Merge pull request #5883 from Firedrake/rogerbw-challenge-159

Solutions for challenge #159

18 files changed, 1684 insertions, 0 deletions

diff --git a/challenge-159/roger-bell-west/javascript/ch-1.js b/challenge-159/roger-bell-west/javascript/ch-1.js
new file mode 100755
index 0000000000..c18b03883d
--- /dev/null
+++ b/challenge-159/roger-bell-west/javascript/ch-1.js
@@ -0,0 +1,97 @@
+#! /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 gcd (m0,n0) {
+    let m=m0
+    let n=n0
+    while (n != 0) {
+        [m,n]=[n,m % n]
+    }
+    return m
+}
+
+function lcm (m,n) {
+    return m/gcd(m,n)*n
+}
+
+function lcmseries(a0,b) {
+    let a=a0
+    for (let i=a+1;i <= b;i++) {
+        a=lcm(a,i)
+    }
+    return a
+}
+
+function farey (n) {
+    let l=lcmseries(2,n)
+    let d=new Map()
+    let s=[]
+    for (let i=1;i <= n;i++) {
+        let m=l/i
+        for (let j=0;j <= i;j++) {
+            let k=m*j
+            if (!d.has(k)) {
+                d.set(k,[j,i])
+                s.push(k)
+            }
+        }
+    }
+    s.sort(function(a,b) {
+        return a-b;
+    })
+    return s.map(i => d.get(i))
+}
+
+if (deepEqual(farey(5),[
+    [0, 1], [1, 5], [1, 4], [1, 3], [2, 5], [1, 2], [3, 5], [2, 3],
+    [3, 4], [4, 5], [1, 1]
+])) {
+    process.stdout.write("Pass")
+} else {
+    process.stdout.write("FAIL")
+}
+process.stdout.write(" ");
+
+if (deepEqual(farey(7),[
+    [0, 1], [1, 7], [1, 6], [1, 5], [1, 4], [2, 7], [1, 3], [2, 5],
+    [3, 7], [1, 2], [4, 7], [3, 5], [2, 3], [5, 7], [3, 4], [4, 5],
+    [5, 6], [6, 7], [1, 1]
+])) {
+    process.stdout.write("Pass")
+} else {
+    process.stdout.write("FAIL")
+}
+process.stdout.write(" ");
+
+if (deepEqual(farey(4),[
+    [0, 1], [1, 4], [1, 3], [1, 2], [2, 3], [3, 4], [1, 1]
+])) {
+    process.stdout.write("Pass")
+} else {
+    process.stdout.write("FAIL")
+}
+process.stdout.write("\n");
diff --git a/challenge-159/roger-bell-west/javascript/ch-2.js b/challenge-159/roger-bell-west/javascript/ch-2.js
new file mode 100755
index 0000000000..619b239213
--- /dev/null
+++ b/challenge-159/roger-bell-west/javascript/ch-2.js
@@ -0,0 +1,94 @@
+#! /usr/bin/node
+
+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 primefactor (n) {
+    let f=new Map()
+    let m=n
+    for (let p of genprimes(Math.floor(Math.sqrt(n)))) {
+        while (m % p == 0) {
+            m=Math.floor(m/p)
+            if (f.has(p)) {
+                f.set(p,f.get(p)+1)
+            } else {
+                f.set(p,1)
+            }
+            if (m == 1) {
+                break
+            }
+        }
+    }
+    if (m > 1) {
+        if (f.has(m)) {
+            f.set(m,f.get(m)+1)
+        } else {
+            f.set(m,1)
+        }
+    }
+    return f
+}
+
+function moebius (n) {
+    let z=0
+    for (let v of primefactor(n).values()) {
+        if (v > 1) {
+            return 0
+        }
+        z++
+    }
+    if (z % 2 == 0) {
+        return 1
+    }
+    return -1
+}
+
+if (moebius(5) == -1) {
+    process.stdout.write("Pass");
+} else {
+    process.stdout.write("FAIL");
+}
+process.stdout.write(" ");
+
+if (moebius(10) == 1) {
+    process.stdout.write("Pass");
+} else {
+    process.stdout.write("FAIL");
+}
+process.stdout.write(" ");
+
+if (moebius(20) == 0) {
+    process.stdout.write("Pass");
+} else {
+    process.stdout.write("FAIL");
+}
+process.stdout.write("\n");
diff --git a/challenge-159/roger-bell-west/kotlin/ch-1.kt b/challenge-159/roger-bell-west/kotlin/ch-1.kt
new file mode 100644
index 0000000000..362aa1c7f6
--- /dev/null
+++ b/challenge-159/roger-bell-west/kotlin/ch-1.kt
@@ -0,0 +1,72 @@
+import kotlin.math.*
+
+fun gcd(m0: Int,n0: Int): Int {
+    var m=m0
+    var n=n0
+    while (n != 0) {
+        val tmp=m % n
+        m = n
+        n = tmp
+    }
+    return m
+}
+
+fun lcm(m: Int,n: Int): Int {
+    return m/gcd(m,n)*n
+}
+
+fun lcmseries(s: List<Int>): Int {
+    return s.reduce { acc, x -> lcm(acc,x) }
+}
+
+fun farey(n: Int): List<Pair<Int,Int>> {
+    val l = lcmseries((2..n).toList())
+    var d = mutableMapOf<Int,Pair<Int,Int>>()
+    var s = ArrayList<Int>()
+    for (i in 1..n) {
+        val m = l / i
+        for (j in 0..i) {
+            val k = m * j
+            if (!d.contains(k)) {
+                d[k]=Pair(j,i)
+                s.add(k)
+            }
+        }
+    }
+    s.sort()
+    return s.map {d[it]!!}
+}
+
+fun main() {
+    if (farey(5) == listOf(
+            Pair(0, 1), Pair(1, 5), Pair(1, 4), Pair(1, 3),
+            Pair(2, 5), Pair(1, 2), Pair(3, 5), Pair(2, 3),
+            Pair(3, 4), Pair(4, 5), Pair(1, 1)
+    )) {
+        print("Pass")
+    } else {
+        print("FAIL")
+    }
+    print(" ")
+    if (farey(7) == listOf(
+            Pair(0, 1), Pair(1, 7), Pair(1, 6), Pair(1, 5),
+            Pair(1, 4), Pair(2, 7), Pair(1, 3), Pair(2, 5),
+            Pair(3, 7), Pair(1, 2), Pair(4, 7), Pair(3, 5),
+            Pair(2, 3), Pair(5, 7), Pair(3, 4), Pair(4, 5),
+            Pair(5, 6), Pair(6, 7), Pair(1, 1)
+    )) {
+        print("Pass")
+    } else {
+        print("FAIL")
+    }
+    print(" ")
+    if (farey(4) == listOf(
+            Pair(0, 1), Pair(1, 4), Pair(1, 3), Pair(1, 2),
+            Pair(2, 3), Pair(3, 4), Pair(1, 1)
+    )) {
+        print("Pass")
+    } else {
+        print("FAIL")
+    }
+    println("")
+}
diff --git a/challenge-159/roger-bell-west/kotlin/ch-2.kt b/challenge-159/roger-bell-west/kotlin/ch-2.kt
new file mode 100644
index 0000000000..8cbe15e254
--- /dev/null
+++ b/challenge-159/roger-bell-west/kotlin/ch-2.kt
@@ -0,0 +1,94 @@
+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 primefactor(n: Int): Map<Int,Int> {
+    var f=mutableMapOf<Int,Int>()
+    var m=n
+    for (p in genprimes(sqrt(m.toDouble()).toInt())) {
+        while (m % p == 0) {
+            m /= p
+            if (f.containsKey(p)) {
+                f[p] = f[p]!!+1
+            } else {
+                f[p]=1
+            }
+        }
+        if (m == 1) {
+            break
+        }
+    }
+    if (m > 1) {
+        if (f.containsKey(m)) {
+            f[m] = f[m]!!+1
+        } else {
+            f[m]=1
+        }
+    }
+    return f
+}
+
+fun moebius(n: Int): Int {
+    var z: Int=0
+    for (v in primefactor(n).values) {
+        if (v > 1) {
+            return 0
+        }
+        z += 1
+    }
+    if (z % 2 == 0) {
+        return 1
+    }
+    return -1
+}
+
+fun main() {
+    if (moebius(5) == -1) {
+        print("Pass")
+    } else {
+        print("FAIL")
+    }
+    print(" ")
+    if (moebius(10) == 1) {
+        print("Pass")
+    } else {
+        print("FAIL")
+    }
+    print(" ")
+    if (moebius(20) == 0) {
+        print("Pass")
+    } else {
+        print("FAIL")
+    }
+    println("")
+}
diff --git a/challenge-159/roger-bell-west/lua/ch-1.lua b/challenge-159/roger-bell-west/lua/ch-1.lua
new file mode 100755
index 0000000000..d10299f584
--- /dev/null
+++ b/challenge-159/roger-bell-west/lua/ch-1.lua
@@ -0,0 +1,104 @@
+#! /usr/bin/lua
+
+-- 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 gcd(m0,n0)
+   local m,n = m0,n0
+   while n ~= 0 do
+      m,n = n,m % n
+   end
+   return m
+end
+
+function lcm(m,n)
+   return m/gcd(m,n)*n
+end
+
+function lcmseries(a,b)
+   local t=1
+   for v = a,b do
+      t = lcm(t,v)
+   end
+   return t
+end
+
+function farey(n)
+   local l=lcmseries(2,n)
+   local d={}
+   local s={}
+   for i = 1,n do
+      local m = l / i
+      for j = 0,i do
+         local k = m * j
+         if d[k] == nil then
+            d[k] = {j,i}
+            table.insert(s,k)
+         end
+      end
+   end
+   table.sort(s)
+   local out={}
+   for k,v in ipairs(s) do
+      table.insert(out,d[v])
+   end
+   return out
+end
+
+if recursive_compare(farey(5),{
+                        {0, 1}, {1, 5}, {1, 4}, {1, 3}, {2, 5},
+                        {1, 2}, {3, 5}, {2, 3}, {3, 4}, {4, 5},
+                        {1, 1}
+                    }) then
+   io.write("Pass")
+else
+   io.write("FAIL")
+end
+io.write(" ")
+
+if recursive_compare(farey(7),{
+                        {0, 1}, {1, 7}, {1, 6}, {1, 5}, {1, 4},
+                        {2, 7}, {1, 3}, {2, 5}, {3, 7}, {1, 2},
+                        {4, 7}, {3, 5}, {2, 3}, {5, 7}, {3, 4},
+                        {4, 5}, {5, 6}, {6, 7}, {1, 1}
+                    }) then
+   io.write("Pass")
+else
+   io.write("FAIL")
+end
+io.write(" ")
+
+if recursive_compare(farey(4),{
+                        {0, 1}, {1, 4}, {1, 3}, {1, 2}, {2, 3},
+                        {3, 4}, {1, 1}
+                    }) then
+   io.write("Pass")
+else
+   io.write("FAIL")
+end
+print("")
diff --git a/challenge-159/roger-bell-west/lua/ch-2.lua b/challenge-159/roger-bell-west/lua/ch-2.lua
new file mode 100755
index 0000000000..1e79067d53
--- /dev/null
+++ b/challenge-159/roger-bell-west/lua/ch-2.lua
@@ -0,0 +1,97 @@
+#! /usr/bin/lua
+
+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 primefactor(n)
+   local f={}
+   local m=n
+   for k,p in pairs(genprimes(math.floor(math.sqrt(m)))) do
+      while m % p == 0 do
+         m=math.floor(m/p)
+         if f[p] == nil then
+            f[p]=1
+         else
+            f[p] = f[p] + 1
+         end
+         if m==1 then
+            break
+         end
+      end
+   end
+   if m>1 then
+      if f[m] == nil then
+         f[m]=1
+      else
+         f[m] = f[m] + 1
+      end
+   end
+   return f
+end
+
+function moebius(n)
+   local z=0
+   for k,v in pairs(primefactor(n)) do
+      if v > 1 then
+         return 0
+      end
+      z = z + 1
+   end
+   if z % 2 == 0 then
+      return 1
+   end
+   return -1
+end
+
+if moebius(5) == -1 then
+   io.write("Pass")
+else
+   io.write("FAIL")
+end
+io.write(" ")
+
+if moebius(10) == 1 then
+   io.write("Pass")
+else
+   io.write("FAIL")
+end
+io.write(" ")
+
+if moebius(20) == 0 then
+   io.write("Pass")
+else
+   io.write("FAIL")
+end
+print("")
diff --git a/challenge-159/roger-bell-west/perl/ch-1.pl b/challenge-159/roger-bell-west/perl/ch-1.pl
new file mode 100755
index 0000000000..e99d1d11f3
--- /dev/null
+++ b/challenge-159/roger-bell-west/perl/ch-1.pl
@@ -0,0 +1,56 @@
+#! /usr/bin/perl
+
+use strict;
+use warnings;
+
+use Test::More tests => 3;
+use List::Util qw(reduce);
+
+is_deeply(farey(5),[
+  [0, 1], [1, 5], [1, 4], [1, 3], [2, 5], [1, 2], [3, 5], [2, 3],
+  [3, 4], [4, 5], [1, 1]
+    ],'example 1');
+
+is_deeply(farey(7),[
+  [0, 1], [1, 7], [1, 6], [1, 5], [1, 4], [2, 7], [1, 3], [2, 5],
+  [3, 7], [1, 2], [4, 7], [3, 5], [2, 3], [5, 7], [3, 4], [4, 5],
+  [5, 6], [6, 7], [1, 1]
+    ],'example 2');
+
+is_deeply(farey(4),[
+  [0, 1], [1, 4], [1, 3], [1, 2], [2, 3], [3, 4], [1, 1]
+    ],'example 3');
+
+sub gcd {
+  my ($m,$n)=@_;
+  while ($n!=0) {
+    ($m,$n)=($n,$m % $n);
+  }
+  return $m;
+}
+
+sub lcm {
+  my ($m,$n)=@_;
+  return $m/gcd($m,$n)*$n;
+}
+
+sub lcmseries {
+  my $s=shift;
+  return reduce {lcm($a,$b)} @{$s};
+}
+
+sub farey {
+  my $n=shift;
+  my $l=lcmseries([2..$n]);
+  my %d;
+  foreach my $i (1..$n) {
+    my $m=$l/$i;
+    foreach my $j (0..$i) {
+      my $k=$m*$j;
+      unless (exists $d{$k}) {
+        $d{$k}=[$j,$i];
+      }
+    }
+  }
+  return [map {$d{$_}} sort {$a <=> $b} keys %d];
+}
diff --git a/challenge-159/roger-bell-west/perl/ch-2.pl b/challenge-159/roger-bell-west/perl/ch-2.pl
new file mode 100755
index 0000000000..4893c02740
--- /dev/null
+++ b/challenge-159/roger-bell-west/perl/ch-2.pl
@@ -0,0 +1,78 @@
+#! /usr/bin/perl
+
+use strict;
+use warnings;
+
+use Test::More tests => 3;
+
+is(moebius(5),-1,'example 1');
+is(moebius(10),1,'example 2');
+is(moebius(20),0,'example 3');
+
+sub genprimes {
+  my $mx=shift;
+  my @primes;
+  {
+    my %primesh=map {$_ => 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 primefactor {
+  my $n=shift;
+  my %f;
+  my $m=$n;
+  foreach my $p (@{genprimes(int(sqrt($n)))}) {
+    while ($m % $p == 0) {
+      $f{$p}++;
+      $m=int($m/$p);
+      if ($m == 1) {
+        last;
+      }
+    }
+  }
+  if ($m > 1) {
+    $f{$m}++;
+  }
+  return \%f;
+}
+
+sub moebius {
+  my $n=shift;
+  my $z=0;
+  foreach my $v (values %{primefactor($n)}) {
+    if ($v>1) {
+      return 0;
+    }
+    $z++;
+  }
+  if ($z % 2 == 0) {
+    return 1;
+  }
+  return -1;
+}
diff --git a/challenge-159/roger-bell-west/postscript/ch-1.ps b/challenge-159/roger-bell-west/postscript/ch-1.ps
new file mode 100644
index 0000000000..30c9d167ab
--- /dev/null
+++ b/challenge-159/roger-bell-west/postscript/ch-1.ps
@@ -0,0 +1,256 @@
+%!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
+
+/reduce { % array proc -> value
+    2 dict begin
+    /p exch def
+    /a exch def
+    a 0 get
+    1 1 a length 1 sub {
+        a exch get
+        p
+    } for
+    end
+} bind def
+
+
+/apush { % [a b] c -> [a b c]
+    exch
+    [ exch aload length 2 add -1 roll ]
+} bind def
+
+/map { % array proc -> array
+    2 dict begin
+    /p exch def
+    [ exch
+      {
+          p
+      } forall
+    ]
+} bind def
+
+/keys { % dict -> array of dict keys
+    [ exch
+      {
+          pop
+      } forall
+    ]
+} bind def
+
+% end library code
+
+/gcd {
+    {
+        dup
+        3 1 roll
+        mod
+        dup 0 eq {
+            pop exit
+        } if
+    } loop
+} bind def
+
+/lcm {
+    dup 3 -1 roll
+    dup 4 -1 roll
+    gcd idiv mul
+} bind def
+
+/lcmseries {
+    { lcm } reduce
+} bind def
+
+/farey {
+    7 dict begin
+    /n exch def
+    /l [ 2 1 n { } for ] lcmseries def
+    /d n dup mul dict def
+    1 1 n {
+        /i exch def
+        /m l i idiv def
+        0 1 i {
+            /j exch def
+            /k m j mul def
+            d k known not {
+                d k [ j i ] put
+            } if
+        } for
+    } for
+    d keys quicksort { d exch get } map
+    end
+} bind def
+
+(farey) test.start
+
+5 farey
+[ [0 1] [1 5] [1 4] [1 3] [2 5] [1 2] [3 5] [2 3] [3 4] [4 5] [1 1] ]
+deepeq test
+
+7 farey
+[ [0 1] [1 7] [1 6] [1 5] [1 4] [2 7] [1 3] [2 5] [3 7] [1 2] [4 7]
+  [3 5] [2 3] [5 7] [3 4] [4 5] [5 6] [6 7] [1 1] ]
+deepeq test
+
+4 farey
+[ [0 1] [1 4] [1 3] [1 2] [2 3] [3 4] [1 1] ]
+deepeq test
+
+test.end
diff --git a/challenge-159/roger-bell-west/postscript/ch-2.ps b/challenge-159/roger-bell-west/postscript/ch-2.ps
new file mode 100644
index 0000000000..bfc28ad691
--- /dev/null
+++ b/challenge-159/roger-bell-west/postscript/ch-2.ps
@@ -0,0 +1,217 @@
+%!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
+
+/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
+
+/values { % dict -> array of dict values
+    [ exch
+      {
+          exch pop
+      } forall
+    ]
+} bind def
+
+% end library code
+
+/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 {