improved ch-2.p6 speed

1 files changed, 92 insertions, 50 deletions

diff --git a/challenge-168/steve-g-lynn/raku/ch-2.p6 b/challenge-168/steve-g-lynn/raku/ch-2.p6
index b4183fd6d3..bfe46ec923 100755
--- a/challenge-168/steve-g-lynn/raku/ch-2.p6
+++ b/challenge-168/steve-g-lynn/raku/ch-2.p6
@@ -1,44 +1,66 @@
 #!/usr/bin/raku
 
+#time (bash command): 
+#real	0m0.490s
+#user	0m0.729s
+#sys	0m0.056s
+
+
+# acknowledgement:
+
+# I improved the previous grossly inefficient version 
+# (> 1 min script run time) after looking 
+# at the raku and python submissions from Roger Bell-West
+
+
+say homeprime(10);
+#773
 say homeprime(16);
-# 31636373
-#-- works but slow
+#31636373
 
 #-- sub for home prime
 
-sub homeprime(Int $n){
+sub homeprime(Int $n) returns Int { 
+	$n.Int.is-prime && return $n;
 	my $ncopy=$n;
 	while (1) {
-		$ncopy=factor($ncopy).Int;
-		($ncopy.is-prime) && last;
+		my $last=$ncopy;
+		$ncopy=factor($ncopy);
+		($ncopy==$last) && last;
 	}
 	return $ncopy;
 }
 
 #--sub for factorizing
 
-multi sub factor (1) {1}
+multi sub factor (1) returns Int {1}
 
-multi sub factor (Int $n where $n > 1){
-#-- returns string concatenation of prime factors
-#	my @primes=prime_sieve($n);
-	my @primes=find_primes($n);
-	my $retstring="";
-	my $ncopy=$n;
+multi sub factor (Int $n where $n > 1) returns Int {
+#-- returns the concatenated prime factors as an int
+	$n.Int.is-prime && (return $n.Int );
+	my $sqrt_n = sqrt($n).Int+1;
+	my @primes=find_primes($sqrt_n);
+	my @factors=();
 
-	($n.is-prime) && (return $n);	
+	my $retstring="";
+	my $ncopy=$n;	
 	
 	for @primes -> $prime {
 		while ( ($ncopy % $prime)==0) {
 			$ncopy /= $prime;
-			$retstring ~= $prime;
+			push @factors, $prime;
 		}
 	}
-	return $retstring;
+	($ncopy > 1) && push @factors, $ncopy;
+	#-- any factor bigger than sqrt(n) is a prime factor
+	$retstring = @factors.list.join;
+
+	return $retstring.Int;
 }
 
-multi sub find_primes(Int $n where $n <= 13) {
-	my @primes=(2,3,5,7,11,13);
+multi sub find_primes(Int $n where $n <= 100) {
+	my @primes=
+	(2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97); 
 	my @retval=();
 	for @primes -> $prime {
 		($prime < $n) && (push @retval, $prime);
@@ -46,39 +68,59 @@ multi sub find_primes(Int $n where $n <= 13) {
 	return (@retval.sort);
 }
 
-multi sub find_primes(Int $n where $n > 13) {
-#-- naive approach by trial factorization    
-    my @primes=(3,7,11,13);
-    
-    my $i=13;
-    
-    while ($i < $n) {
-    	#-- count only odd numbers not ending in 5. Take 4 at a time.
-        my @testarray=();
-    
-    	(($i+4) < $n) && (push @testarray, ($i+4));
-        (($i+6) < $n) && (push @testarray, ($i+6));
-        (($i+8) < $n) && (push @testarray, ($i+8));
-        (($i+10) < $n) && (push @testarray, ($i+10));
-
-        while (@testarray.elems > 0) {
-            my $testitem=shift(@testarray);
-            unless ((($testitem % 6)==1) || (($testitem % 6)==5)) {
-            #-- use the property that prime numbers above 5 are 6k+1 or 6k-1  
-            	next;
-            }
-            for @primes -> $prime {
-                ($prime > sqrt($testitem)) && last;
-                (($testitem % $prime)==0) && last;
-            }
-            push @primes, $testitem;
-        }
-        $i += 10;
-    }
-
-    splice(@primes,0,1, <2 3 5>); #-- left out 2 and 5 earlier to avoid
-    				  #   unnecessary redundant factorizing
-    return (@primes.sort);
+multi sub find_primes (Int $n where $n > 100) {
+	my @primes=[7,11,13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97]; #-- candidate primes
+	my %primes{Int}=(); #-- we will return keys of this
+	my $sqrt_n = sqrt($n); #-- ceiling for iterating thru' sieve
+	
+	#-- initialize primes hash
+	#-- store candidates of the form 6k-1 to 6k+1
+	#-- eliminate multiples of known primes
+	loop (my $i=102; $i <= $n+1; $i += 6) {
+		my @temp=($i-1, $i+1);
+		TEMP: for @temp -> $temp {
+			($temp % 3) || next;
+			($temp % 5) || next;
+			for @primes -> $prime {
+				($prime > $sqrt_n) && last;
+				($temp % $prime) || next TEMP;
+			}
+			($temp <= $n) && (%primes{$temp}=True);
+		}
+	}
+		
+	#-- for prime candidates k greater than @primes[*-1]
+	#-- use odd numbers not divisible by 3 (last value + 4 and +6 if
+	#   we start counting from 97)
+	#-- loop through factors kk+jk < n and delete
+	#-- any %hash entries with key matching these factors.
+
+	my $last_prime = @primes[*-1];
+	if ($last_prime < $sqrt_n) { 
+		@primes=[$last_prime+4, $last_prime+2];
+		while (1) {
+			my $prime = shift @primes;
+			(@primes.elems==0) && 
+				(@primes.append($prime+4, $prime+2));
+			#-- avoid multiples of 3
+			
+			last if $prime > $sqrt_n;
+		
+			#-- only loop if the candidate is in the primes hash
+			if  ( %primes{$prime} ) {
+				loop (my $i=$prime*$prime; 
+					$i <= $n;
+					$i += $prime) {
+						%primes{$i}:delete;
+				}
+			}
+		}
+	}
+	my @retval=(2,3,5,7,11,13,17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97);
+	return (@retval.append(%primes.keys.sort));
+
+	return 1;
 }
 
 
+