From 396867334ee4fe6295c5fa8415537f857e9b0063 Mon Sep 17 00:00:00 2001
From: E7-87-83 <fungcheokyin@gmail.com>
Date: Sun, 15 Aug 2021 09:52:31 +0800
Subject: improve bound on ch-1.pl

---
 challenge-125/cheok-yin-fung/perl/ch-1.pl | 5 +++--
 1 file changed, 3 insertions(+), 2 deletions(-)

diff --git a/challenge-125/cheok-yin-fung/perl/ch-1.pl b/challenge-125/cheok-yin-fung/perl/ch-1.pl
index 10fabf76ef..6258feda8a 100644
--- a/challenge-125/cheok-yin-fung/perl/ch-1.pl
+++ b/challenge-125/cheok-yin-fung/perl/ch-1.pl
@@ -7,7 +7,7 @@ use warnings;
 use v5.10.0;
 use experimental 'signatures';
 use List::Util qw/max/;
-use Test::More tests => 7;
+use Test::More tests => 8;
 
 my $num = $ARGV[0] || 5;
 my @arr = pyth($num)->@*;
@@ -37,7 +37,7 @@ sub pyth ($n) {
         }
     }
 
-    for my $b0 ($n+1..$n*$n) {
+    for my $b0 ($n+1..int ($n*$n-1)/2) {
         my $is_sq = $b0*$b0 + $n*$n;
         if (sqrt($is_sq) == int sqrt($is_sq)) {
             push @ans, [$n , $b0 ,sqrt($is_sq)];
@@ -55,3 +55,4 @@ ok scalar @{pyth(4)} == 1, "Number 4";
 ok scalar @{pyth(5)} == 2, "Number 5";
 ok scalar @{pyth(8)} == 2, "Number 8";
 ok scalar @{pyth(13)} == 2, "Number 13";
+ok scalar @{pyth(5740)} == 44, "Number 5740"  # oeis.org/A046081
-- 
cgit 


From ac1325e6eee9ccff046085735d61aa969dc09b75 Mon Sep 17 00:00:00 2001
From: E7-87-83 <fungcheokyin@gmail.com>
Date: Sun, 15 Aug 2021 10:02:48 +0800
Subject: improve bound on ch-1.pl

---
 challenge-125/cheok-yin-fung/perl/ch-1.pl | 5 +++++
 1 file changed, 5 insertions(+)

diff --git a/challenge-125/cheok-yin-fung/perl/ch-1.pl b/challenge-125/cheok-yin-fung/perl/ch-1.pl
index 6258feda8a..7a700d2ed0 100644
--- a/challenge-125/cheok-yin-fung/perl/ch-1.pl
+++ b/challenge-125/cheok-yin-fung/perl/ch-1.pl
@@ -37,6 +37,11 @@ sub pyth ($n) {
         }
     }
 
+
+    # (C+1)^2 - C^2 = 2C + 1
+    # 2C + 1 <= n^2
+    # C <= (n^2-1)/2
+
     for my $b0 ($n+1..int ($n*$n-1)/2) {
         my $is_sq = $b0*$b0 + $n*$n;
         if (sqrt($is_sq) == int sqrt($is_sq)) {
-- 
cgit 


From 12e2ed795e741c3070ffb5ead04b6e2b857e4696 Mon Sep 17 00:00:00 2001
From: E7-87-83 <fungcheokyin@gmail.com>
Date: Sun, 15 Aug 2021 17:26:11 +0800
Subject: better expression of logic

---
 challenge-125/cheok-yin-fung/perl/ch-1.pl | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/challenge-125/cheok-yin-fung/perl/ch-1.pl b/challenge-125/cheok-yin-fung/perl/ch-1.pl
index 7a700d2ed0..8d0c3a650a 100644
--- a/challenge-125/cheok-yin-fung/perl/ch-1.pl
+++ b/challenge-125/cheok-yin-fung/perl/ch-1.pl
@@ -38,9 +38,9 @@ sub pyth ($n) {
     }
 
 
-    # (C+1)^2 - C^2 = 2C + 1
-    # 2C + 1 <= n^2
-    # C <= (n^2-1)/2
+    # c^2 - b_max^2 >= (b_max+1)^2 - b_max^2 = 2*b_max + 1
+    # 2*b_max + 1 <= n^2
+    # b_max <= (n^2-1)/2
 
     for my $b0 ($n+1..int ($n*$n-1)/2) {
         my $is_sq = $b0*$b0 + $n*$n;
-- 
cgit