Solution to task 2

1 files changed, 83 insertions, 0 deletions

diff --git a/challenge-172/jo-37/perl/ch-2.pl b/challenge-172/jo-37/perl/ch-2.pl
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+#!/usr/bin/perl -s
+
+use v5.16;
+use Test2::V0;
+use Math::Utils qw(ceil floor);
+
+our $examples;
+
+run_tests() if $examples;	# does not return
+
+die <<EOS unless @ARGV;
+usage: $0 [-examples] [--] [N...]
+
+-examples
+    run some examples
+ 
+N...
+    Calculate the five-number summary over the given numbers.
+
+EOS
+
+
+### Input and Output
+
+say "@{[fivenum(@ARGV)]}";
+
+
+### Implementation
+
+# According to Wiki (https://en.wikipedia.org/wiki/Quartile), there is
+# no agreement about the method to calculate the quartiles of discrete
+# distributions.  For aesthetic reasons I prefer "Method 2" because the
+# five-number summary for a distribution of five numbers consist of
+# these five numbers.  The characteristic of "Method 2" is the inclusion
+# of the median in both, the upper and the lower part for the
+# determination of the first and third quartile in case of odd-sized
+# samples.
+# We may take the value of a non-integer index of an array as the mean
+# of the surrounding values.  No weighting is required here, as all
+# indices will be multiples of 1/2.
+# If the sample size is odd, the median index is an integer and thus the
+# median is naturally part of the lower and the upper half of the sample
+# as in "Method 2".  The 1/4 and 3/4 indices thus will give the correct
+# index for the first and third quartile.  Otherwise in the case of an
+# even sample size, the median index is in the middle between two
+# integers and the 1/4 and 3/4 indices are therefore off by ±1/4.
+#
+sub fivenum {
+    # numbers need to be sorted.
+    my @n = sort {$a <=> $b} @_;
+
+    # non-integer index around the first quartile.
+    my $q = $#n / 4;
+    # Offset for the exact (non-integer) indices of the first
+    # and third quartile.
+    my $o = ($#n % 2) / 4;
+    # zeroth (min), first, second (median), third and fourth (max)
+    # quartile. Interpolated if necessary by taking the mean of the
+    # surrounding values for non-integer indices.
+    map +($n[floor $_] + $n[ceil $_]) / 2,
+        0, $q - $o, $#n / 2, 3 * $q + $o, $#n;
+}
+
+
+### Examples and tests
+
+sub run_tests {
+    is [fivenum(0, 0, 1, 2, 63, 61, 27, 13)],
+        [0, 0.5, 7.5, 44, 63], 'example from Wiki "Five-number summary';
+
+    is [fivenum(6, 7, 15, 36, 39, 40, 41, 42, 43, 47, 49)],
+        [6, 25.5, 40, 42.5, 49], 'example 1 from Wiki "Quartile"';
+
+
+    is [fivenum(7, 15, 36, 39, 40, 41)],
+        [7, 15, 37.5, 40, 41], 'example 2 from Wiki "Quartile"';
+
+    is [fivenum(3, 5, 8, 13, 21)],
+        [3, 5, 8, 13, 21], "five numbers";
+
+    done_testing;
+    exit;
+}