Transportation problem: Difference between revisions

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m (→‎{{header|Wren}}: Minor tidy)
 
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=={{header|1C}}==
<syntaxhighlight lang="text">// based on the program of <romix>
 
перем m,n; // Table size
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Процедура КомандаРассчитать(Команда)
РешениеТранспортнойЗадачи();
КонецПроцедуры</langsyntaxhighlight>
 
=={{header|C sharp|C#}}==
{{trans|Java}}
<langsyntaxhighlight lang="csharp">using System;
using System.Collections.Generic;
using System.IO;
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}
}
}</langsyntaxhighlight>
{{out}}
<pre>Optimal solution input1.txt
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=={{header|C++}}==
{{trans|Kotlin}}
<langsyntaxhighlight lang="cpp">#include <algorithm>
#include <iomanip>
#include <iostream>
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#include <string>
#include <vector>
#include <cfloat>
 
using namespace std;
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return 0;
}</langsyntaxhighlight>
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<pre>input1.txt
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=={{header|D}}==
{{trans|Java}}
<langsyntaxhighlight lang="d">import std.stdio, std.range, std.algorithm, std.conv, std.math, std.traits;
 
final class Shipment {
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printResult(fileName, demand, supply, costs, matrix);
}
}</langsyntaxhighlight>
{{out}}
<pre>Optimal solution transportation_problem1.txt
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=={{header|Glagol}}==
<syntaxhighlight lang="text">ОТДЕЛ Транспорт+;
ИСПОЛЬЗУЕТ
Вывод ИЗ "...\Отделы\Обмен\",
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ВывестиПлан
 
КОН Транспорт.</langsyntaxhighlight>
 
=== Input ===
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=={{header|Go}}==
{{trans|Java}}
<langsyntaxhighlight lang="go">package main
 
import (
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t.printResult()
}
}</langsyntaxhighlight>
 
{{out}}
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In other words:
 
<langsyntaxhighlight Jlang="j">NB. C's y[m] v= x implemented as x m ndxasgn v y
ndxasgn=: conjunction define
:
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r=. n (<ndxs)} r
end.
)</langsyntaxhighlight>
 
Task data:
 
<langsyntaxhighlight Jlang="j">need=: 20 30 10
supply=: 25 35
cost=:3 5 7,:3 2 5</langsyntaxhighlight>
 
Task example:
 
<langsyntaxhighlight Jlang="j"> need cost trans supply
20 0 5
0 30 5</langsyntaxhighlight>
 
=={{header|Java}}==
{{works with|Java|8}}
<langsyntaxhighlight lang="java">import java.io.File;
import java.util.*;
import static java.util.Arrays.stream;
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}
}
}</langsyntaxhighlight>
 
<pre>input1.txt
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=={{header|Julia}}==
Code taken from [https://github.com/dylanomics/transportation_problem here] using [https://jump.dev/JuMP.jl/stable/ JuMP].
<langsyntaxhighlight lang="julia">using JuMP, GLPK
 
# cost vector
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λ = [JuMP.dual(C1[1]),JuMP.dual(C1[2])]
μ = [JuMP.dual(C2[1]),JuMP.dual(C2[2]),JuMP.dual(C2[3])]
</syntaxhighlight>
</lang>
 
{{out}}
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=={{header|Kotlin}}==
{{trans|Java}}
<langsyntaxhighlight lang="scala">// version 1.1.51
 
import java.io.File
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}
}
}</langsyntaxhighlight>
 
{{out}}
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=={{header|Nim}}==
{{trans|Go}}
<langsyntaxhighlight Nimlang="nim">import fenv, lists, math, sequtils, strformat, strutils
 
type
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tr.northWestCornerRule()
tr.steppingStone()
tr.printResult()</langsyntaxhighlight>
 
{{out}}
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=={{header|Pascal}}==
<langsyntaxhighlight lang="pascal">Program transport;
{ based on the program of <Svetlana Belashova> }
 
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GotoXY(40,1);
l1: d:=ReadKey;
END.</langsyntaxhighlight>
 
=={{header|Perl}}==
Just re-using the code from [[Vogel's_approximation_method#Perl|Vogel's approximation method]], tweaked to handle specific input:
<syntaxhighlight lang="perl">use strict;
use warnings;
use feature 'say';
use List::AllUtils qw( max_by nsort_by min );
 
my $data = <<END;
A=20 B=30 C=10
S=25 T=35
AS=3 BS=5 CS=7
CT=3 BT=2 CT=5
END
 
my $table = sprintf +('%4s' x 4 . "\n") x 3,
map {my $t = $_; map "$_$t", '', 'A' .. 'C' } '' , 'S' .. 'T';
 
my ($cost, %assign) = (0);
while( $data =~ /\b\w=\d/ ) {
my @penalty;
for ( $data =~ /\b(\w)=\d/g ) {
my @all = map /(\d+)/, nsort_by { /\d+/ && $& }
grep { my ($t, $c) = /(.)(.)=/; $data =~ /\b$c=\d/ and $data =~ /\b$t=\d/ }
$data =~ /$_\w=\d+|\w$_=\d+/g;
push @penalty, [ $_, ($all[1] // 0) - $all[0] ];
}
my $rc = (max_by { $_->[1] } nsort_by
{ my $x = $_->[0]; $data =~ /(?:$x\w|\w$x)=(\d+)/ && $1 } @penalty)->[0];
my @lowest = nsort_by { /\d+/ && $& }
grep { my ($t, $c) = /(.)(.)=/; $data =~ /\b$c=\d/ and $data =~ /\b$t=\d/ }
$data =~ /$rc\w=\d+|\w$rc=\d+/g;
my ($t, $c) = $lowest[0] =~ /(.)(.)/;
my $allocate = min $data =~ /\b[$t$c]=(\d+)/g;
$table =~ s/$t$c/ sprintf "%2d", $allocate/e;
$cost += $data =~ /$t$c=(\d+)/ && $1 * $allocate;
$data =~ s/\b$_=\K\d+/ $& - $allocate || '' /e for $t, $c;
}
 
say my $result = "cost $cost\n\n" . $table =~ s/[A-Z]{2}/--/gr;</syntaxhighlight>
{{out}}
<pre>cost 170
 
A B C
S 20 -- 5
T -- 30 5</pre>
 
=={{header|Phix}}==
The simplest solution I could think of.<br>
Assumes 0 cost is not allowed, but using say -1 as the "done" cost instead should be fine.
<!--<syntaxhighlight lang="phix">(phixonline)-->
<lang Phix>procedure solve(sequence needs, avail, costs)
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
sequence res = repeat(repeat(0,length(needs)),length(avail))
<span style="color: #008080;">procedure</span> <span style="color: #000000;">solve</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">needs</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">avail</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">costs</span><span style="color: #0000FF;">)</span>
while true do
<span style="color: #000080;font-style:italic;">-- the costs parameter should be length(avail/*aka suppliers*/) rows
integer best = 0, supplier, customer
-- for s=1 to of length(costsneeds/*aka customers*/) docols</span>
<span style="color: #7060A8;">assert</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">costs</span><span style="color: #0000FF;">)==</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">avail</span><span style="color: #0000FF;">))</span>
for c=1 to length(costs[s]) do
<span style="color: #7060A8;">assert</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">apply</span><span style="color: #0000FF;">(</span><span style="color: #000000;">costs</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">)==</span><span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">needs</span><span style="color: #0000FF;">),</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">avail</span><span style="color: #0000FF;">)))</span>
integer csc = costs[s][c]
<span style="color: #004080;">sequence</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">needs</span><span style="color: #0000FF;">)),</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">avail</span><span style="color: #0000FF;">))</span>
if csc!=0 and (best=0 or csc<best) then
<span style="color: #008080;">while</span> <span style="color: #004600;">true</span> <span style="color: #008080;">do</span>
best = csc
<span style="color: #004080;">integer</span> <span style="color: #000000;">best</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">supplier</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">customer</span>
supplier = s
<span style="color: #008080;">for</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">costs</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
customer = c
<span style="color: #008080;">for</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">costs</span><span style="color: #0000FF;">[</span><span style="color: #000000;">s</span><span style="color: #0000FF;">])</span> <span style="color: #008080;">do</span>
end if
<span style="color: #004080;">integer</span> <span style="color: #000000;">csc</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">costs</span><span style="color: #0000FF;">[</span><span style="color: #000000;">s</span><span style="color: #0000FF;">][</span><span style="color: #000000;">c</span><span style="color: #0000FF;">]</span>
end for
<span style="color: #008080;">if</span> <span style="color: #000000;">csc</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">0</span> <span style="color: #008080;">and</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">best</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">or</span> <span style="color: #000000;">csc</span><span style="color: #0000FF;"><</span><span style="color: #000000;">best</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
end for
<span style="color: #000000;">best</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">csc</span>
if best=0 then exit end if -- all costs examined
<span style="color: #000000;">supplier</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">s</span>
integer amt = min(avail[supplier],needs[customer])
<span style="color: #000000;">customer</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">c</span>
-- obviously amt can be 0, in which case this just
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
-- removes cost entry from further consideration.
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
avail[supplier] -= amt
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
needs[customer] -= amt
<span style="color: #008080;">if</span> <span style="color: #000000;">best</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #008080;">exit</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> <span style="color: #000080;font-style:italic;">-- all costs examined</span>
res[supplier,customer] = amt
<span style="color: #004080;">integer</span> <span style="color: #000000;">amt</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">min</span><span style="color: #0000FF;">(</span><span style="color: #000000;">avail</span><span style="color: #0000FF;">[</span><span style="color: #000000;">supplier</span><span style="color: #0000FF;">],</span><span style="color: #000000;">needs</span><span style="color: #0000FF;">[</span><span style="color: #000000;">customer</span><span style="color: #0000FF;">])</span>
costs[supplier,customer] = 0
<span style="color: #000080;font-style:italic;">-- obviously amt can be 0, in which case this just
end while
-- removes cost entry from further consideration.</span>
pp(res,{pp_Nest,1})
<span style="color: #000000;">avail</span><span style="color: #0000FF;">[</span><span style="color: #000000;">supplier</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">-=</span> <span style="color: #000000;">amt</span>
end procedure
<span style="color: #000000;">needs</span><span style="color: #0000FF;">[</span><span style="color: #000000;">customer</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">-=</span> <span style="color: #000000;">amt</span>
 
<span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">supplier</span><span style="color: #0000FF;">,</span><span style="color: #000000;">customer</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">amt</span>
constant needs = {20,30,10}, -- (customers)
<span style="color: #000000;">costs</span><span style="color: #0000FF;">[</span><span style="color: #000000;">supplier</span><span style="color: #0000FF;">,</span><span style="color: #000000;">customer</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
avail = {25,35}, -- (suppliers)
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
costs = {{3,5,7}, -- (length suppliers rows of
<span style="color: #7060A8;">pp</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">,{</span><span style="color: #004600;">pp_Nest</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">})</span>
{3,2,5}} -- length customers columns)
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
 
solve(needs,avail,costs)</lang>
<span style="color: #000000;">solve</span><span style="color: #0000FF;">({</span><span style="color: #000000;">20</span><span style="color: #0000FF;">,</span><span style="color: #000000;">30</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">25</span><span style="color: #0000FF;">,</span><span style="color: #000000;">35</span><span style="color: #0000FF;">},{{</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">7</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5</span><span style="color: #0000FF;">}})</span>
<!--</syntaxhighlight>-->
{{out}}
<pre>
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Obviously I did not really quite understand the problem when I rattled out the above... this does much better.
{{trans|Go}}
<!--<syntaxhighlight lang="phix">(phixonline)-->
<lang Phix>-- demo\rosetta\Transportation_problem.exw
<span style="color: #000080;font-style:italic;">-- demo\rosetta\Transportation_problem.exw</span>
enum QTY, COST, R, C -- (a shipment)
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
constant eps = 1e-12
<span style="color: #008080;">enum</span> <span style="color: #000000;">QTY</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">COST</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">R</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">C</span> <span style="color: #000080;font-style:italic;">-- (a shipment)</span>
<span style="color: #008080;">constant</span> <span style="color: #000000;">eps</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1e-12</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">print_matrix</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">matrix</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">total_costs</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0.0</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">matrix</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">matrix</span><span style="color: #0000FF;">[</span><span style="color: #000000;">r</span><span style="color: #0000FF;">])</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">object</span> <span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">matrix</span><span style="color: #0000FF;">[</span><span style="color: #000000;">r</span><span style="color: #0000FF;">][</span><span style="color: #000000;">c</span><span style="color: #0000FF;">]</span>
<span style="color: #004080;">string</span> <span style="color: #000000;">st</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">" - "</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">0</span> <span style="color: #008080;">and</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">R</span><span style="color: #0000FF;">]==</span><span style="color: #000000;">r</span> <span style="color: #008080;">and</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">C</span><span style="color: #0000FF;">]==</span><span style="color: #000000;">c</span> <span style="color: #008080;">then</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">qty</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">round</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">QTY</span><span style="color: #0000FF;">])</span> <span style="color: #000080;font-style:italic;">-- (remove +/-eps)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">qty</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">st</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sprintf</span><span style="color: #0000FF;">(</span><span style="color: #008000;">" %3d "</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">qty</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">total_costs</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">qty</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">COST</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #7060A8;">puts</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">st</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"\n"</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">total_costs</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">procedure</span> <span style="color: #000000;">print_result</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">transport</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">atom</span> <span style="color: #000000;">expected</span><span style="color: #0000FF;">)</span>
function print_matrix(sequence matrix)
<span style="color: #004080;">sequence</span> <span style="color: #000000;">matrix</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">transport</span><span style="color: #0000FF;">[</span><span style="color: #000000;">4</span><span style="color: #0000FF;">]</span>
atom total_costs = 0.0
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"Optimal solution\n\n"</span><span style="color: #0000FF;">)</span>
for r=1 to length(matrix) do
<span style="color: #004080;">atom</span> <span style="color: #000000;">total_costs</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">print_matrix</span><span style="color: #0000FF;">(</span><span style="color: #000000;">matrix</span><span style="color: #0000FF;">)</span>
for c=1 to length(matrix[r]) do
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"\nTotal costs: %g (expected %g)\n\n"</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">total_costs</span><span style="color: #0000FF;">,</span><span style="color: #000000;">expected</span><span style="color: #0000FF;">})</span>
object s = matrix[r][c]
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
string st = " - "
if s!=0 and s[R]==r and s[C]==c then
atom qty = round(s[QTY]) -- (remove +/-eps)
if qty!=0 then
st = sprintf(" %3d ", qty)
total_costs += qty * s[COST]
end if
end if
puts(1,st)
end for
printf(1,"\n")
end for
return total_costs
end function
 
procedure print_result(sequence transport, atom expected)
sequence matrix = transport[4]
printf(1,"Optimal solution\n\n")
atom total_costs = print_matrix(matrix)
printf(1,"\nTotal costs: %g (expected %g)\n\n", {total_costs,expected})
end procedure
 
function get_neighbors(sequence shipment, lst)
sequence nbrs = {0,0}
for e=1 to length(lst) do
sequence o = lst[e]
if o!=shipment then
if o[R]==shipment[R] and nbrs[1]==0 then
nbrs[1] = o
elsif o[C]==shipment[C] and nbrs[2]==0 then
nbrs[2] = o
end if
if nbrs[1]!=0 and nbrs[2]!=0 then
exit
end if
end if
end for
return nbrs
end function
 
function matrix_to_list(sequence matrix)
sequence l = {}
for r=1 to length(matrix) do
for c=1 to length(matrix[r]) do
if matrix[r,c]!=0 then
l = append(l,matrix[r,c])
end if
end for
end for
return l
end function
 
function get_closed_path(sequence matrix, shipment)
sequence path = matrix_to_list(matrix)
path = prepend(path,shipment)
 
-- remove (and keep removing) elements that do not have a
-- vertical AND horizontal neighbor
while true do
integer removals = 0
for e=length(path) to 1 by -1 do
sequence nbrs = get_neighbors(path[e], path)
if nbrs[1]==0 or nbrs[2]==0 then
path[e..e] = {}
removals += 1
end if
end for
if removals==0 then exit end if
end while
<span style="color: #008080;">function</span> <span style="color: #000000;">get_neighbors</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">shipment</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">lst</span><span style="color: #0000FF;">)</span>
-- place the remaining elements in the correct plus-minus order
<span style="color: #004080;">sequence</span> <span style="color: #000000;">nbrs</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">}</span>
sequence stones = repeat(0,length(path)),
<span style="color: #008080;">for</span> <span style="color: #000000;">e</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">lst</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
prev = shipment
<span style="color: #004080;">sequence</span> <span style="color: #000000;">o</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">lst</span><span style="color: #0000FF;">[</span><span style="color: #000000;">e</span><span style="color: #0000FF;">]</span>
for i=1 to length(stones) do
<span style="color: #008080;">if</span> <span style="color: #000000;">o</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">shipment</span> <span style="color: #008080;">then</span>
stones[i] = prev
<span style="color: #008080;">if</span> <span style="color: #000000;">o</span><span style="color: #0000FF;">[</span><span style="color: #000000;">R</span><span style="color: #0000FF;">]==</span><span style="color: #000000;">shipment</span><span style="color: #0000FF;">[</span><span style="color: #000000;">R</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">and</span> <span style="color: #000000;">nbrs</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]==</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
prev = get_neighbors(prev, path)[mod(i,2)+1]
<span style="color: #000000;">nbrs</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">o</span>
end for
<span style="color: #008080;">elsif</span> <span style="color: #000000;">o</span><span style="color: #0000FF;">[</span><span style="color: #000000;">C</span><span style="color: #0000FF;">]==</span><span style="color: #000000;">shipment</span><span style="color: #0000FF;">[</span><span style="color: #000000;">C</span><span style="color: #0000FF;">]</span> <span style="color: #008080;">and</span> <span style="color: #000000;">nbrs</span><span style="color: #0000FF;">[</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]==</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
return stones
<span style="color: #000000;">nbrs</span><span style="color: #0000FF;">[</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">o</span>
end function
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">nbrs</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]!=</span><span style="color: #000000;">0</span> <span style="color: #008080;">and</span> <span style="color: #000000;">nbrs</span><span style="color: #0000FF;">[</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]!=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
<span style="color: #008080;">exit</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">nbrs</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">matrix_to_list</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">matrix</span><span style="color: #0000FF;">)</span>
function fix_degenerate_case(sequence matrix, costs)
<span style="color: #004080;">sequence</span> <span style="color: #000000;">l</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span>
if length(matrix)+length(matrix[1])-1 != length(matrix_to_list(matrix)) then
<span style="color: #008080;">for</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">matrix</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
printf(1,"fixing degenerate case...\n")
<span style="color: #008080;">for</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">matrix</span><span style="color: #0000FF;">[</span><span style="color: #000000;">r</span><span style="color: #0000FF;">])</span> <span style="color: #008080;">do</span>
for r=1 to length(matrix) do
<span style="color: #008080;">if</span> <span style="color: #000000;">matrix</span><span style="color: #0000FF;">[</span><span style="color: #000000;">r</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">]!=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
for c=1 to length(matrix[r]) do
<span style="color: #000000;">l</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">l</span><span style="color: #0000FF;">,</span><span style="color: #000000;">matrix</span><span style="color: #0000FF;">[</span><span style="color: #000000;">r</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">])</span>
if matrix[r][c] == 0 then
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
sequence dummy = {eps, costs[r][c], r, c}
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
if length(get_closed_path(matrix,dummy)) == 0 then
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
matrix[r][c] = dummy
<span style="color: #008080;">return</span> <span style="color: #000000;">l</span>
return matrix
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
end if
end if
end for
end for
?9/0 -- ??
end if
return matrix
end function
 
function initialise(sequence tests, integer t)
sequence {src,dst,costs} = tests[t]
string cs = ppf(costs,{pp_Nest,1,pp_StrFmt,3,pp_IntCh,false,pp_Indent,7})
printf(1,"test %d:\nsrc: %v,\ndst: %v,\ncosts: %s\n",{t,src,dst,cs})
<span style="color: #008080;">function</span> <span style="color: #000000;">get_closed_path</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">matrix</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">shipment</span><span style="color: #0000FF;">)</span>
-- check for and fix any imbalance
<span style="color: #004080;">sequence</span> <span style="color: #000000;">path</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">matrix_to_list</span><span style="color: #0000FF;">(</span><span style="color: #000000;">matrix</span><span style="color: #0000FF;">)</span>
atom totalSrc = sum(src),
<span style="color: #000000;">path</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">prepend</span><span style="color: #0000FF;">(</span><span style="color: #000000;">path</span><span style="color: #0000FF;">,</span><span style="color: #000000;">shipment</span><span style="color: #0000FF;">)</span>
totalDst = sum(dst),
diff = totalSrc-totalDst
if diff>0 then
puts(1,"adding dummy consumer...\n")
dst = append(dst, diff)
for i=1 to length(costs) do
costs[i] &= 0
end for
elsif diff<0 then
puts(1,"adding dummy supplier...\n")
src = append(src, -diff)
costs = append(costs,repeat(0,length(dst)))
end if
<span style="color: #000080;font-style:italic;">-- remove (and keep removing) elements that do not have a
printf(1,"generating initial feasible solution using northwest corner method...\n")
-- vertical AND horizontal neighbor</span>
sequence matrix = repeat(repeat(0,length(dst)),length(src))
<span style="color: #008080;">while</span> <span style="color: #004600;">true</span> <span style="color: #008080;">do</span>
integer northwest = 1
<span style="color: #004080;">integer</span> <span style="color: #000000;">removals</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
for r=1 to length(src) do
<span style="color: #008080;">for</span> <span style="color: #000000;">e</span><span style="color: #0000FF;">=</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">path</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">to</span> <span style="color: #000000;">1</span> <span style="color: #008080;">by</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
for c=northwest to length(dst) do
<span style="color: #004080;">sequence</span> <span style="color: #000000;">nbrs</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">get_neighbors</span><span style="color: #0000FF;">(</span><span style="color: #000000;">path</span><span style="color: #0000FF;">[</span><span style="color: #000000;">e</span><span style="color: #0000FF;">],</span> <span style="color: #000000;">path</span><span style="color: #0000FF;">)</span>
atom qty = min(src[r],dst[c])
<span style="color: #008080;">if</span> <span style="color: #000000;">nbrs</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]==</span><span style="color: #000000;">0</span> <span style="color: #008080;">or</span> <span style="color: #000000;">nbrs</span><span style="color: #0000FF;">[</span><span style="color: #000000;">2</span><span style="color: #0000FF;">]==</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
if qty>0 then
<span style="color: #000000;">path</span><span style="color: #0000FF;">[</span><span style="color: #000000;">e</span><span style="color: #0000FF;">..</span><span style="color: #000000;">e</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span>
matrix[r][c] = {qty,costs[r,c],r,c}
<span style="color: #000000;">removals</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span>
src[r] -= qty
<span style="color: #008080;">end</span> dst[c]<span -style="color: qty#008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
if src[r]=0 then
<span style="color: #008080;">if</span> <span style="color: #000000;">removals</span><span style="color: #0000FF;">==</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> <span style="color: #008080;">exit</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
northwest = c
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
exit
end if
<span style="color: #000080;font-style:italic;">-- place the remaining elements in the correct plus-minus order</span>
end if
<span style="color: #004080;">sequence</span> <span style="color: #000000;">stones</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">path</span><span style="color: #0000FF;">)),</span>
end for
<span style="color: #000000;">prev</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">shipment</span>
end for
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">stones</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
printf(1,"\nTotal costs: %g\n\n", print_matrix(matrix))
<span style="color: #000000;">stones</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">prev</span>
<span style="color: #000000;">prev</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">get_neighbors</span><span style="color: #0000FF;">(</span><span style="color: #000000;">prev</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">path</span><span style="color: #0000FF;">)[</span><span style="color: #7060A8;">mod</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span>
return {src,dst,costs,matrix}
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
end function
<span style="color: #008080;">return</span> <span style="color: #000000;">stones</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">fix_degenerate_case</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">matrix</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">costs</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">matrix</span><span style="color: #0000FF;">)+</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">matrix</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">])-</span><span style="color: #000000;">1</span> <span style="color: #0000FF;">!=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">matrix_to_list</span><span style="color: #0000FF;">(</span><span style="color: #000000;">matrix</span><span style="color: #0000FF;">))</span> <span style="color: #008080;">then</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"fixing degenerate case...\n"</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">matrix</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">matrix</span><span style="color: #0000FF;">[</span><span style="color: #000000;">r</span><span style="color: #0000FF;">])</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">matrix</span><span style="color: #0000FF;">[</span><span style="color: #000000;">r</span><span style="color: #0000FF;">][</span><span style="color: #000000;">c</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">==</span> <span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">dummy</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">eps</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">costs</span><span style="color: #0000FF;">[</span><span style="color: #000000;">r</span><span style="color: #0000FF;">][</span><span style="color: #000000;">c</span><span style="color: #0000FF;">],</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">}</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">get_closed_path</span><span style="color: #0000FF;">(</span><span style="color: #000000;">matrix</span><span style="color: #0000FF;">,</span><span style="color: #000000;">dummy</span><span style="color: #0000FF;">))</span> <span style="color: #0000FF;">==</span> <span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">matrix</span><span style="color: #0000FF;">[</span><span style="color: #000000;">r</span><span style="color: #0000FF;">][</span><span style="color: #000000;">c</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">dummy</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">matrix</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #0000FF;">?</span><span style="color: #000000;">9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">0</span> <span style="color: #000080;font-style:italic;">-- ??</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">matrix</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">initialise</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">tests</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">integer</span> <span style="color: #000000;">t</span><span style="color: #0000FF;">)</span>
function stepping_stone(sequence transport)
<span style="color: #004080;">sequence</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">src</span><span style="color: #0000FF;">,</span><span style="color: #000000;">dst</span><span style="color: #0000FF;">,</span><span style="color: #000000;">costs</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">deep_copy</span><span style="color: #0000FF;">(</span><span style="color: #000000;">tests</span><span style="color: #0000FF;">[</span><span style="color: #000000;">t</span><span style="color: #0000FF;">])</span>
sequence {src, dst, costs, matrix} = transport
<span style="color: #004080;">string</span> <span style="color: #000000;">cs</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">ppf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">costs</span><span style="color: #0000FF;">,{</span><span style="color: #004600;">pp_Nest</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #004600;">pp_StrFmt</span><span style="color: #0000FF;">,</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span><span style="color: #004600;">pp_IntCh</span><span style="color: #0000FF;">,</span><span style="color: #004600;">false</span><span style="color: #0000FF;">,</span><span style="color: #004600;">pp_Indent</span><span style="color: #0000FF;">,</span><span style="color: #000000;">7</span><span style="color: #0000FF;">})</span>
atom maxReduction = 0
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"test %d:\nsrc: %v,\ndst: %v,\ncosts: %s\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span><span style="color: #000000;">src</span><span style="color: #0000FF;">,</span><span style="color: #000000;">dst</span><span style="color: #0000FF;">,</span><span style="color: #000000;">cs</span><span style="color: #0000FF;">})</span>
object move = NULL, leaving
matrix = fix_degenerate_case(matrix, costs)
<span style="color: #000080;font-style:italic;">-- check for and fix any imbalance</span>
for r=1 to length(src) do
<span style="color: #004080;">atom</span> <span style="color: #000000;">totalSrc</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sum</span><span style="color: #0000FF;">(</span><span style="color: #000000;">src</span><span style="color: #0000FF;">),</span>
for c=1 to length(dst) do
<span style="color: #000000;">totalDst</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sum</span><span style="color: #0000FF;">(</span><span style="color: #000000;">dst</span><span style="color: #0000FF;">),</span>
if matrix[r][c] = 0 then
<span style="color: #000000;">diff</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">totalSrc</span><span style="color: #0000FF;">-</span><span style="color: #000000;">totalDst</span>
sequence trial_shipment = {0, costs[r][c], r, c},
<span style="color: #008080;">if</span> <span style="color: #000000;">diff</span><span style="color: #0000FF;">></span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
path = get_closed_path(matrix,trial_shipment)
<span style="color: #7060A8;">puts</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"adding dummy consumer...\n"</span><span style="color: #0000FF;">)</span>
atom reduction = 0.0,
<span style="color: #000000;">dst</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">dst</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">diff</span><span style="color: #0000FF;">)</span>
lowestQuantity = 1e308
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">costs</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
object leavingCandidate = 0
<span style="color: #000080;font-style:italic;">--DEV...
bool plus = true
-- costs[i] for i&=1 to length(path) do0</span>
<span style="color: #000000;">costs</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">deep_copy</span><span style="color: #0000FF;">(</span><span style="color: #000000;">costs</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">])</span> <span style="color: #0000FF;">&</span> <span style="color: #000000;">0</span>
sequence s = path[i]
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
if plus then
<span style="color: #008080;">elsif</span> <span style="color: #000000;">diff</span><span style="color: #0000FF;"><</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
reduction += s[COST]
<span style="color: #7060A8;">puts</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"adding dummy supplier...\n"</span><span style="color: #0000FF;">)</span>
else
<span style="color: #000000;">src</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">src</span><span style="color: #0000FF;">,</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">diff</span><span style="color: #0000FF;">)</span>
reduction -= s[COST]
<span style="color: #000000;">costs</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">costs</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">dst</span><span style="color: #0000FF;">)))</span>
if s[QTY] < lowestQuantity then
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
leavingCandidate = s
lowestQuantity = s[QTY]
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"generating initial feasible solution using northwest corner method...\n"</span><span style="color: #0000FF;">)</span>
end if
<span style="color: #004080;">sequence</span> <span style="color: #000000;">matrix</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">dst</span><span style="color: #0000FF;">)),</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">src</span><span style="color: #0000FF;">))</span>
end if
<span style="color: #004080;">integer</span> <span style="color: #000000;">northwest</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span>
plus = not plus
<span style="color: #008080;">for</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">src</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
end for
<span style="color: #008080;">for</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">=</span><span style="color: #000000;">northwest</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">dst</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
if reduction < maxReduction then
<span style="color: #004080;">atom</span> <span style="color: #000000;">qty</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">min</span><span style="color: #0000FF;">(</span><span style="color: #000000;">src</span><span style="color: #0000FF;">[</span><span style="color: #000000;">r</span><span style="color: #0000FF;">],</span><span style="color: #000000;">dst</span><span style="color: #0000FF;">[</span><span style="color: #000000;">c</span><span style="color: #0000FF;">])</span>
move = path
<span style="color: #008080;">if</span> <span style="color: #000000;">qty</span><span style="color: #0000FF;">></span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
leaving = leavingCandidate
<span style="color: #000000;">matrix</span><span style="color: #0000FF;">[</span><span style="color: #000000;">r</span><span style="color: #0000FF;">][</span><span style="color: #000000;">c</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">qty</span><span style="color: #0000FF;">,</span><span style="color: #000000;">costs</span><span style="color: #0000FF;">[</span><span style="color: #000000;">r</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">],</span><span style="color: #000000;">r</span><span style="color: #0000FF;">,</span><span style="color: #000000;">c</span><span style="color: #0000FF;">}</span>
maxReduction = reduction
<span style="color: #000000;">src</span><span style="color: #0000FF;">[</span><span style="color: #000000;">r</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">-=</span> <span style="color: #000000;">qty</span>
end if
<span style="color: #000000;">dst</span><span style="color: #0000FF;">[</span><span style="color: #000000;">c</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">-=</span> <span style="color: #000000;">qty</span>
end if
<span style="color: #008080;">if</span> <span style="color: #000000;">src</span><span style="color: #0000FF;">[</span><span style="color: #000000;">r</span><span style="color: #0000FF;">]=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
end for
<span style="color: #000000;">northwest</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">c</span>
end for
<span style="color: #008080;">exit</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"\nTotal costs: %g\n\n"</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">print_matrix</span><span style="color: #0000FF;">(</span><span style="color: #000000;">matrix</span><span style="color: #0000FF;">))</span>
<span style="color: #008080;">return</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">src</span><span style="color: #0000FF;">,</span><span style="color: #000000;">dst</span><span style="color: #0000FF;">,</span><span style="color: #000000;">costs</span><span style="color: #0000FF;">,</span><span style="color: #000000;">matrix</span><span style="color: #0000FF;">}</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">stepping_stone</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">transport</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">sequence</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">src</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">dst</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">costs</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">matrix</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">deep_copy</span><span style="color: #0000FF;">(</span><span style="color: #000000;">transport</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">maxReduction</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
<span style="color: #004080;">object</span> <span style="color: #000000;">move</span> <span style="color: #0000FF;">=</span> <span style="color: #004600;">NULL</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">leaving</span>
<span style="color: #000000;">matrix</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">fix_degenerate_case</span><span style="color: #0000FF;">(</span><span style="color: #000000;">matrix</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">costs</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">src</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">dst</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">matrix</span><span style="color: #0000FF;">[</span><span style="color: #000000;">r</span><span style="color: #0000FF;">][</span><span style="color: #000000;">c</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">trial_shipment</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">costs</span><span style="color: #0000FF;">[</span><span style="color: #000000;">r</span><span style="color: #0000FF;">][</span><span style="color: #000000;">c</span><span style="color: #0000FF;">],</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">},</span>
<span style="color: #000000;">path</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">get_closed_path</span><span style="color: #0000FF;">(</span><span style="color: #000000;">matrix</span><span style="color: #0000FF;">,</span><span style="color: #000000;">trial_shipment</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">reduction</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0.0</span><span style="color: #0000FF;">,</span>
<span style="color: #000000;">lowestQuantity</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1e308</span>
<span style="color: #004080;">object</span> <span style="color: #000000;">leavingCandidate</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
<span style="color: #004080;">bool</span> <span style="color: #000000;">plus</span> <span style="color: #0000FF;">=</span> <span style="color: #004600;">true</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">path</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">path</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">plus</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">reduction</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">COST</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">else</span>
<span style="color: #000000;">reduction</span> <span style="color: #0000FF;">-=</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">COST</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">QTY</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;"><</span> <span style="color: #000000;">lowestQuantity</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">leavingCandidate</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">s</span>
<span style="color: #000000;">lowestQuantity</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">QTY</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">plus</span> <span style="color: #0000FF;">=</span> <span style="color: #008080;">not</span> <span style="color: #000000;">plus</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">reduction</span> <span style="color: #0000FF;"><</span> <span style="color: #000000;">maxReduction</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">move</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">path</span>
<span style="color: #000000;">leaving</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">leavingCandidate</span>
<span style="color: #000000;">maxReduction</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">reduction</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">move</span><span style="color: #0000FF;">!=</span><span style="color: #004600;">NULL</span> <span style="color: #008080;">then</span>
<span style="color: #004080;">atom</span> <span style="color: #000000;">q</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">leaving</span><span style="color: #0000FF;">[</span><span style="color: #000000;">QTY</span><span style="color: #0000FF;">]</span>
<span style="color: #004080;">bool</span> <span style="color: #000000;">plus</span> <span style="color: #0000FF;">=</span> <span style="color: #004600;">true</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">move</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">deep_copy</span><span style="color: #0000FF;">(</span><span style="color: #000000;">move</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">])</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">plus</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">QTY</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">q</span>
<span style="color: #008080;">else</span>
<span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">QTY</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">-=</span> <span style="color: #000000;">q</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">QTY</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">==</span> <span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">matrix</span><span style="color: #0000FF;">[</span><span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">R</span><span style="color: #0000FF;">]][</span><span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">C</span><span style="color: #0000FF;">]]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
<span style="color: #008080;">else</span>
<span style="color: #000000;">matrix</span><span style="color: #0000FF;">[</span><span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">R</span><span style="color: #0000FF;">]][</span><span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">C</span><span style="color: #0000FF;">]]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">s</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #000000;">plus</span> <span style="color: #0000FF;">=</span> <span style="color: #008080;">not</span> <span style="color: #000000;">plus</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">src</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">dst</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">costs</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">matrix</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">stepping_stone</span><span style="color: #0000FF;">({</span><span style="color: #000000;">src</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">dst</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">costs</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">matrix</span><span style="color: #0000FF;">})</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">return</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">src</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">dst</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">costs</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">matrix</span><span style="color: #0000FF;">}</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #000080;font-style:italic;">-- -- source dest costs expected total</span>
<span style="color: #008080;">constant</span> <span style="color: #000000;">tests</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{{{</span><span style="color: #000000;">25</span><span style="color: #0000FF;">,</span><span style="color: #000000;">35</span><span style="color: #0000FF;">},</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">20</span><span style="color: #0000FF;">,</span><span style="color: #000000;">30</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">},</span> <span style="color: #0000FF;">{{</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">7</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5</span><span style="color: #0000FF;">}},</span> <span style="color: #000000;">180</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{{</span><span style="color: #000000;">12</span><span style="color: #0000FF;">,</span><span style="color: #000000;">40</span><span style="color: #0000FF;">,</span><span style="color: #000000;">33</span><span style="color: #0000FF;">},</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">20</span><span style="color: #0000FF;">,</span><span style="color: #000000;">30</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">},</span> <span style="color: #0000FF;">{{</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">7</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">4</span><span style="color: #0000FF;">,</span><span style="color: #000000;">6</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">9</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">8</span><span style="color: #0000FF;">}},</span> <span style="color: #000000;">130</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{{</span><span style="color: #000000;">14</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">,</span><span style="color: #000000;">15</span><span style="color: #0000FF;">,</span><span style="color: #000000;">12</span><span style="color: #0000FF;">},</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">10</span><span style="color: #0000FF;">,</span><span style="color: #000000;">15</span><span style="color: #0000FF;">,</span><span style="color: #000000;">12</span><span style="color: #0000FF;">,</span><span style="color: #000000;">15</span><span style="color: #0000FF;">},</span> <span style="color: #0000FF;">{{</span><span style="color: #000000;">10</span><span style="color: #0000FF;">,</span><span style="color: #000000;">30</span><span style="color: #0000FF;">,</span><span style="color: #000000;">25</span><span style="color: #0000FF;">,</span><span style="color: #000000;">15</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">20</span><span style="color: #0000FF;">,</span><span style="color: #000000;">15</span><span style="color: #0000FF;">,</span><span style="color: #000000;">20</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">10</span><span style="color: #0000FF;">,</span><span style="color: #000000;">30</span><span style="color: #0000FF;">,</span><span style="color: #000000;">20</span><span style="color: #0000FF;">,</span><span style="color: #000000;">20</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">30</span><span style="color: #0000FF;">,</span><span style="color: #000000;">40</span><span style="color: #0000FF;">,</span><span style="color: #000000;">35</span><span style="color: #0000FF;">,</span><span style="color: #000000;">45</span><span style="color: #0000FF;">}},</span> <span style="color: #000000;">1000</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{{</span><span style="color: #000000;">100</span><span style="color: #0000FF;">,</span><span style="color: #000000;">300</span><span style="color: #0000FF;">,</span><span style="color: #000000;">300</span><span style="color: #0000FF;">},</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">300</span><span style="color: #0000FF;">,</span><span style="color: #000000;">200</span><span style="color: #0000FF;">,</span><span style="color: #000000;">200</span><span style="color: #0000FF;">},</span> <span style="color: #0000FF;">{{</span><span style="color: #000000;">50</span><span style="color: #0000FF;">,</span><span style="color: #000000;">40</span><span style="color: #0000FF;">,</span><span style="color: #000000;">30</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">80</span><span style="color: #0000FF;">,</span><span style="color: #000000;">40</span><span style="color: #0000FF;">,</span><span style="color: #000000;">30</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">90</span><span style="color: #0000FF;">,</span><span style="color: #000000;">70</span><span style="color: #0000FF;">,</span><span style="color: #000000;">50</span><span style="color: #0000FF;">}},</span> <span style="color: #000000;">39000</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{{</span><span style="color: #000000;">40</span><span style="color: #0000FF;">,</span><span style="color: #000000;">60</span><span style="color: #0000FF;">,</span><span style="color: #000000;">50</span><span style="color: #0000FF;">},</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">20</span><span style="color: #0000FF;">,</span><span style="color: #000000;">30</span><span style="color: #0000FF;">,</span><span style="color: #000000;">50</span><span style="color: #0000FF;">,</span><span style="color: #000000;">50</span><span style="color: #0000FF;">},</span> <span style="color: #0000FF;">{{</span><span style="color: #000000;">4</span><span style="color: #0000FF;">,</span><span style="color: #000000;">6</span><span style="color: #0000FF;">,</span><span style="color: #000000;">8</span><span style="color: #0000FF;">,</span><span style="color: #000000;">8</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">6</span><span style="color: #0000FF;">,</span><span style="color: #000000;">8</span><span style="color: #0000FF;">,</span><span style="color: #000000;">6</span><span style="color: #0000FF;">,</span><span style="color: #000000;">7</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">7</span><span style="color: #0000FF;">,</span><span style="color: #000000;">6</span><span style="color: #0000FF;">,</span><span style="color: #000000;">8</span><span style="color: #0000FF;">}},</span> <span style="color: #000000;">920</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{{</span><span style="color: #000000;">12</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5</span><span style="color: #0000FF;">},</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">10</span><span style="color: #0000FF;">,</span><span style="color: #000000;">8</span><span style="color: #0000FF;">},</span> <span style="color: #0000FF;">{{</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">4</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span> <span style="color: #000000;">8</span><span style="color: #0000FF;">,</span><span style="color: #000000;">12</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">12</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">6</span><span style="color: #0000FF;">}},</span> <span style="color: #000000;">68</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{{</span><span style="color: #000000;">7</span><span style="color: #0000FF;">,</span><span style="color: #000000;">9</span><span style="color: #0000FF;">,</span><span style="color: #000000;">18</span><span style="color: #0000FF;">},</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">8</span><span style="color: #0000FF;">,</span><span style="color: #000000;">7</span><span style="color: #0000FF;">,</span><span style="color: #000000;">14</span><span style="color: #0000FF;">},</span> <span style="color: #0000FF;">{{</span><span style="color: #000000;">19</span><span style="color: #0000FF;">,</span><span style="color: #000000;">30</span><span style="color: #0000FF;">,</span><span style="color: #000000;">50</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">70</span><span style="color: #0000FF;">,</span><span style="color: #000000;">30</span><span style="color: #0000FF;">,</span><span style="color: #000000;">40</span><span style="color: #0000FF;">,</span><span style="color: #000000;">60</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">40</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">8</span><span style="color: #0000FF;">,</span><span style="color: #000000;">70</span><span style="color: #0000FF;">,</span><span style="color: #000000;">20</span><span style="color: #0000FF;">}},</span> <span style="color: #000000;">743</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{{</span><span style="color: #000000;">12</span><span style="color: #0000FF;">,</span><span style="color: #000000;">11</span><span style="color: #0000FF;">,</span><span style="color: #000000;">14</span><span style="color: #0000FF;">,</span><span style="color: #000000;">8</span><span style="color: #0000FF;">},</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">10</span><span style="color: #0000FF;">,</span><span style="color: #000000;">11</span><span style="color: #0000FF;">,</span><span style="color: #000000;">15</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">4</span><span style="color: #0000FF;">},</span> <span style="color: #0000FF;">{{</span> <span style="color: #000000;">7</span><span style="color: #0000FF;">,</span><span style="color: #000000;">12</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">5</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">6</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">15</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">12</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">6</span><span style="color: #0000FF;">,</span><span style="color: #000000;">14</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span> <span style="color: #000000;">8</span><span style="color: #0000FF;">,</span><span style="color: #000000;">16</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10</span><span style="color: #0000FF;">,</span><span style="color: #000000;">12</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">7</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">18</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">8</span><span style="color: #0000FF;">,</span><span style="color: #000000;">17</span><span style="color: #0000FF;">,</span><span style="color: #000000;">11</span><span style="color: #0000FF;">,</span><span style="color: #000000;">16</span><span style="color: #0000FF;">}},</span> <span style="color: #000000;">259</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{{</span><span style="color: #000000;">50</span><span style="color: #0000FF;">,</span><span style="color: #000000;">60</span><span style="color: #0000FF;">,</span><span style="color: #000000;">50</span><span style="color: #0000FF;">,</span><span style="color: #000000;">50</span><span style="color: #0000FF;">},</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">30</span><span style="color: #0000FF;">,</span><span style="color: #000000;">20</span><span style="color: #0000FF;">,</span><span style="color: #000000;">70</span><span style="color: #0000FF;">,</span><span style="color: #000000;">30</span><span style="color: #0000FF;">,</span><span style="color: #000000;">60</span><span style="color: #0000FF;">},{{</span><span style="color: #000000;">16</span><span style="color: #0000FF;">,</span><span style="color: #000000;">16</span><span style="color: #0000FF;">,</span><span style="color: #000000;">13</span><span style="color: #0000FF;">,</span><span style="color: #000000;">22</span><span style="color: #0000FF;">,</span><span style="color: #000000;">17</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">14</span><span style="color: #0000FF;">,</span><span style="color: #000000;">14</span><span style="color: #0000FF;">,</span><span style="color: #000000;">13</span><span style="color: #0000FF;">,</span><span style="color: #000000;">19</span><span style="color: #0000FF;">,</span><span style="color: #000000;">15</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">19</span><span style="color: #0000FF;">,</span><span style="color: #000000;">19</span><span style="color: #0000FF;">,</span><span style="color: #000000;">20</span><span style="color: #0000FF;">,</span><span style="color: #000000;">23</span><span style="color: #0000FF;">,</span><span style="color: #000000;">50</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">50</span><span style="color: #0000FF;">,</span><span style="color: #000000;">12</span><span style="color: #0000FF;">,</span><span style="color: #000000;">50</span><span style="color: #0000FF;">,</span><span style="color: #000000;">15</span><span style="color: #0000FF;">,</span><span style="color: #000000;">11</span><span style="color: #0000FF;">}},</span> <span style="color: #000000;">3100</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{{</span><span style="color: #000000;">50</span><span style="color: #0000FF;">,</span><span style="color: #000000;">75</span><span style="color: #0000FF;">,</span><span style="color: #000000;">25</span><span style="color: #0000FF;">},</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">20</span><span style="color: #0000FF;">,</span><span style="color: #000000;">20</span><span style="color: #0000FF;">,</span><span style="color: #000000;">50</span><span style="color: #0000FF;">,</span><span style="color: #000000;">60</span><span style="color: #0000FF;">},</span> <span style="color: #0000FF;">{{</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">7</span><span style="color: #0000FF;">,</span><span style="color: #000000;">6</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">8</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">},</span>
<span style="color: #0000FF;">{</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,</span><span style="color: #000000;">6</span><span style="color: #0000FF;">,</span><span style="color: #000000;">9</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">}},</span> <span style="color: #000000;">610</span><span style="color: #0000FF;">}}</span>
if move!=NULL then
atom q = leaving[QTY]
bool plus = true
for i=1 to length(move) do
sequence s = move[i]
if plus then
s[QTY] += q
else
s[QTY] -= q
end if
if s[QTY] == 0 then
matrix[s[R]][s[C]] = 0
else
matrix[s[R]][s[C]] = s
end if
plus = not plus
end for
{src, dst, costs, matrix} = stepping_stone({src, dst, costs, matrix})
end if
return {src, dst, costs, matrix}
end function
<span style="color: #000080;font-style:italic;">--for i=1 to length(tests) do</span>
-- -- source dest costs expected total
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">3</span> <span style="color: #008080;">to</span> <span style="color: #000000;">3</span> <span style="color: #008080;">do</span>
constant tests = {{{25,35}, {20,30,10}, {{3,5,7},
<span style="color: #000000;">print_result</span><span style="color: #0000FF;">(</span><span style="color: #000000;">stepping_stone</span><span style="color: #0000FF;">(</span><span style="color: #000000;">initialise</span><span style="color: #0000FF;">(</span><span style="color: #000000;">tests</span><span style="color: #0000FF;">,</span><span style="color: #000000;">i</span><span style="color: #0000FF;">)),</span><span style="color: #000000;">tests</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">][</span><span style="color: #000000;">4</span><span style="color: #0000FF;">])</span>
{3,2,5}}, 180},
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
{{12,40,33}, {20,30,10}, {{3,5,7},
{2,4,6},
<span style="color: #0000FF;">?</span><span style="color: #008000;">"done"</span>
{9,1,8}}, 130},
<span style="color: #0000FF;">{}</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">wait_key</span><span style="color: #0000FF;">()</span>
{{14,10,15,12}, {10,15,12,15}, {{10,30,25,15},
<!--</syntaxhighlight>-->
{20,15,20,10},
{10,30,20,20},
{30,40,35,45}}, 1000},
{{100,300,300}, {300,200,200}, {{50,40,30},
{80,40,30},
{90,70,50}}, 39000},
{{40,60,50}, {20,30,50,50}, {{4,6,8,8},
{6,8,6,7},
{5,7,6,8}}, 920},
{{12,1,5}, {10,8}, {{ 2, 4},
{ 8,12},
{12, 6}}, 68},
{{7,9,18}, {5,8,7,14}, {{19,30,50,10},
{70,30,40,60},
{40, 8,70,20}}, 743},
{{12,11,14,8}, {10,11,15,5,4}, {{ 7,12, 1, 5, 6},
{15, 3,12, 6,14},
{ 8,16,10,12, 7},
{18, 8,17,11,16}}, 259},
{{50,60,50,50}, {30,20,70,30,60},{{16,16,13,22,17},
{14,14,13,19,15},
{19,19,20,23,50},
{50,12,50,15,11}}, 3100},
{{50,75,25}, {20,20,50,60}, {{3,5,7,6},
{2,5,8,2},
{3,6,9,2}}, 610}}
 
--for i=1 to length(tests) do
for i=3 to 3 do
print_result(stepping_stone(initialise(tests,i)),tests[i][4])
end for</lang>
{{out}}
(Obviously the other eight tests all work fine and produce similar output.)
Line 3,810 ⟶ 3,869:
Using <code>lpSolve::lp.transport</code>.
 
<langsyntaxhighlight Rlang="r">library(lpSolve)
 
# cost matrix
Line 3,829 ⟶ 3,888:
rownames(sol) <- c("Supplier 1", "Supplier 2")
colnames(sol) <- c("Customer 1", "Customer 2", "Customer 3")
sol </langsyntaxhighlight>
{{out}}
<pre>Success: the objective function is 180
Line 3,843 ⟶ 3,902:
Using <code>typed/racket</code>, to keep track of Vectors of Vectors of data.
 
<langsyntaxhighlight lang="racket">#lang typed/racket
;; {{trans|Java}}
(define-type (V2 A) (Vectorof (Vectorof A)))
Line 4,069 ⟶ 4,128:
30 40 35 45
$
1000))</langsyntaxhighlight>
{{out}}
Output of: <code>raco test Transportation-problem.rkt</code>:
Line 4,099 ⟶ 4,158:
{{works with|Rakudo|2019.03.1}}
Using [[Vogel's_approximation_method#Raku|Vogel's approximation method]]:
<syntaxhighlight lang="raku" perl6line>my %costs = :S1{:3C1, :5C2, :7C3}, :S2{:3C1, :2C2, :5C3};
my %demand = :20C1, :30C2, :10C3;
my %supply = :25S1, :35S2;
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print "\n";
}
say "\nTotal cost: $total";</langsyntaxhighlight>
{{out}}
<pre> C1 C2 C3
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=={{header|REXX}}==
{{trans|Java}}
<langsyntaxhighlight lang="rexx">/* REXX ***************************************************************
* Solve the Transportation Problem using the Northwest Corner Method
Default Input
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Nop
End
Exit 12</langsyntaxhighlight>
{{out}}
<pre>F:\>rexx tpx2 input1.txt
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Use network solver in SAS/OR:
 
<langsyntaxhighlight lang="sas">/* create SAS data sets */
data cost_data;
input from $ to $ cost;
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print _OROPTMODEL_NUM_['OBJECTIVE'];
print flow;
quit;</langsyntaxhighlight>
 
Output:
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=={{header|Visual Basic .NET}}==
{{trans|C#}}
<langsyntaxhighlight lang="vbnet">Module Module1
 
Class Shipment
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End Sub
 
End Module</langsyntaxhighlight>
{{out}}
<pre>Optimal solution input1.txt
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{{libheader|Wren-seq}}
{{libheader|Wren-fmt}}
<langsyntaxhighlight ecmascriptlang="wren">import "./dynamic" for Struct
import "./ioutil" for FileUtil, File
import "./math" for Nums
import "./seq" for Lst
import "./fmt" for Fmt
 
var Shipment = Struct.create("Shipment", ["quantity", "costPerUnit", "r", "c"])
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t.steppingStone()
t.printResult()
}</langsyntaxhighlight>
 
{{out}}
9,476

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