss = substr($ss,1) ~ substr($ss,0,1);
+        @o.push(0+$ss);
+    }
+    return @o;
+}
+
+sub circular($mindigits, $ct) {
+    my @o;
+    my $base = 1;
+    for (2..$mindigits) {
+        $base *= 10;
+    }
+    while (@o.elems < $ct) {
+        my @pr = genprimes($base * 10);
+        my $prs = @pr.SetHash;
+        for (@pr) -> $cp {
+            if ($cp >= $base) {
+                my $v = True;
+                my @cpp = cyclicpermute($cp);
+                for (@cpp) -> $cpc {
+                    unless ($prs{$cpc}:exists) {
+                        $v = False;
+                        last;
+                    }
+                }
+                if ($v) {
+                    @o.push($cp);
+                    if (@o.elems >= $ct) {
+                        last;
+                    }
+                    for (@cpp) -> $cpc {
+                        $prs{$cpc}:delete;
+                    }
+                }
+            }
+        }
+        $base *= 10;
+    }
+    return @o;
+}
diff --git a/challenge-167/roger-bell-west/raku/ch-2.p6 b/challenge-167/roger-bell-west/raku/ch-2.p6
new file mode 100755
index 0000000000..8d27b26dee
--- /dev/null
+++ b/challenge-167/roger-bell-west/raku/ch-2.p6
@@ -0,0 +1,50 @@
+#! /usr/bin/perl6
+
+use Test;
+
+plan 3;
+
+my $EPSILON = 1e-7;
+
+my @p = (676.5203681218851,
+        -1259.1392167224028,
+        771.32342877765313,
+        -176.61502916214059,
+        12.507343278686905,
+        -0.13857109526572012,
+        9.9843695780195716e-6,
+        1.5056327351493116e-7);
+
+is-approx(gamma(3),2,$EPSILON,'example 1');
+is-approx(gamma(5),24,$EPSILON,'example 2');
+is-approx(gamma(7),720,$EPSILON,'example 3');
+
+sub drop_imag($z0) {
+    my $z = $z0;
+    if (abs($z0.re) <= $EPSILON) {
+        $z = Complex.new($z.re,0);
+    }
+    return $z;
+}
+
+sub gamma($z0) {
+    my $z;
+    if ($z0.isa("Complex")) {
+        $z = Complex.new($z0.re, 0);
+    } else {
+        $z = Complex.new($z0, 0);
+    }
+    my $y;
+    if ($z.re < 0.5) {
+        $y = pi / (sin(pi * $z) * gamma(1-$z));
+    } else {
+        $z--;
+        my $x = 0.99999999999980993;
+        for (0..@p.end) -> $i {
+            $x += @p[$i] / ($z + $i + 1);
+        }
+        my $t = $z + @p.elems - 0.5;
+        $y = sqrt(2 * pi) * $t ** ($z + 0.5) * exp(-$t) * $x;
+    }
+    return drop_imag($y);
+}
diff --git a/challenge-167/roger-bell-west/ruby/ch-1.rb b/challenge-167/roger-bell-west/ruby/ch-1.rb
new file mode 100755
index 0000000000..2c7293768f
--- /dev/null
+++ b/