对于那些不熟悉游戏的人。您将获得8个数字，并且必须使用+， - ，/和*。
来达到目标因此，如果目标是254并且您的游戏数量是2,50,5,2,1，那么您将通过说5 * 50 = 250来正确回答问题。然后2 + 2是4。添加它以及获得254。
游戏的一些视频在这里：
基本上我通过生成所有大小的所有权限以及符号的所有权限来强制使用游戏，并使用基本的inflix计算器来计算解决方案。
然而它包含一个缺陷，因为所有解决方案都解决如下：（（（（1 + 1）* 2）* 3）* 4）。它没有排列括号，这让我很头疼。
因此我无法解决所有方程式。例如，给定
目标16和数字1,1,1,1,1,1,1,1它应该做的时候失败（1 + 1 + 1 + 1）*（1 + 1 + 1 + 1） = 16
我喜欢有人可以用任何语言帮助完成这个......
这是我到目前为止所写的：
#!/usr/bin/env perl
use strict;
use warnings;
use Algorithm::Permute;
# GAME PARAMETERS TO FILL IN
my $target = 751;
my @numbers = ( '2', '4', '7', '9', '1', '6', '50', '25' );
my $num_numbers = scalar(@numbers);
my @symbols = ();
foreach my $n (@numbers) {
push(@symbols, ('+', '-', '/', '*'));
}
my $num_symbols = scalar(@symbols);
print "Symbol table: " . join(", ", @symbols);
my $lst = [];
my $symb_lst = [];
my $perms = '';
my @perm = ();
my $symb_perms = '';
my @symb_perm;
my $print_mark = 0;
my $progress = 0;
my $total_perms = 0;
my @closest_numbers;
my @closest_symb;
my $distance = 999999;
sub calculate {
my @oprms = @{ $_[0] };
my @ooperators = @{ $_[1] };
my @prms = @oprms;
my @operators = @ooperators;
#print "PERMS: " . join(", ", @prms) . ", OPERATORS: " . join(", ", @operators);
my $total = pop(@prms);
foreach my $operator (@operators) {
my $x = pop(@prms);
if ($operator eq '+') {
$total += $x;
}
if ($operator eq '-') {
$total -= $x;
}
if ($operator eq '*') {
$total *= $x;
}
if ($operator eq '/') {
$total /= $x;
}
}
#print "Total: $total\n";
if ($total == $target) {
#print "ABLE TO ACCURATELY SOLVE WITH THIS ALGORITHM:\n";
#print "PERMS: " . join(", ", @oprms) . ", OPERATORS: " . join(", ", @ooperators) . ", TOTAL=$total\n";
sum_print(\@oprms, \@ooperators, $total, 0);
exit(0);
}
my $own_distance = ($target - $total);
if ($own_distance < 0) {
$own_distance *= -1;
}
if ($own_distance < $distance) {
#print "found a new solution - only $own_distance from target $target\n";
#print "PERMS: " . join(", ", @oprms) . ", OPERATORS: " . join(", ", @ooperators) . ", TOTAL=$total\n";
sum_print(\@oprms, \@ooperators, $total, $own_distance);
@closest_numbers = @oprms;
@closest_symb = @ooperators;
$distance = $own_distance;
}
$progress++;
if (($progress % $print_mark) == 0) {
print "Tested $progress permutations. " . (($progress / $total_perms) * 100) . "%\n";
}
}
sub factorial {
my $f = shift;
$f == 0 ? 1 : $f*factorial($f-1);
}
sub sum_print {
my @prms = @{ $_[0] };
my @operators = @{ $_[1] };
my $total = $_[2];
my $distance = $_[3];
my $tmp = '';
my $op_len = scalar(@operators);
print "BEST SOLUTION SO FAR: ";
for (my $x = 0; $x < $op_len; $x++) {
print "(";
}
$tmp = pop(@prms);
print "$tmp";
foreach my $operator (@operators) {
$tmp = pop(@prms);
print " $operator $tmp)";
}
if ($distance == 0) {
print " = $total\n";
}
else {
print " = $total (distance from target $target is $distance)\n";
}
}
# look for straight match
foreach my $number (@numbers) {
if ($number == $target) {
print "matched!\n";
}
}
for (my $x = 1; $x < (($num_numbers*2)-1); $x++) {
$total_perms += factorial($x);
}
print "Total number of permutations: $total_perms\n";
$print_mark = $total_perms / 100;
if ($print_mark == 0) {
$print_mark = $total_perms;
}
for (my $num_size=2; $num_size <= $num_numbers; $num_size++) {
$lst = \@numbers;
$perms = new Algorithm::Permute($lst, $num_size);
print "Perms of size: $num_size.\n";
# print matching symb permutations
$symb_lst = \@symbols;
$symb_perms = new Algorithm::Permute($symb_lst, $num_size-1);
while (@perm = $perms->next) {
while (@symb_perm = $symb_perms->next) {
calculate(\@perm, \@symb_perm);
}
$symb_perms = new Algorithm::Permute($symb_lst, $num_size-1);
}
}
print "exhausted solutions";
print "CLOSEST I CAN GET: $distance\n";
sum_print(\@closest_numbers, \@closest_symb, $target-$distance, $distance);
exit(0);
以下是示例输出：
[15:53: /mnt/mydocuments/git_working_dir/countdown_solver$] perl countdown_solver.pl
Symbol table: +, -, /, *, +, -, /, *, +, -, /, *, +, -, /, *, +, -, /, *, +, -, /, *, +, -, /, *, +, -, /, *Total number of permutations: 93928268313
Perms of size: 2.
BEST SOLUTION SO FAR: (2 + 4) = 6 (distance from target 751 is 745)
BEST SOLUTION SO FAR: (2 * 4) = 8 (distance from target 751 is 743)
BEST SOLUTION SO FAR: (4 + 7) = 11 (distance from target 751 is 740)
BEST SOLUTION SO FAR: (4 * 7) = 28 (distance from target 751 is 723)
BEST SOLUTION SO FAR: (4 * 9) = 36 (distance from target 751 is 715)
BEST SOLUTION SO FAR: (7 * 9) = 63 (distance from target 751 is 688)
BEST SOLUTION SO FAR: (4 * 50) = 200 (distance from target 751 is 551)
BEST SOLUTION SO FAR: (7 * 50) = 350 (distance from target 751 is 401)
BEST SOLUTION SO FAR: (9 * 50) = 450 (distance from target 751 is 301)
Perms of size: 3.
BEST SOLUTION SO FAR: ((4 + 7) * 50) = 550 (distance from target 751 is 201)
BEST SOLUTION SO FAR: ((2 * 7) * 50) = 700 (distance from target 751 is 51)
BEST SOLUTION SO FAR: ((7 + 9) * 50) = 800 (distance from target 751 is 49)
BEST SOLUTION SO FAR: ((9 + 6) * 50) = 750 (distance from target 751 is 1)
Perms of size: 4.
BEST SOLUTION SO FAR: (((9 + 6) * 50) + 1) = 751
答案 0 :(得分：2)
答案 1 :(得分：0)
使用反向抛光记谱法的建议非常好。
如果您有N = 5个数字，则模板为
{num} {num} {ops} {num} {ops} {num} {ops} {num} {ops}
任何地点都可以有0到N个操作，但总数将是N-1。你只需要尝试不同的数字和操作位置。
尝试
时会找到(((1+1)+1)+1)*(((1+1)+1)+1)=16解决方案
1 1 + 1 + 1 + 1 1 + 1 + 1 + *
更新：可能不太好，因为找到上述内容可能需要433,701,273,600次尝试。该数字是使用以下方法获得的：
use strict;
use warnings;
{
my %cache = ( 0 => 1 );
sub fact { my ($n) = @_; $cache{$n} ||= fact($n-1) * $n }
}
{
my %cache;
sub C {
my ($n,$r) = @_;
return $cache{"$n,$r"} ||= do {
my $i = $n;
my $j = $n-$r;
my $c = 1;
$c *= $i--/$j-- while $j;
$c
};
}
}
my @nums = (1,1,1,1,1,1,1,1);
my $Nn = 0+@nums; # Number of numbers.
my $No = $Nn-1; # Number of operators.
my $max_tries = do {
my $num_orderings = fact($Nn);
{
my %counts;
++$counts{$_} for @nums;
$num_orderings /= fact($_) for values(%counts);
}
my $op_orderings = 4 ** $No;
my $op_placements = 1;
$op_placements *= C($No, $_) for 1..$No-1;
$num_orderings * $op_orderings * $op_placements
};
printf "At most %.f tries needed\n", $max_tries;