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### Re: Split range 0 to M into N non-overlapping (roughly equal) ranges.

by ELISHEVA (Prior)
 on Mar 12, 2011 at 19:40 UTC ( #892856=note: print w/replies, xml ) Need Help??

Why not adapt the solution ikegami suggested a few weeks back on the Near equal partitions. thread?

```sub ranges_beth2 {
my (\$M, \$N) = @_;
my \$r = (\$M+1)%\$N;
my \$q = (\$M+1-\$r)/\$N;
my \$iEnd=0;
return [ map { my \$iStart=\$iEnd; [\$iStart, (\$iEnd+=\$_) - 1]
} ((\$q+1) x \$r, (\$q) x (\$N-\$r)) ];
}

Sample output

```---------------------------
0 : from       0 to 9999997 (9999998)
---------------------------
0 : from       0 to 4999998 (4999999)
1 : from 4999999 to 9999997 (4999999)
---------------------------
0 : from       0 to 3333332 (3333333)
1 : from 3333333 to 6666665 (3333333)
2 : from 6666666 to 9999997 (3333332)
---------------------------
0 : from       0 to 2499999 (2500000)
1 : from 2500000 to 4999999 (2500000)
2 : from 5000000 to 7499998 (2499999)
3 : from 7499999 to 9999997 (2499999)

It ensures that partitions never differ by more than 1 in size and avoids rounding errors. On benchmark results it is also marginally faster (4-8%) than the code in the OP (actual result varies between runs)

```       s/iter   buk eli_ik
buk      1.01    --   -8%
eli_ik   0.923    9%   --

Rate   buk eli_ik
buk    1.02/s    --   -4%
eli_ik 1.06/s    4%    --

Benchmark code

```use Benchmark qw(cmpthese);

sub testRanges {
my \$cr=\$_[0];
for my \$M (1..1e2) {
for my \$N (1..\$M) {
\$cr->(\$M,\$N);
}
}
}

cmpthese(10
, { 'buk' => sub { testRanges(\&ranges_buk) }
, 'eli_ik' => sub { testRanges(\&ranges_beth2) }
}
);

Update: added that it avoids rounding errors.

Update: minor revision to account for OP desiring range to go from 0..\$M (\$M+1 values) not 0..(\$M-1), i.e. \$M values.

Replies are listed 'Best First'.
Re^2: Split range 0 to M into N non-overlapping (roughly equal) ranges.
by BrowserUk (Pope) on Mar 12, 2011 at 21:10 UTC

I don't find that to be particularly clean. It uses more intermediate variables and terms.

Efficiency isn't a consideration here as this usually precedes the spawning of N threads that each iterate over \$M/\$N elements of data.

Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.
"Science is about questioning the status quo. Questioning authority".
In the absence of evidence, opinion is indistinguishable from prejudice.

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