Chinaunix
标题:
最短的距离
[打印本页]
作者:
patagonia2
时间:
2016-05-07 15:44
标题:
最短的距离
遇到这个问题,没什么思路。
请问各位大圣这种情况怎么处理呢。
必须拜访每个地点一次。
最短的距离是?
列出
一条
有最短距离的途径
例如,给出以下距离:
pit-01 -> pit-02 = 464
pit-01 -> pit-03 = 518
pit-02 -> pit-03 = 141
因此,可能的途径有:
pit-01 -> pit-02 -> pit-03 = 605
pit-01 -> pit-03 -> pit-02 = 659
pit-02 -> pit-01 -> pit-03 = 982
pit-02 -> pit-03 -> pit-01 = 659
pit-03 -> pit-02 -> pit-01 = 605
pit-03 -> pit-01 -> pit-02 = 982
所以答案是
pit-01 -> pit-02 -> pit-03 = 605
请问各位大圣这种情况怎么处理呢。
PIT-001 PIT-002 9665
PIT-001 PIT-003 5794
PIT-001 PIT-004 96
PIT-001 PIT-005 5750
PIT-001 PIT-006 6394
PIT-001 PIT-007 5750
PIT-001 PIT-008 3478
PIT-001 PIT-009 262
PIT-001 PIT-010 8954
PIT-001 PIT-011 3751
PIT-001 PIT-012 5253
PIT-001 PIT-013 6988
PIT-001 PIT-014 1364
PIT-001 PIT-015 9415
PIT-001 PIT-016 6156
PIT-001 PIT-017 6015
PIT-001 PIT-018 7931
PIT-001 PIT-019 5082
PIT-001 PIT-020 9891
PIT-002 PIT-003 6580
PIT-002 PIT-004 4325
PIT-002 PIT-005 5355
PIT-002 PIT-006 7221
PIT-002 PIT-007 4093
PIT-002 PIT-008 6098
PIT-002 PIT-009 2720
PIT-002 PIT-010 4662
PIT-002 PIT-011 9336
PIT-002 PIT-012 378
PIT-002 PIT-013 4632
PIT-002 PIT-014 3403
PIT-002 PIT-015 6736
PIT-002 PIT-016 7797
PIT-002 PIT-017 5479
PIT-002 PIT-018 9189
PIT-002 PIT-019 1372
PIT-002 PIT-020 4367
PIT-003 PIT-004 9601
PIT-003 PIT-005 6529
PIT-003 PIT-006 1255
PIT-003 PIT-007 2524
PIT-003 PIT-008 5562
PIT-003 PIT-009 5222
PIT-003 PIT-010 998
PIT-003 PIT-011 8214
PIT-003 PIT-012 3623
PIT-003 PIT-013 5083
PIT-003 PIT-014 470
PIT-003 PIT-015 6274
PIT-003 PIT-016 7125
PIT-003 PIT-017 6897
PIT-003 PIT-018 1281
PIT-003 PIT-019 9852
PIT-003 PIT-020 8675
PIT-004 PIT-005 6886
PIT-004 PIT-006 456
PIT-004 PIT-007 4762
PIT-004 PIT-008 5580
PIT-004 PIT-009 5893
PIT-004 PIT-010 3720
PIT-004 PIT-011 6098
PIT-004 PIT-012 8211
PIT-004 PIT-013 7543
PIT-004 PIT-014 6081
PIT-004 PIT-015 9590
PIT-004 PIT-016 4647
PIT-004 PIT-017 5801
PIT-004 PIT-018 9606
PIT-004 PIT-019 2766
PIT-004 PIT-020 5154
PIT-005 PIT-006 7815
PIT-005 PIT-007 3318
PIT-005 PIT-008 2698
PIT-005 PIT-009 8343
PIT-005 PIT-010 3150
PIT-005 PIT-011 8051
PIT-005 PIT-012 5387
PIT-005 PIT-013 5225
PIT-005 PIT-014 3237
PIT-005 PIT-015 6158
PIT-005 PIT-016 2743
PIT-005 PIT-017 8072
PIT-005 PIT-018 2154
PIT-005 PIT-019 7430
PIT-005 PIT-020 3015
PIT-006 PIT-007 3927
PIT-006 PIT-008 970
PIT-006 PIT-009 5107
PIT-006 PIT-010 9473
PIT-006 PIT-011 771
PIT-006 PIT-012 6491
PIT-006 PIT-013 33
PIT-006 PIT-014 5768
PIT-006 PIT-015 1480
PIT-006 PIT-016 2144
PIT-006 PIT-017 3695
PIT-006 PIT-018 8603
PIT-006 PIT-019 2669
PIT-006 PIT-020 4192
PIT-007 PIT-008 8087
PIT-007 PIT-009 3979
PIT-007 PIT-010 3726
PIT-007 PIT-011 2743
PIT-007 PIT-012 9232
PIT-007 PIT-013 217
PIT-007 PIT-014 4633
PIT-007 PIT-015 1088
PIT-007 PIT-016 2993
PIT-007 PIT-017 3154
PIT-007 PIT-018 8646
PIT-007 PIT-019 2484
PIT-007 PIT-020 4101
PIT-008 PIT-009 8297
PIT-008 PIT-010 9313
PIT-008 PIT-011 4124
PIT-008 PIT-012 8629
PIT-008 PIT-013 4267
PIT-008 PIT-014 7456
PIT-008 PIT-015 9067
PIT-008 PIT-016 4293
PIT-008 PIT-017 7649
PIT-008 PIT-018 7310
PIT-008 PIT-019 8391
PIT-008 PIT-020 3848
PIT-009 PIT-010 3381
PIT-009 PIT-011 6493
PIT-009 PIT-012 4667
PIT-009 PIT-013 2612
PIT-009 PIT-014 7146
PIT-009 PIT-015 9488
PIT-009 PIT-016 678
PIT-009 PIT-017 8957
PIT-009 PIT-018 8025
PIT-009 PIT-019 1089
PIT-009 PIT-020 2631
PIT-010 PIT-011 4976
PIT-010 PIT-012 5045
PIT-010 PIT-013 5178
PIT-010 PIT-014 8014
PIT-010 PIT-015 5851
PIT-010 PIT-016 357
PIT-010 PIT-017 5471
PIT-010 PIT-018 4935
PIT-010 PIT-019 9617
PIT-010 PIT-020 2907
PIT-011 PIT-012 1515
PIT-011 PIT-013 1778
PIT-011 PIT-014 1773
PIT-011 PIT-015 8704
PIT-011 PIT-016 3318
PIT-011 PIT-017 5180
PIT-011 PIT-018 582
PIT-011 PIT-019 9573
PIT-011 PIT-020 7458
PIT-012 PIT-013 6710
PIT-012 PIT-014 2171
PIT-012 PIT-015 9788
PIT-012 PIT-016 2127
PIT-012 PIT-017 7630
PIT-012 PIT-018 8959
PIT-012 PIT-019 5590
PIT-012 PIT-020 7108
PIT-013 PIT-014 9409
PIT-013 PIT-015 9030
PIT-013 PIT-016 3654
PIT-013 PIT-017 714
PIT-013 PIT-018 118
PIT-013 PIT-019 7472
PIT-013 PIT-020 1517
PIT-014 PIT-015 890
PIT-014 PIT-016 2776
PIT-014 PIT-017 7240
PIT-014 PIT-018 2120
PIT-014 PIT-019 3314
PIT-014 PIT-020 7544
PIT-015 PIT-016 6725
PIT-015 PIT-017 587
PIT-015 PIT-018 9877
PIT-015 PIT-019 1254
PIT-015 PIT-020 3023
PIT-016 PIT-017 9444
PIT-016 PIT-018 5608
PIT-016 PIT-019 3084
PIT-016 PIT-020 4228
PIT-017 PIT-018 7387
PIT-017 PIT-019 8076
PIT-017 PIT-020 6686
PIT-018 PIT-019 5275
PIT-018 PIT-020 816
PIT-019 PIT-020 7673
复制代码
作者:
tolilong
时间:
2016-05-07 15:48
本帖最后由 tolilong 于 2016-05-07 15:49 编辑
已经所有点的距离?
作者:
mswsg
时间:
2016-05-07 17:20
本帖最后由 mswsg 于 2016-05-07 17:26 编辑
求大神。。!这个看了一会
一共有20个点, 要求一次经过每个点(点不重复),并且总距离最短。
已经给出任意每个点之间的距离(a,b)=x
第一个点的可能性是20,依次是19 ,18 ,... 3,2,1
。。。。。
作者:
Herowinter
时间:
2016-05-07 18:17
求一条路径最短的哈密尔顿回路,这种题目用shell来解,
真的合适吗?
作者:
patagonia2
时间:
2016-05-09 18:04
回复
2#
tolilong
谢谢大圣指导。
作者:
patagonia2
时间:
2016-05-09 18:05
回复
3#
mswsg
谢谢大神指导。
大神们什么好的代码?
作者:
patagonia2
时间:
2016-05-09 18:08
回复
4#
Herowinter
这数据量也不大,大圣来一发
谢谢大圣指导。
作者:
Herowinter
时间:
2016-05-09 18:16
回复
7#
patagonia2
这个问题远比你想象的复杂, 我算法没学好, 写不来.
维基百科:
寻找哈密顿路的确定算法虽然很难有多项式时间的,但是这并不意味着只能进行时间复杂度为O(n!*n)暴力搜索。
利用状态压缩动态规划,可以将时间复杂度降低到O(2^n*n^3)。
n=20, 优化算法也不简单.
你可以把这题发到一些高级语言的版块(如C++ Java)等, 看看有没有大神能帮你.
作者:
patagonia2
时间:
2016-05-10 15:42
回复
8#
Herowinter
谢谢大圣指导。
作者:
lll1985911
时间:
2016-05-10 20:51
百度文库中搜了一篇文章(关于物流系统方面的)可能有点帮助。
QQ20160510.png
(32.49 KB, 下载次数: 99)
下载附件
2016-05-10 20:51 上传
(我没有发url的权限)
这个是较为典型的哈密尔顿回路问题。
参考A*算法和Dijkstra应该会有一些提示。
严格的说,shell不说不能做,而是shell天生并不是解决这类复杂问题的。
另外针对现代物流系统,我个人认为不能只单单考虑路径长短,货物装卸,堵车概率,海拔高低,都是影响运行成本的因素。
作者:
patagonia2
时间:
2016-05-17 17:29
回复
10#
lll1985911
谢谢大圣指导
作者:
rubyish
时间:
2016-05-29 05:41
本帖最后由 rubyish 于 2017-10-01 20:16 编辑
maybe
output:
21090|20377|19194|17904|17809|16540|
MIN = 16540
PIT-005 > PIT-008 > PIT-006 > PIT-004 > PIT-001 > PIT-009 > PIT-016 > PIT-010 > PIT-003 > PIT-014 > PIT-015 > PIT-017 > PIT-013 > PIT-007 > PIT-019 > PIT-002 > PIT-012 > PIT-011 > PIT-018 > PIT-020
v1: time 2.25s
v2: time 1.35s
v2: perl abc.pl
#!/usr/bin/perl -w
# version 26, subversion 0 (v5.26.0)
use 5.016; # >= 5.016
my @PITS;
my @DISTE;
my $ENDPITS;
my $MIN;
my @TAIL;
my $PATH;
explore();
# ____________________SUB____________________
sub init {
my %dup;
my $i = 0;
while (<DATA>) {
my ( $a, $b, $d ) = split;
$dup{$a} //= $i++;
$dup{$b} //= $i++;
push @DISTE, [ $dup{$a}, $dup{$b}, $d ];
}
@PITS = sort { $dup{$a} <=> $dup{$b} } keys %dup;
@DISTE = sort { $a->[2] <=> $b->[2] } @DISTE;
$ENDPITS = @PITS - 1;
$MIN = $DISTE[-1] * @PITS;
}
sub explore {
init();
E_( 0, 0, 0 );
say "\nMIN = $MIN\n";
echo($PATH);
}
sub tail {
my ( $i, $l, $tail ) = ( @_, 0 );
$tail += $DISTE[$_][2] for $i .. $i + $ENDPITS - $l - 1;
$tail;
}
sub E_ {
my ( $n, $b, $sum ) = @_;
state $MAYBE = [];
state $quek = [ (0) x @PITS ];
if ( $n == $ENDPITS ) {
if ( $MIN > $sum && ok($MAYBE) ) {
$MIN = $sum;
$PATH = [@$MAYBE];
print STDERR "$MIN|";
}
return;
}
for my $i ( $b .. @DISTE - $ENDPITS + $n ) {
return if $sum + ( $TAIL[$i][$n] ||= tail( $i, $n ) ) >= $MIN;
my ( $dit, $dat ) = @{ $DISTE[$i] };
next if $quek->[$dit] > 1 || $quek->[$dat] > 1;
$quek->[$dit]++, $quek->[$dat]++;
$MAYBE->[$n] = $i;
E_( $n + 1, $i + 1, $sum + $DISTE[$i][2] );
$quek->[$dit]--, $quek->[$dat]--;
}
}
sub echo {
my $path = shift;
ok( $path, 1 );
}
sub ok {
my ( $path, $echo ) = @_;
my @that;
for my $p (@$path) {
my ( $a, $b ) = @{ $DISTE[$p] };
push @{ $that[$a] }, $b;
push @{ $that[$b] }, $a;
}
my $start;
for my $t ( 0 .. $#that ) {
return 0 if not defined $that[$t];
next if @{ $that[$t] } == 2;
$start = [$t];
last;
}
my @has;
my @these;
my $go = sub {
my $pits = shift;
for (@$pits) {
next if $has[$_];
push @these, $_;
$has[$_] = 1;
__SUB__->( $that[$_] );
}
};
$go->($start);
return @these == @PITS if !$echo;
say join ' > ', @PITS[@these];
}
__DATA__
PIT-001 PIT-002 9665
PIT-001 PIT-003 5794
PIT-001 PIT-004 96
PIT-001 PIT-005 5750
PIT-001 PIT-006 6394
PIT-001 PIT-007 5750
PIT-001 PIT-008 3478
PIT-001 PIT-009 262
PIT-001 PIT-010 8954
PIT-001 PIT-011 3751
PIT-001 PIT-012 5253
PIT-001 PIT-013 6988
PIT-001 PIT-014 1364
PIT-001 PIT-015 9415
PIT-001 PIT-016 6156
PIT-001 PIT-017 6015
PIT-001 PIT-018 7931
PIT-001 PIT-019 5082
PIT-001 PIT-020 9891
PIT-002 PIT-003 6580
PIT-002 PIT-004 4325
PIT-002 PIT-005 5355
PIT-002 PIT-006 7221
PIT-002 PIT-007 4093
PIT-002 PIT-008 6098
PIT-002 PIT-009 2720
PIT-002 PIT-010 4662
PIT-002 PIT-011 9336
PIT-002 PIT-012 378
PIT-002 PIT-013 4632
PIT-002 PIT-014 3403
PIT-002 PIT-015 6736
PIT-002 PIT-016 7797
PIT-002 PIT-017 5479
PIT-002 PIT-018 9189
PIT-002 PIT-019 1372
PIT-002 PIT-020 4367
PIT-003 PIT-004 9601
PIT-003 PIT-005 6529
PIT-003 PIT-006 1255
PIT-003 PIT-007 2524
PIT-003 PIT-008 5562
PIT-003 PIT-009 5222
PIT-003 PIT-010 998
PIT-003 PIT-011 8214
PIT-003 PIT-012 3623
PIT-003 PIT-013 5083
PIT-003 PIT-014 470
PIT-003 PIT-015 6274
PIT-003 PIT-016 7125
PIT-003 PIT-017 6897
PIT-003 PIT-018 1281
PIT-003 PIT-019 9852
PIT-003 PIT-020 8675
PIT-004 PIT-005 6886
PIT-004 PIT-006 456
PIT-004 PIT-007 4762
PIT-004 PIT-008 5580
PIT-004 PIT-009 5893
PIT-004 PIT-010 3720
PIT-004 PIT-011 6098
PIT-004 PIT-012 8211
PIT-004 PIT-013 7543
PIT-004 PIT-014 6081
PIT-004 PIT-015 9590
PIT-004 PIT-016 4647
PIT-004 PIT-017 5801
PIT-004 PIT-018 9606
PIT-004 PIT-019 2766
PIT-004 PIT-020 5154
PIT-005 PIT-006 7815
PIT-005 PIT-007 3318
PIT-005 PIT-008 2698
PIT-005 PIT-009 8343
PIT-005 PIT-010 3150
PIT-005 PIT-011 8051
PIT-005 PIT-012 5387
PIT-005 PIT-013 5225
PIT-005 PIT-014 3237
PIT-005 PIT-015 6158
PIT-005 PIT-016 2743
PIT-005 PIT-017 8072
PIT-005 PIT-018 2154
PIT-005 PIT-019 7430
PIT-005 PIT-020 3015
PIT-006 PIT-007 3927
PIT-006 PIT-008 970
PIT-006 PIT-009 5107
PIT-006 PIT-010 9473
PIT-006 PIT-011 771
PIT-006 PIT-012 6491
PIT-006 PIT-013 33
PIT-006 PIT-014 5768
PIT-006 PIT-015 1480
PIT-006 PIT-016 2144
PIT-006 PIT-017 3695
PIT-006 PIT-018 8603
PIT-006 PIT-019 2669
PIT-006 PIT-020 4192
PIT-007 PIT-008 8087
PIT-007 PIT-009 3979
PIT-007 PIT-010 3726
PIT-007 PIT-011 2743
PIT-007 PIT-012 9232
PIT-007 PIT-013 217
PIT-007 PIT-014 4633
PIT-007 PIT-015 1088
PIT-007 PIT-016 2993
PIT-007 PIT-017 3154
PIT-007 PIT-018 8646
PIT-007 PIT-019 2484
PIT-007 PIT-020 4101
PIT-008 PIT-009 8297
PIT-008 PIT-010 9313
PIT-008 PIT-011 4124
PIT-008 PIT-012 8629
PIT-008 PIT-013 4267
PIT-008 PIT-014 7456
PIT-008 PIT-015 9067
PIT-008 PIT-016 4293
PIT-008 PIT-017 7649
PIT-008 PIT-018 7310
PIT-008 PIT-019 8391
PIT-008 PIT-020 3848
PIT-009 PIT-010 3381
PIT-009 PIT-011 6493
PIT-009 PIT-012 4667
PIT-009 PIT-013 2612
PIT-009 PIT-014 7146
PIT-009 PIT-015 9488
PIT-009 PIT-016 678
PIT-009 PIT-017 8957
PIT-009 PIT-018 8025
PIT-009 PIT-019 1089
PIT-009 PIT-020 2631
PIT-010 PIT-011 4976
PIT-010 PIT-012 5045
PIT-010 PIT-013 5178
PIT-010 PIT-014 8014
PIT-010 PIT-015 5851
PIT-010 PIT-016 357
PIT-010 PIT-017 5471
PIT-010 PIT-018 4935
PIT-010 PIT-019 9617
PIT-010 PIT-020 2907
PIT-011 PIT-012 1515
PIT-011 PIT-013 1778
PIT-011 PIT-014 1773
PIT-011 PIT-015 8704
PIT-011 PIT-016 3318
PIT-011 PIT-017 5180
PIT-011 PIT-018 582
PIT-011 PIT-019 9573
PIT-011 PIT-020 7458
PIT-012 PIT-013 6710
PIT-012 PIT-014 2171
PIT-012 PIT-015 9788
PIT-012 PIT-016 2127
PIT-012 PIT-017 7630
PIT-012 PIT-018 8959
PIT-012 PIT-019 5590
PIT-012 PIT-020 7108
PIT-013 PIT-014 9409
PIT-013 PIT-015 9030
PIT-013 PIT-016 3654
PIT-013 PIT-017 714
PIT-013 PIT-018 118
PIT-013 PIT-019 7472
PIT-013 PIT-020 1517
PIT-014 PIT-015 890
PIT-014 PIT-016 2776
PIT-014 PIT-017 7240
PIT-014 PIT-018 2120
PIT-014 PIT-019 3314
PIT-014 PIT-020 7544
PIT-015 PIT-016 6725
PIT-015 PIT-017 587
PIT-015 PIT-018 9877
PIT-015 PIT-019 1254
PIT-015 PIT-020 3023
PIT-016 PIT-017 9444
PIT-016 PIT-018 5608
PIT-016 PIT-019 3084
PIT-016 PIT-020 4228
PIT-017 PIT-018 7387
PIT-017 PIT-019 8076
PIT-017 PIT-020 6686
PIT-018 PIT-019 5275
PIT-018 PIT-020 816
PIT-019 PIT-020 7673
复制代码
v1: perl abc.pl
#!/usr/bin/perl
my ( $ord, %ord );
my @dis =
sort { $a->[1] <=> $b->[1] }
map {
my ( $a, $b, $v ) = split;
$ord{$a} //= $ord++;
$ord{$b} //= $ord++;
[ [ $ord{$a}, $ord{$b} ], $v ];
} <DATA>;
my $pits = keys %ord;
my $len = $pits - 1;
my @inv = sort { $ord{$a} <=> $ord{$b} } keys %ord;
my @tl = map [ map 0, 1 .. $len ], 1 .. @dis;
my ( $min, $path ) = $dis[-1][1] * $len;
sub ok {
my ( $a, $r, $x ) = @_;
for my $i ( 0 .. $#$a ) {
$x = $a->[$i][0], $r = [$i], last if @{ $a->[$i] } <= 1;
}
while ( defined $x ) {
push @$r, $x;
$x = $a->[$x][ $a->[$x][0] != $r->[-2] ? 0 : 1 ];
}
@$r == $pits ? $r : ();
}
sub tl {
my ( $i, $l, $tl ) = ( @_, 0 );
$tl += $dis[$_][1] for $i .. $i + $len - $l - 1;
$tl;
}
sub go {
my ( $n, $i, $a, $l, $hd ) = @_;
if ( $n == 0 ) {
if ( my $b = ok $a ) {
$min = $hd;
$path = $b;
print STDERR $min, '|';
}
return;
}
for my $j ( $i .. @dis - $n ) {
last if $hd + ( $tl[$j][$l] ||= tl $j, $l ) >= $min;
my ( $A, $B ) = @{ $dis[$j][0] };
next if @{ $a->[$A] } > 1 or @{ $a->[$B] } > 1;
my $b = [@$a];
$b->[$A] = [ @{ $b->[$A] }, $B ];
$b->[$B] = [ @{ $b->[$B] }, $A ];
go( $n - 1, $j + 1, $b, $l + 1, $hd + $dis[$j][1] );
}
}
my @now = ( $len, 0, [ map [], 0 .. $len ], 0, 0 );
go @now;
print "\nmin = ", $min, $/;
print join( ' > ', @inv[@$path] ), $/;
__DATA__
PIT-001 PIT-002 9665
PIT-001 PIT-003 5794
PIT-001 PIT-004 96
PIT-001 PIT-005 5750
PIT-001 PIT-006 6394
PIT-001 PIT-007 5750
PIT-001 PIT-008 3478
PIT-001 PIT-009 262
PIT-001 PIT-010 8954
PIT-001 PIT-011 3751
PIT-001 PIT-012 5253
PIT-001 PIT-013 6988
PIT-001 PIT-014 1364
PIT-001 PIT-015 9415
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作者:
523066680
时间:
2021-10-10 14:10
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rubyish
Hi Rubyish你的邮箱是多少? 或者有QQ/微信之类的联系方式吗?
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