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Re: Hamming Sequences and Lazy Lists

by Roy Johnson (Monsignor)
on Mar 17, 2005 at 18:00 UTC ( #440460=note: print w/ replies, xml ) Need Help??


in reply to Hamming Sequences and Lazy Lists

Lazy, fast, and I think it's correct.

use strict; use warnings; sub lazy_ham { my ($how_many) = @_; my @output_stream = (1); my @streams = map { my $base = $_; # All your base are belong to us my $index = 0; sub { if (@_) { return $base * $output_stream[$index]; } else { return $base * $output_stream[$index++]; } } } (2, 3, 5); for (1..$how_many) { # Find the lowest next item in the available streams my ($lowest) = sort {$a <=> $b} map {$_->('peek')} @streams; $_->('peek') == $lowest and $_->() for @streams; push(@output_stream, $lowest); } shift @output_stream; # Get rid of the seed 1 @output_stream; } print join(', ', lazy_ham(1000)), "\n";
2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 25, 27, 30, 32, 36, 4 +0, 45, 48, 50, 54, 60, 64, 72, 75, 80, 81, 90, 96, 100, 108, 120, 125 +, 128, 135, 144, 150, 160, 162, 180, 192, 200, 216, 225, 240, 243, 25 +0, 256, 270, 288, 300, 320, 324, 360, 375, 384, 400, 405, 432, 450, 4 +80, 486, 500, 512, 540, 576, 600, 625, 640, 648, 675, 720, 729, 750, +768, 800, 810, 864, 900, 960, 972, 1000, 1024, 1080, 1125, 1152, 1200 +, 1215, 1250, 1280, 1296, 1350, 1440, 1458, 1500, 1536, 1600, 1620, 1 +728, 1800, 1875,...

Caution: Contents may have been coded under pressure.


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Re^2: Hamming Sequences and Lazy Lists
by Limbic~Region (Chancellor) on Mar 17, 2005 at 18:03 UTC
    Roy Johnson,
    Shouldn't 14 be in the results since it is a multiple of 2?

    Cheers - L~R

      No, my understanding is that we only want numbers that factor as 2^X * 3^Y * 5^Z.

      Caution: Contents may have been coded under pressure.
        Roy Johnson,
        You are correct, I am wrong. I was so focused on lazy evaluation that I misunderstood "how do you generate the series of numbers composed of a given list of prime factors, where each can be used an unlimited number of times?" To me, that meant any positive multiple of any factor was valid.

        Cheers - L~R

Re^2: Hamming Sequences and Lazy Lists
by tall_man (Parson) on Mar 17, 2005 at 18:25 UTC
    The number 1 = 2**0 * 3**0 * 5**0, so it is a legitimate part of the series, not just a seed to be stripped off. It is part of the answer produced by the Haskell genHam above. Otherwise, your generator looks great and the output checks with the Haskell one.
      Ok, well here it is, corrected for that, and without using coderefs for streams. I realized there really wasn't much point to that. All I really need to know is what my multiplier is, and which element of the output stream I'm looking at.
      use strict; use warnings; sub lazy_ham { my ($how_many) = @_; my @output_stream = (1); my @streams = map [$_,0], (2, 3, 5); for (@output_stream+1..$how_many) { # Find the lowest next item in the available streams my @peeks = map {$output_stream[$_->[1]] * $_->[0]} @streams; my ($lowest) = sort {$a <=> $b} @peeks; $peeks[$_] == $lowest and $streams[$_][1]++ for 0..$#streams; push(@output_stream, $lowest); } @output_stream; } print join(', ', lazy_ham(80)), "\n";

      Caution: Contents may have been coded under pressure.

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