use warnings; use strict; sub perm_decode { my(@perm) = @_; my($n, $k, $b, $v, $e); ($n, $k, $b, $v) = (0, 0, 0, 0); for $e (@perm) { #$b == choose($n, $k - 1) or die "assertion failed"; $e or $v += $b; $n++; $e and $k++; $b = $k <= 1 ? ($k < 1 ? 0 : 1) : ($b * $n / ($e ? $k - 1 : $n - $k + 1)); } $b = $k <= 0 ? 1 : ($b * ($n - $k + 1)) / $k; #$b == choose($n, $k) or die "assertion failed"; $n, $k, $v, $b; } sub perm_encode { my($n, $k, $v) = @_; my(@r, $bi); while (0 < $n) { $n--; $bi = choose($n, $k - 1); if ($v < $bi) { unshift @r, 1; $k--; } else { $v -= $bi; unshift @r, 0; } } @r; } #### # 2**28 < fact(12) < 2**29 < 2**32 < fact(13) < 2**33 < # < 2**52 < fact(18) < 2**53 < 2**56 < fact(19) < 2**57 sub choose { my($n, $k) = @_; my($v, $l); $k < 0 and return 0; $v = 1; $n - $k < $k and $k = $n - $k; for $l ($n - $k + 1 .. $n) { $v *= $l; } for $l (2 .. $k) { $v /= $l; } $v; } sub each_variation { my($n, $callb) = @_; my(@a, $k); @a = (0) x $n; OUT: while (1) { &$callb(@a); $k = $n; IN: { 0 <= --$k or last OUT; 2 == ++$a[$k] and do { $a[$k] = 0; redo IN; }; } } } if (1) { my(@k, @p, @pp, $r, @r, $n); for $n (0 .. 6) { #warn "= $n"; @r = (); each_variation($n, sub { @p = @_; @k = perm_decode(@p); $r = sprintf "%1d %1d %2d %2d : %s\n", @k[0 .. 3], join(" ", @p); push @r, $r; }); print sort @r; } } if (0) { my(@k, @p, @pp, $r, @r, $n); for $n (0 .. 60) { warn "= $n"; @r = (); each_variation($n, sub { @p = @_; @k = perm_decode(@p); @pp = perm_encode(@k); $r = sprintf "%1d %1d %2d : %s : %s\n", @k[0 .. 2], join(" ", @p), join(" ", @pp); join(",", @p) eq join(",", @pp) or do { $r = sprintf "%1d %1d %2d : %s : %s\n", @k[0 .. 2], join(" ", @p), join(" ", @pp); die "perm_encode wrong: $r"; }; }); warn "ok"; }; } if (0) { my($n, $k); for $n (0 .. 15) { for $k (0 .. $n) { printf "% 5d", choose($n, $k); } print "\n"; } } if (0) { # 9 3 27 my($n, $k, $b, $v, @p, $nn, $kk, $vv); $b = choose(($n, $k) = (9, 3)); for $v (27 .. 28) { @p = perm_encode($n, $k, $v); ($nn, $kk, $vv) = perm_decode(@p); printf "%d %d %2d : %d %d %2d : %s\n", $n, $k, $v, $nn, $kk, $vv, join(" ", @p); } warn join(" ", perm_decode(perm_encode(9, 3, 28))); } __END__ #### sub word_to_indicator { my($n, $w) = @_; my($p, $d) = 0; reverse map { $p += $d = chr(ord("A") + $_) eq substr($w, $p, 1) ? 1 : 0; $d; } 0 .. $n - 1; } if (1) { # here, N = 5, K = 2. my @combination = qw{AB AC AD AE BC BD BE CD CE DE}; for my $combination (@combination) { my @indicator = word_to_indicator(5, $combination); my($N, $K, $rank, $C) = perm_decode(@indicator); print "$combination : @indicator : $N $K $C $rank\n"; } }