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Re^3: Modified Binary Search

by salva (Canon)
on Jan 14, 2010 at 14:32 UTC ( #817412=note: print w/replies, xml ) Need Help??


in reply to Re^2: Modified Binary Search
in thread Modified Binary Search

... and some benchmarking code just to probe it is not worse:
#!/usr/bin/perl use strict; use warnings; use File::Slurp qw(slurp); use Benchmark qw(cmpthese); sub binary_search { my ($str, $a) = @_; my $l = 0; my $h = @$a; while ($l < $h) { my $p = int (($l + $h) / 2); if ($a->[$p] lt $str) { $l = $p + 1; } else { $h = $p; } } $l } sub make_start { my $a = shift; my $last = $a->[0]; my @start = (0); for my $ix (1..$#$a) { my $current = $a->[$ix]; if ($current ne $last) { push @start, $ix; $last = $current; } } return \@start; } chomp (my @words = slurp '/usr/share/dict/words'); @words = grep /^\w+$/, @words; for my $size (100, 1000, 100_000, 1_000_000) { for my $dups (3, 10, 100) { next unless $size > $dups; for my $reps (100, 100_000, 1_000_000) { print "size: $size, dups: $dups, reps: $reps\n"; # generate data: my @a = map $words[rand @words], 1..1+($size/$dups); push @a, $a[rand @a] while @a < $size; @a = sort @a; cmpthese(-30, { naive => sub { my $ix; $ix = binary_search($a[rand @a], \@a) for + (1..$reps); }, salva => sub { my $ix; my $start = make_start(\@a); my @a_start = @a[@$start]; $ix = $start->[binary_search($a[rand @a], + \@a_start)] for (1..$reps); } }); print "\n"; } } }
The parameters in the benchmarks are:
  • $size: the size of the array
  • $dups: average number of times any string is repeated in the array
  • $reps: number of binary searchs to perform over one given array.

Note also than this code only looks for the lowest index where some given string is found. Handling the case described by the OP where he also needs to find the highest index is trivially handled in my algorithm without increasing its computation cost but will require an additional binary search when using the naive algorithm.

Here are the results I have gotten on my machine:

size: 100, dups: 3, reps: 100 Rate salva naive salva 837/s -- -2% naive 854/s 2% -- size: 100, dups: 3, reps: 100000 s/iter naive salva naive 1.21 -- -10% salva 1.09 11% -- size: 100, dups: 3, reps: 1000000 s/iter naive salva naive 13.0 -- -16% salva 10.9 19% -- size: 100, dups: 10, reps: 100 Rate naive salva naive 817/s -- -20% salva 1020/s 25% -- size: 100, dups: 10, reps: 100000 s/iter naive salva naive 1.19 -- -26% salva 0.878 36% -- size: 100, dups: 10, reps: 1000000 s/iter naive salva naive 11.9 -- -24% salva 9.08 31% -- size: 1000, dups: 3, reps: 100 Rate salva naive salva 476/s -- -31% naive 692/s 45% -- size: 1000, dups: 3, reps: 100000 s/iter naive salva naive 1.46 -- -10% salva 1.32 11% -- size: 1000, dups: 3, reps: 1000000 s/iter naive salva naive 14.8 -- -12% salva 13.1 13% -- size: 1000, dups: 10, reps: 100 Rate salva naive salva 597/s -- -12% naive 681/s 14% -- size: 1000, dups: 10, reps: 100000 s/iter naive salva naive 1.46 -- -20% salva 1.17 25% -- size: 1000, dups: 10, reps: 1000000 s/iter naive salva naive 15.2 -- -25% salva 11.4 33% -- size: 1000, dups: 100, reps: 100 Rate naive salva naive 688/s -- -9% salva 755/s 10% -- size: 1000, dups: 100, reps: 100000 s/iter naive salva naive 1.46 -- -40% salva 0.879 66% -- size: 1000, dups: 100, reps: 1000000 s/iter naive salva naive 14.7 -- -39% salva 8.99 64% -- size: 100000, dups: 3, reps: 100 Rate salva naive salva 9.62/s -- -98% naive 420/s 4268% -- size: 100000, dups: 3, reps: 100000 s/iter naive salva naive 2.38 -- -12% salva 2.11 13% -- size: 100000, dups: 3, reps: 1000000 s/iter naive salva naive 24.1 -- -11% salva 21.4 13% -- size: 100000, dups: 10, reps: 100 Rate salva naive salva 11.4/s -- -97% naive 415/s 3557% -- size: 100000, dups: 10, reps: 100000 s/iter naive salva naive 2.42 -- -14% salva 2.07 17% -- size: 100000, dups: 10, reps: 1000000 s/iter naive salva naive 23.8 -- -17% salva 19.7 21% -- size: 100000, dups: 100, reps: 100 Rate salva naive salva 14.5/s -- -97% naive 423/s 2821% -- size: 100000, dups: 100, reps: 100000 s/iter naive salva naive 2.36 -- -34% salva 1.55 52% -- size: 100000, dups: 100, reps: 1000000 s/iter naive salva naive 23.7 -- -35% salva 15.5 53% -- size: 1000000, dups: 3, reps: 100 Rate salva naive salva 1.22/s -- -100% naive 337/s 27580% -- size: 1000000, dups: 3, reps: 100000 s/iter salva naive salva 3.35 -- -10% naive 3.01 11% -- size: 1000000, dups: 3, reps: 1000000 s/iter naive salva naive 30.1 -- -14% salva 25.9 16% -- size: 1000000, dups: 10, reps: 100 Rate salva naive salva 1.16/s -- -100% naive 332/s 28395% -- size: 1000000, dups: 10, reps: 100000 s/iter salva naive salva 3.20 -- -4% naive 3.06 5% -- size: 1000000, dups: 10, reps: 1000000 s/iter naive salva naive 30.1 -- -18% salva 24.8 21% -- size: 1000000, dups: 100, reps: 100 Rate salva naive salva 1.36/s -- -100% naive 330/s 24141% -- size: 1000000, dups: 100, reps: 100000 s/iter naive salva naive 3.01 -- -8% salva 2.78 9% -- size: 1000000, dups: 100, reps: 1000000 s/iter naive salva naive 30.3 -- -29% salva 21.4 41% --

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Re^4: Modified Binary Search
by ikegami (Pope) on Jan 14, 2010 at 23:10 UTC

    Of course the array construction won't add to the time if you don't include it in the code that's timed.

    You assume the same list is always searched.

    I suppose a more precise analysis is O(log(N) + N/M) where M is the number of searched performed between modifications of the list. The number of such searches have to be proportional to the size of the list to get less than O(N).

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