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-rwxr-xr-xchallenge-211/jo-37/perl/ch-2.pl73
1 files changed, 73 insertions, 0 deletions
diff --git a/challenge-211/jo-37/perl/ch-2.pl b/challenge-211/jo-37/perl/ch-2.pl
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+#!/usr/bin/perl -s
+
+use v5.16;
+use Test2::V0;
+use Math::Prime::Util qw(forcomb lastfor);
+use List::Util qw(sum);
+use experimental qw(signatures);
+
+our ($tests, $examples);
+
+run_tests() if $tests || $examples; # does not return
+
+die <<EOS unless @ARGV;
+usage: $0 [-examples] [-tests] [--] [N...]
+
+-examples
+ run the examples from the challenge
+
+-tests
+ run some tests
+
+N...
+ list of numbers
+
+EOS
+
+
+### Input and Output
+
+say same_average(@ARGV) ? 'true' : 'false';
+
+
+### Implementation
+
+# It can easily be shown that if two partitions of the list have the
+# same average, this common average equals the average of the whole
+# list. Thus all we need to do is find a nonempty true subset of the
+# list having the same average as the list. The complement will have
+# the same average.
+
+sub same_average (@list) {
+ state $delta = 1e-6;
+ my $avg = sum(@list) / @list;
+ my $res;
+ # Loop over all subsets.
+ forcomb {
+ # Skip non true subsets.
+ return unless @_ && @_ != @list;
+ $res = 1, lastfor if abs($avg - sum(@list[@_]) / @_) < $delta;
+ } @list;
+
+ $res;
+}
+
+
+### Examples and tests
+
+sub run_tests {
+ SKIP: {
+ skip "examples" unless $examples;
+
+ ok same_average(1, 2, 3, 4, 5, 6, 7, 8), 'example 1';
+ ok !same_average(1, 3), 'example 2';
+ }
+
+ SKIP: {
+ skip "tests" unless $tests;
+ ok same_average(1, 1, 1, 1, 5, 9,), '(1 5), (1 1 1 9)';
+ }
+
+ done_testing;
+ exit;
+}