Create ch-2.pl

1 files changed, 33 insertions, 0 deletions

diff --git a/challenge-050/cheok-yin-fung/perl/ch-2.pl b/challenge-050/cheok-yin-fung/perl/ch-2.pl
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+#!/usr/bin/perl
+use strict;
+
+# Caution: This script is valid only when the list of integers DISTINCT.
+
+# Proposition: There can only be 1 noble integer. 
+# Proof by Contradiction: 
+# Let r be the length of the list, 
+# k be the firstly found noble integer 
+# and j be the secondly found noble integer
+# (by this algorithm, the first found noble integer will be the smallest noble integer;)
+# (by the DISTINCT assumption, k<j     #(a)
+# numbers of integers larger than k: r - position(k)
+# numbers of integers larger than j: r - position(j) , 
+#     while r-position(j) < r-position(k),             #(b)
+#               since position(j) > position(k) after sorting.
+# By the nobleness condition
+#     k == r-position(k)     #(c)
+#     j == r-position(j)     #(d)
+#     Substituting (c) & (d) into (a) implies r-position(k) < r-position(j) , while this inequality violates (b) !!! QED
+
+my @L = @ARGV; #usage: perl ch-2.pl 2 6 1 3
+
+
+@L = sort {$a <=> $b} @L;
+
+
+my $i=0;
+while ($i<=$#L) {
+	if ($L[$i] == $#L-$i ) {print $L[$i]; exit;} 
+	$i++;
+}
+print "-1";