use strict;
use warnings;

#
# The display will be divided into two areas, each containing
# a grid of Xterm windows. One grid will be $a1 by $b tiles
# and the other will be $a2 by ($b-1) tiles.
#
# For each number of screens ($n), determine $a1, $a2 and $b such that
# ($a1*$b)+($a2*($b-1) == $n, the minimum aspect ratio (width/height)
# of an Xterm exceeds a threshold and the difference in size between
# the larger and smaller Xterm windows is minimized.
#
$| = 1;

my ( $width, $height) = ( 1024, 768 );  # display dimensions in conven
+ient units
my $aspect = 5/4;   # threshold aspect ratio

foreach my $n (1..100) {
    my $minx = 1e100;  # to be minimized
    my $maxb = 0;
    my @solution;
    foreach my $a1 (1..$n) {
        foreach my $a2 (0..($n-1)) {
            next if($a1 + $a2 > $n);
            foreach my $b (1..$n) {
                next unless( ( $a1 * $b ) + ( $a2 * ( $b - 1 ) ) == $n
+ );
                next unless( ( $width * ( $a1 + $a1 ) / $height / $b) 
+> $aspect );
                if( $b > $maxb ) {
                    @solution = ( $a1, $a2, $b );
                    $maxb = $b;
                }
            }
        }
    }
    print "$n: @solution\n";
}
__END__
1: 1 0 1
2: 1 0 2
3: 1 1 2
4: 1 2 2
5: 1 3 2
6: 2 0 3
7: 1 5 2
8: 2 0 4
9: 3 0 3
10: 2 2 3
11: 2 1 4
12: 3 0 4
13: 3 2 3
14: 2 2 4
15: 3 0 5
16: 4 0 4
17: 2 3 4
18: 3 0 6
19: 3 1 5
20: 4 0 5
21: 3 3 4
22: 4 2 4
23: 3 1 6
24: 4 0 6
25: 5 0 5
26: 2 6 4
27: 3 3 5
28: 4 0 7
29: 4 1 6
30: 5 0 6
31: 3 4 5
32: 4 0 8
33: 3 3 6
34: 4 1 7
35: 5 0 7
36: 6 0 6
37: 5 3 5
38: 3 4 6
39: 4 1 8
40: 5 0 8
41: 5 1 7
42: 6 0 7
43: 3 5 6
44: 4 4 6
45: 5 0 9
46: 4 2 8
47: 5 1 8
48: 6 0 8
49: 7 0 7
50: 5 0 10
51: 6 3 6
52: 4 4 7
53: 5 1 9
54: 6 0 9
55: 6 1 8
56: 7 0 8
57: 7 3 6
58: 4 5 7
59: 5 1 10
60: 6 0 10
61: 5 2 9
62: 6 1 9
63: 7 0 9
64: 8 0 8
65: 5 5 7
66: 6 0 11
67: 4 5 8
68: 5 2 10
69: 6 1 10
70: 7 0 10
71: 7 1 9
72: 6 0 12
73: 7 4 7
74: 4 6 8
75: 5 5 8
76: 6 1 11
77: 7 0 11
78: 6 2 10
79: 7 1 10
80: 8 0 10
81: 9 0 9
82: 5 6 8
83: 6 1 12
84: 7 0 12
85: 5 5 9
86: 6 2 11
87: 7 1 11
88: 8 0 11
89: 8 1 10
90: 9 0 10
91: 7 0 13
92: 8 4 8
93: 5 6 9
94: 6 2 12
95: 7 1 12
96: 8 0 12
97: 7 2 11
98: 7 0 14
99: 9 0 11
100: 10 0 10
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