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You can look up all the test points in parallel.

Some code showing how to do it for a simplified version of your problem where the ranges cover all the domain (there are no gaps):

#!/usr/bin/perl use strict; use warnings; my @ranges = 0; push @ranges, $ranges[-1] + 1 + int rand 200 for 1..10000; my @tests = map int rand $ranges[-1], 0..1000000; match (\@ranges, \@tests); sub div { my ($border, $tests) = @_; my ($lt, $ge) = ([], []); push @{$_ < $border ? $lt : $ge}, $_ for @$tests; ($lt, $ge); } sub match { my ($ranges, $tests) = @_; if (@$ranges == 1) { if (@$tests) { print "tests in range $ranges->[0]:\n", join(", ", @$tests +), "\n"; } else { print "range $ranges->[0] is empty\n"; } } else { my $pivot = int((@$ranges + 1)/ 2); my ($lt, $ge) = div($ranges->[$pivot], $tests); match([@{$ranges}[0..$pivot-1]], $lt); match([@{$ranges}[$pivot..$#$ranges]], $ge); } }
And a version optimized to not copy data around but to use indexes inside the main arrays:
#!/usr/bin/perl use strict; use warnings; my @ranges = 0; push @ranges, $ranges[-1] + 1 + int rand 200 for 1..1_000_000; my @tests = map int rand $ranges[-1], 0..10_000_000; match(0, scalar @ranges, 0, scalar @tests); sub div { my ($border, $start, $end) = @_; while ($end > $start) { if ($tests[$start] < $border) { $start++; } else { if (--$end > $start) { @tests[$start, $end] = @tests[$end, $start]; } } } $end; } sub match { my ($r_start, $r_end, $t_start, $t_end) = @_; if ($r_end - $r_start <= 1) { if ($t_end - $t_start > 0) { print "tests in range $ranges[$r_start]:\n", join(", ", @t +ests[$t_start..$t_end-1]), "\n"; } else { print "range $ranges[$r_start] is empty\n"; } } else { my $r_pivot = int(($r_start + $r_end)/ 2); my $t_pivot = div($ranges[$r_pivot], $t_start, $t_end); match($r_start, $r_pivot - 1, $t_start, $t_pivot - 1); match($r_pivot, $r_end, $t_pivot, $t_end); } }
This algorithm, for N ranges and M test points where M > N has complexity O(MlogN) and does not require extra memory besides that used to store the ranges and the test points.

On my not so new computer, with the print sentences commented out, it runs in a couple of minutes.


In reply to Re: Range overlap (with a lot of ranges) by salva
in thread Range overlap (with a lot of ranges) by BioLion

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