Merge pull request #9216 from steve-g-lynn/branch-for-challenge-246

pwc 246

3 files changed, 117 insertions, 0 deletions

diff --git a/challenge-246/steve-g-lynn/blog.txt b/challenge-246/steve-g-lynn/blog.txt
new file mode 100644
index 0000000000..6f893b585d
--- /dev/null
+++ b/challenge-246/steve-g-lynn/blog.txt
@@ -0,0 +1 @@
+https://thiujiac.blogspot.com/2023/12/pwc-246.html
diff --git a/challenge-246/steve-g-lynn/perl/ch-1.pl b/challenge-246/steve-g-lynn/perl/ch-1.pl
new file mode 100755
index 0000000000..3c41dd98c5
--- /dev/null
+++ b/challenge-246/steve-g-lynn/perl/ch-1.pl
@@ -0,0 +1,12 @@
+#!/usr/bin/env -S perl -wl
+
+
+local *six_out_of_49 = sub {
+    local @six_out_of_49 = map {rand} 0 .. 48;
+    return (sort {$six_out_of_49[$a-1] <=> $six_out_of_49[$b-1]} 1 .. 49) [0 .. 5];
+};
+
+local @six_out_of_49=&six_out_of_49;
+print "@six_out_of_49";
+
+1;
diff --git a/challenge-246/steve-g-lynn/perl/ch-2.pl b/challenge-246/steve-g-lynn/perl/ch-2.pl
new file mode 100755
index 0000000000..12d59609b8
--- /dev/null
+++ b/challenge-246/steve-g-lynn/perl/ch-2.pl
@@ -0,0 +1,104 @@
+#!/usr/bin/env -S perl -wl
+
+#real	0m23.427s
+#user	0m23.300s
+#sys	0m0.015s
+
+
+use List::Util qw(sum);
+use Math::Utils qw(hcf);
+
+local *linear_recurrence_2 = sub {
+    local *is_int = sub {
+       ($_[0] =~ /^[-]?[0-9]+$/ ) || (return 0);
+       ($_[0] - int($_[0])) == 0;
+    };
+    
+    #-- input validation (vector of 5 integers)
+    
+    (@_ == 5) || return "linear_recurrence_2: Input must have 5 elements.";
+    
+    (sum( map {&is_int($_)} @_ )==5) || return "linear_recurrence_2: Input must be integers."; 
+    
+    @_ = map {int($_)} @_;
+
+    (scalar(grep {$_==0} @_)==5) && (return 1);
+    (($_[0]==0) && ($_[1]==0) && ($_[2] != 0)) && (return 0);
+    (($_[1]==0) && ($_[2]==0) && ($_[3] != 0)) && (return 0);
+    (($_[2]==0) && ($_[3]==0) && ($_[4] != 0)) && (return 0); 
+    
+    #-- if hcf of 1st 2 elements does not divide into all others, reject
+    if (($_[0] != 0) && ($_[1] != 0)){
+        local $hcf=hcf( $_[0],$_[1] );
+        ( grep { ($_ % $hcf) != 0 } @_[2..4] ) && (return 0);
+    }
+
+    {
+    #-- solve for p and q from 1st 2 triplets. Check if is_int.
+    #-- p*a[0]+q*a[1]=a[2]; p*a[1]+q*a[2]=a[3];
+    local ($p, $q);
+    
+    if (($_[0]==0) && ($_[1] != 0)) {
+        $q=$_[2]/$_[1];
+        $p=($_[3]-$_[2]*$q)/$_[1];
+    }
+    elsif (($_[0] != 0) && ($_[1] == 0) && ($_[2] != 0)) {
+        $p=$_[2]/$_[0];
+        $q=$_[3]/$_[2];
+    }
+    elsif (($_[0] != 0) && ($_[1] != 0) && ($_[2] == 0)) {
+        $p=$_[3]/$_[1];
+        $q = -($p*$_[0])/$_[1];
+    }
+    elsif ( abs($_[1]/$_[0] - $_[2]/$_[1]) < 0.000001 ) {
+        local $ratio = $_[1]/$_[0];
+        ($_[3]/$_[2] != $ratio) && return 0;
+        ($_[4]/$_[3] != $ratio) ? (return 0) : (return 1);
+    }
+    else {
+        $q= ($_[2]/$_[0]-$_[3]/$_[1]) /
+            ($_[1]/$_[0]-$_[2]/$_[1]);
+    
+        $p=($_[2]/$_[1]-$_[3]/$_[2]) /
+            ($_[0]/$_[1]-$_[1]/$_[2]);
+
+    }
+    
+    &is_int($q) || return 0;
+    &is_int($p) || return 0;
+    
+    ($p*$_[2]+$q*$_[3]==$_[4]) || return 0;
+    print "p: ",$p," q: ",$q;
+    return 1;
+    }
+    
+    
+};
+
+print "Ex1 1,1,2,3,5: ", &linear_recurrence_2(1,1,2,3,5); #1
+print "Ex2 4,2,4,5,7: ", &linear_recurrence_2(4,2,4,5,7); #0
+print "Ex3 4,1,2,-3,8: ", &linear_recurrence_2(4,1,2,-3,8); #1
+print "--------------";
+print "";
+
+local *test_lr2 = sub {
+#-- Test &linear_recurrence_2 further:
+#-- create 1 nillion 5-element integer vectors
+#-- with elements between -9 and 9
+#-- and print out those that are linear recurrences of order 2
+    local *rand_seq = sub {    
+        local @rand_seq = map {rand} -9 .. 9;
+        return (sort {$rand_seq[$a+9] <=> $rand_seq[$b+9]} -9 .. 9) [0 .. 4];
+    };
+  
+    my $ctr=0;
+    for (1 .. 1_000_000)  {
+        local @test_lr2 = &rand_seq;
+        if (&linear_recurrence_2(@test_lr2)) { 
+            print "@test_lr2"; $ctr++;
+        }
+    }
+    print "--------\nNUMBER OF LINEAR RECURRENCES SECOND ORDER (out of 1,000,000): ",$ctr;  
+};
+
+&test_lr2;