Transportation problem: Difference between revisions

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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>
{{out}}
<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\",
Line 1,801 ⟶ 1,802:
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
:
Line 2,199 ⟶ 2,200:
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}}==
UsingCode taken from [https://github.com/JuliaOptdylanomics/MathProgBase.jltransportation_problem MathProgBasehere] using [https://jump.dev/JuMP.jl/stable/ JuMP].
<langsyntaxhighlight lang="julia">using MathProgBaseJuMP, ClpGLPK
 
# cost vector
c = [3, 5, 7, 3, 2, 5]
c = [3, 5, 7, 3, 2, 5];
N = size(c,1);
 
# constraints Ax (<,>,=) b
A = [1 1 1 0 0 0
0 0 0 1 1 1
1 0 0 1 0 0
0 1 0 0 1 0
0 0 1 0 0 1];
b = [ 25, 35, 20, 30, 10];
s = ['<', '<', '=', '=', '='];
 
# construct model
b = [ 25, 35, 20, 30, 10]
model = Model(GLPK.Optimizer)
s = ['<', '<', '=', '=', '=']
@variable(model, x[i=1:N] >= 0, base_name="traded quantities")
cost_fn = @expression(model, c'*x) # cost function
@constraint(model, C1, A[1:2,:]*x .<= b[1:2]) # inequality constraints
@constraint(model, C2, A[3:5,:]*x .== b[3:5]) # equality constraints
@objective(model, Min, cost_fn) # objective function
 
# solve model
sol = linprog(c, A, b, s, ClpSolver())
status = JuMP.optimize!(model);
@show sol.status
xstar = value.(x);
@show sol.sol
println("solution vector of quantities = ", xstar)
@show sol.objval</lang>
println("minimum total cost = ", JuMP.objective_value(model))
 
# recover Lagrange multipliers for post-optimality
λ = [JuMP.dual(C1[1]),JuMP.dual(C1[2])]
μ = [JuMP.dual(C2[1]),JuMP.dual(C2[2]),JuMP.dual(C2[3])]
</syntaxhighlight>
 
{{out}}
<pre>solution vector of quantities = [20.0, 0.0, 5.0, 0.0, 30.0, 5.0]
<pre>sol.status = :Optimal
minimum total cost = 180.0</pre>
sol.sol = [20.0, 0.0, 5.0, 0.0, 30.0, 5.0]
sol.objval = 180.0</pre>
 
=={{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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Same as Java entry
</pre>
 
=={{header|Nim}}==
{{trans|Go}}
<syntaxhighlight lang="nim">import fenv, lists, math, sequtils, strformat, strutils
 
type
 
Shipment = object
quantity: float
costPerUnit: float
r, c: int
 
Transport = object
filename: string
supply: seq[int]
demand: seq[int]
costs: seq[seq[float]]
matrix: seq[seq[Shipment]]
 
ShipmentList = DoublyLinkedList[Shipment]
 
const ShipZero = Shipment()
 
 
template emitError(msg: string) =
raise newException(ValueError, msg)
 
 
proc initTransport(filename: string): Transport =
let infile = filename.open()
let fields = infile.readLine().splitWhitespace().map(parseInt)
let numSources = fields[0]
let numDests = fields[1]
if numSources < 1 or numDests < 1:
emitError "wrong number of sources or destinations."
var src = infile.readLine().splitWhitespace().map(parseInt)
if src.len != numSources:
emitError "wrong number of sources; got $1, expected $2.".format(src.len, numSources)
var dst = infile.readLine().splitWhitespace().map(parseInt)
if dst.len != numDests:
emitError "wrong number of destinations; got $1, expected $2.".format(dst.len, numDests)
 
# Fix imbalance.
let totalSrc = sum(src)
let totalDst = sum(dst)
let diff = totalSrc - totalDst
if diff > 0: dst.add diff
elif diff < 0: src.add -diff
 
var costs = newSeqWith(src.len, newSeq[float](dst.len))
var matrix = newSeqWith(src.len, newSeq[Shipment](dst.len))
 
for i in 0..<numSources:
let fields = infile.readLine().splitWhitespace().map(parseFloat)
if fields.len > dst.len:
emitError "wrong number of costs; got $1, expected $2.".format(fields.len, numDests)
for j in 0..<numDests:
costs[i][j] = fields[j]
 
result = Transport(filename: filename, supply: move(src),
demand: move(dst), costs: move(costs), matrix: move(matrix))
 
 
func northWestCornerRule(tr: var Transport) =
var northWest = 0
for r in 0..tr.supply.high:
for c in northWest..tr.demand.high:
let quantity = min(tr.supply[r], tr.demand[c])
if quantity > 0:
tr.matrix[r][c] = Shipment(quantity: quantity.toFloat, costPerUnit: tr.costs[r][c], r: r, c: c)
dec tr.supply[r], quantity
dec tr.demand[c], quantity
if tr.supply[r] == 0:
northWest = c
break
 
 
func getNeighbors(tr: Transport; s: Shipment; list: ShipmentList): array[2, Shipment] =
for o in list:
if o != s:
if o.r == s.r and result[0] == ShipZero:
result[0] = o
elif o.c == s.c and result[1] == ShipZero:
result[1] = o
if result[0] != ShipZero and result[1] != ShipZero:
break
 
 
func matrixToList(tr: Transport): ShipmentList =
for m in tr.matrix:
for s in m:
if s != ShipZero:
result.append(s)
 
 
func getClosedPath(tr: Transport; s: Shipment): seq[Shipment] =
var path = tr.matrixToList
path.prepend(s)
 
# Remove (and keep removing) elements that do not have a
# vertical and horizontal neighbor.
while true:
var removals = 0
for e in path.nodes:
let nbrs = tr.getNeighbors(e.value, path)
if nbrs[0] == ShipZero or nbrs[1] == ShipZero:
path.remove(e)
inc removals
if removals == 0:
break
 
# Place the remaining elements in the correct plus-minus order.
var prev = s
var i = 0
for _ in path:
result.add prev
prev = tr.getNeighbors(prev, path)[i]
i = 1 - i
 
 
func fixDegenerateCase(tr: var Transport) =
const Eps = minimumPositiveValue(float)
if tr.supply.len + tr.demand.len - 1 != tr.matrix.len * tr.matrix[0].len:
for r in 0..tr.supply.high:
for c in 0..tr.demand.high:
if tr.matrix[r][c] == ShipZero:
let dummy = Shipment(quantity: Eps, costPerUnit: tr.costs[r][c], r: r, c: c)
if tr.getClosedPath(dummy).len == 0:
tr.matrix[r][c] = dummy
return
 
 
func steppingStone(tr: var Transport) =
var maxReduction = 0.0
var move: seq[Shipment]
var leaving = ShipZero
tr.fixDegenerateCase()
 
for r in 0..tr.supply.high:
for c in 0..tr.demand.high:
if tr.matrix[r][c] != ShipZero:
continue
let trial = Shipment(quantity: 0, costPerUnit: tr.costs[r][c], r: r, c: c)
var path = tr.getClosedPath(trial)
var reduction = 0.0
var lowestQuantity = float(int32.high)
var leavingCandidate = ShipZero
var plus = true
for s in path:
if plus:
reduction += s.costPerUnit
else:
reduction -= s.costPerUnit
if s.quantity < lowestQuantity:
leavingCandidate = s
lowestQuantity = s.quantity
plus = not plus
if reduction < maxReduction:
move = move(path)
leaving = leavingCandidate
maxReduction = reduction
 
if move.len != 0:
let q = leaving.quantity
var plus = true
for s in move.mitems:
if plus: s.quantity += q
else: s.quantity -= q
tr.matrix[s.r][s.c] = if s.quantity == 0: ShipZero else: s
plus = not plus
tr.steppingStone()
 
 
proc printResult(tr: Transport) =
echo tr.filename, '\n'
stdout.write tr.filename.readFile()
echo "\nOptimal solution for ", tr.filename, '\n'
var totalCosts = 0.0
for r in 0..tr.supply.high:
for c in 0..tr.demand.high:
let s = tr.matrix[r][c]
if s != ShipZero and s.r == r and s.c == c:
stdout.write &" {int(s.quantity):3} "
totalCosts += s.quantity * s.costPerUnit
else:
stdout.write " - "
echo()
echo &"\nTotal costs: {totalCosts:g}\n"
 
 
when isMainModule:
 
const Filenames = ["input1.txt", "input2.txt", "input3.txt"]
for filename in Filenames:
var tr = initTransport(filename)
tr.northWestCornerRule()
tr.steppingStone()
tr.printResult()</syntaxhighlight>
 
{{out}}
<pre>input1.txt
 
2 3
25 35
20 30 10
3 5 7
3 2 5
 
Optimal solution for input1.txt
 
20 - 5
- 30 5
 
Total costs: 180
 
input2.txt
 
3 3
12 40 33
20 30 10
3 5 7
2 4 6
9 1 8
 
Optimal solution for input2.txt
 
- - - 12
20 - 10 10
- 30 - 3
 
Total costs: 130
 
input3.txt
 
4 4
14 10 15 12
10 15 12 15
10 30 25 15
20 15 20 10
10 30 20 20
30 40 35 45
 
Optimal solution for input3.txt
 
- - - 14
- 9 - 1
10 - 5 -
- 5 7 -
- 1 - -
 
Total costs: 1000</pre>
 
=={{header|Pascal}}==
<langsyntaxhighlight lang="pascal">Program transport;
{ based on the program of <Svetlana Belashova> }
 
Line 3,215 ⟶ 3,482:
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>
Line 3,260 ⟶ 3,575:
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},
{{50,75,25}, {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 3,536 ⟶ 3,865:
</pre>
Note that [[Vogel%27s_approximation_method#Phix]] gets a few of the others wrong and loops on #2, then again that is unbalanced (needs a dummy customer), and I'm not sure whether throwing such at VAM is fair or not.
 
=={{header|R}}==
Using <code>lpSolve::lp.transport</code>.
 
<syntaxhighlight lang="r">library(lpSolve)
 
# cost matrix
costs <- matrix(c(3, 5, 7,
3, 2, 5), nrow = 2, byrow = TRUE)
 
# constraints for suppliers
row.signs <- rep("<=", 2)
row.rhs <- c(25, 35)
# constraints for customers
col.signs <- rep("=", 3)
col.rhs <- c(20, 30, 10)
 
# minimum cost (objective value)
lp.transport(costs, "min", row.signs, row.rhs, col.signs, col.rhs)
# solution matrix
sol = lp.transport(costs, "min", row.signs, row.rhs, col.signs, col.rhs)$solution
rownames(sol) <- c("Supplier 1", "Supplier 2")
colnames(sol) <- c("Customer 1", "Customer 2", "Customer 3")
sol </syntaxhighlight>
{{out}}
<pre>Success: the objective function is 180
 
Customer 1 Customer 2 Customer 3
Supplier 1 20 0 5
Supplier 2 0 30 5
</pre>
 
=={{header|Racket}}==
Line 3,542 ⟶ 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 3,768 ⟶ 4,128:
30 40 35 45
$
1000))</langsyntaxhighlight>
{{out}}
Output of: <code>raco test Transportation-problem.rkt</code>:
Line 3,798 ⟶ 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;
Line 3,853 ⟶ 4,213:
print "\n";
}
say "\nTotal cost: $total";</langsyntaxhighlight>
{{out}}
<pre> C1 C2 C3
S1 20 - 5
S2 - 30 5 </pre>
 
=={{header|REXX}}==
{{trans|Java}}
<syntaxhighlight lang="rexx">/* REXX ***************************************************************
* Solve the Transportation Problem using the Northwest Corner Method
Default Input
2 3 # of sources / # of demands
25 35 sources
20 30 10 demands
3 5 7 cost matrix
3 2 5
* 20201210 support no input file -courtesy GS
* Note: correctnes of input is not checked
* 20201226 add optimization
* 20210103 remove debug code
**********************************************************************/
Signal On Halt
Signal On Novalue
Signal On Syntax
 
Parse Arg fid
If fid='' Then
fid='input1.txt'
Call init
matrix.=0
ms=0
Do r=1 To rr
Do c=1 To cc
matrix.r.c=r c cost.r.c 0
End
End
r=1
c=1
Do While r<=rr & c<=cc
q=min(source.r,demand.c)
matrix.r.c=r c cost.r.c q
source.r=source.r-q
demand.c=demand.c-q
If source.r=0 Then r=r+1
If demand.c=0 Then c=c+1
End
Call show_alloc 'after NWC application'
Call steppingstone
Exit
 
/**********************************************************************
* Subroutines for NWC Algorithm
**********************************************************************/
 
init:
If lines(fid)=0 Then Do
Say 'Input file not specified or not found. Using default input instead.'
fid='Default input'
in.1=sourceline(4)
Parse Var in.1 numSources .
Do i=2 To numSources+3
in.i=sourceline(i+3)
End
End
Else Do
Do i=1 By 1 while lines(fid)>0
in.i=linein(fid)
End
End
Parse Var in.1 numSources numDestinations . 1 rr cc .
source_sum=0
Do i=1 To numSources
Parse Var in.2 source.i in.2
ss.i=source.i
source_in.i=source.i
source_sum=source_sum+source.i
End
l=linein(fid)
demand_sum=0
Do i=1 To numDestinations
Parse Var in.3 demand.i in.3
dd.i=demand.i
demand_in.i=demand.i
demand_sum=demand_sum+demand.i
End
Do i=1 To numSources
j=i+3
l=in.j
Do j=1 To numDestinations
Parse Var l cost.i.j l
End
End
Do i=1 To numSources
ol=format(source.i,3)
Do j=1 To numDestinations
ol=ol format(cost.i.j,4)
End
End
ol=' '
Do j=1 To numDestinations
ol=ol format(demand.j,4)
End
 
Select
When source_sum=demand_sum Then Nop /* balanced */
When source_sum>demand_sum Then Do /* unbalanced - add dummy demand */
Say 'This is an unbalanced case (sources exceed demands). We add a dummy consumer.'
cc=cc+1
demand.cc=source_sum-demand_sum
demand_in.cc=demand.cc
dd.cc=demand.cc
Do r=1 To rr
cost.r.cc=0
End
End
Otherwise /* demand_sum>source_sum */ Do /* unbalanced - add dummy source */
Say 'This is an unbalanced case (demands exceed sources). We add a dummy source.'
rr=rr+1
source.rr=demand_sum-source_sum
source_in.rr=source.rr
ss.rr=source.rr
Do c=1 To cc
cost.rr.c=0
End
End
End
Say 'Sources / Demands / Cost'
ol=' '
Do c=1 To cc
ol=ol format(demand.c,3)
End
Say ol
 
Do r=1 To rr
ol=format(source.r,4)
Do c=1 To cc
ol=ol format(cost.r.c,3)
End
Say ol
End
Return
 
show_alloc: Procedure Expose matrix. rr cc demand_in. source_in.
Parse Arg header
If header='' Then
Return
Say ''
Say header
total=0
ol=' '
Do c=1 to cc
ol=ol format(demand_in.c,3)
End
Do r=1 to rr
ol=format(source_in.r,4)
a=word(matrix.r.1,4)
If a>0 Then
ol=format(a,4)
Else
ol=' - '
total=total+word(matrix.r.1,4)*word(matrix.r.1,3)
Do c=2 To cc
a=word(matrix.r.c,4)
If a>0 Then
ol=ol format(a,4)
Else
ol=ol ' - '
total=total+word(matrix.r.c,4)*word(matrix.r.c,3)
End
Say ol
End
Say 'Total costs:' format(total,4,1)
Return
 
/**********************************************************************
* Subroutines for Optimization
**********************************************************************/
 
steppingstone: Procedure Expose matrix. cost. rr cc demand_in.,
source_in. fid
maxReduction=0
move=''
 
Call fixDegenerateCase
 
Do r=1 To rr
Do c=1 To cc
Parse Var matrix.r.c r c cost qrc
If qrc=0 Then Do
path=getclosedpath(r,c)
reduction = 0
lowestQuantity = 1e10
leavingCandidate = ''
plus=1
pathx=path
Do While pathx<>''
Parse Var pathx s '|' pathx
If plus Then
reduction=reduction+word(s,3)
Else Do
reduction=reduction-word(s,3)
If word(s,4)<lowestQuantity Then Do
leavingCandidate = s
lowestQuantity = word(s,4)
End
End
plus=\plus
End
If reduction < maxreduction Then Do
move=path
leaving=leavingCandidate
maxReduction = reduction
End
End
End
End
if move <> '' Then Do
quant=word(leaving,4)
plus=1
Do While move<>''
Parse Var move m '|' move
Parse Var m r c cpu qrc
Parse Var matrix.r.c vr vc vcost vquant
If plus Then
nquant=vquant+quant
Else
nquant=vquant-quant
matrix.r.c = vr vc vcost nquant
plus=\plus
End
move=''
Call steppingStone
End
Else Do
Call show_alloc 'Optimal Solution' fid
End
Return
 
getclosedpath: Procedure Expose matrix. cost. rr cc
Parse Arg rd,cd
path=rd cd cost.rd.cd word(matrix.rd.cd,4)
do r=1 To rr
Do c=1 To cc
If word(matrix.r.c,4)>0 Then Do
path=path'|'r c cost.r.c word(matrix.r.c,4)
End
End
End
path=magic(path)
Return stones(path)
 
magic: Procedure
Parse Arg list
Do Forever
list_1=remove_1(list)
If list_1=list Then Leave
list=list_1
End
Return list_1
 
remove_1: Procedure
Parse Arg list
cntr.=0
cntc.=0
Do i=1 By 1 While list<>''
parse Var list e.i '|' list
Parse Var e.i r c .
cntr.r=cntr.r+1
cntc.c=cntc.c+1
End
n=i-1
keep.=1
Do i=1 To n
Parse Var e.i r c .
If cntr.r<2 |,
cntc.c<2 Then Do
keep.i=0
End
End
list=e.1
Do i=2 To n
If keep.i Then
list=list'|'e.i
End
Return list
 
stones: Procedure
Parse Arg lst
tstc=lst
Do i=1 By 1 While tstc<>''
Parse Var tstc o.i '|' tstc
end
stones=lst
o.0=i-1
prev=o.1
Do i=1 To o.0
st.i=prev
k=i//2
nbrs=getNeighbors(prev, lst)
Parse Var nbrs n.1 '|' n.2
If k=0 Then
prev=n.2
Else
prev=n.1
End
stones=st.1
Do i=2 To o.0
stones=stones'|'st.i
End
Return stones
 
getNeighbors: Procedure
parse Arg s, lst
Do i=1 By 1 While lst<>''
Parse Var lst o.i '|' lst
End
o.0=i-1
nbrs.=''
sr=word(s,1)
sc=word(s,2)
Do i=1 To o.0
If o.i<>s Then Do
or=word(o.i,1)
oc=word(o.i,2)
If or=sr & nbrs.0='' Then
nbrs.0 = o.i
else if oc=sc & nbrs.1='' Then
nbrs.1 = o.i
If nbrs.0<>'' & nbrs.1<>'' Then
Leave
End
End
return nbrs.0'|'nbrs.1
 
pelems: Procedure
Parse Arg p
Do i=1 By 1 While p<>''
Parse Var p x '|' p
End
Return i
 
fixDegenerateCase: Procedure Expose matrix. rr cc ms
Call matrixtolist
If (rr+cc-1)<>ms Then Do
Do r=1 To rr
Do c=1 To cc
If word(matrix.r.c,4)=0 Then Do
matrix.r.c=subword(matrix.r.c,1,3) 1.e-10
Return
End
End
End
End
Return
 
matrixtolist: Procedure Expose matrix. rr cc ms
ms=0
list=''
Do r=1 To rr
Do c=1 To cc
If word(matrix.r.c,4)>0 Then Do
list=list'|'matrix.r.c
ms=ms+1
End
End
End
Return strip(list,,'|')
 
Novalue:
Say 'Novalue raised in line' sigl
Say sourceline(sigl)
Say 'Variable' condition('D')
Signal lookaround
 
Syntax:
Say 'Syntax raised in line' sigl
Say sourceline(sigl)
Say 'rc='rc '('errortext(rc)')'
 
halt:
lookaround:
If fore() Then Do
Say 'You can look around now.'
Trace ?R
Nop
End
Exit 12</syntaxhighlight>
{{out}}
<pre>F:\>rexx tpx2 input1.txt
Sources / Demands / Cost
20 30 10
25 3 5 7
35 3 2 5
 
after NWC application
20 5 -
- 25 10
Total costs: 185.0
 
Optimal Solution input1.txt
20 - 5
- 30 5
Total costs: 180.0
 
F:\>rexx tpx2 input2.txt
This is an unbalanced case (sources exceed demands). We add a dummy consumer.
Sources / Demands / Cost
20 30 10 25
12 3 5 7 0
40 2 4 6 0
33 9 1 8 0
 
after NWC application
12 - - -
8 30 2 -
- - 8 25
Total costs: 248.0
 
Optimal Solution input2.txt
- - - 12
20 - 10 10
- 30 - 3
Total costs: 130.0
 
F:\>rexx tpx2 input3.txt
This is an unbalanced case (demands exceed sources). We add a dummy source.
Sources / Demands / Cost
10 15 12 15
14 10 30 25 15
10 20 15 20 10
15 10 30 20 20
12 30 40 35 45
1 0 0 0 0
 
after NWC application
10 4 - -
- 10 - -
- 1 12 2
- - - 12
- - - 1
Total costs: 1220.0
 
Optimal Solution input3.txt
- - - 14
- 9 - 1
10 - 5 -
- 5 7 -
- 1 - -
Total costs: 1000.0</pre>
 
=={{header|SAS}}==
Use network solver in SAS/OR:
 
<langsyntaxhighlight lang="sas">/* create SAS data sets */
data cost_data;
input from $ to $ cost;
Line 3,902 ⟶ 4,706:
print _OROPTMODEL_NUM_['OBJECTIVE'];
print flow;
quit;</langsyntaxhighlight>
 
Output:
Line 3,912 ⟶ 4,716:
s1 20 0 5
s2 0 30 5
</pre>
 
=={{header|Visual Basic .NET}}==
{{trans|C#}}
<syntaxhighlight lang="vbnet">Module Module1
 
Class Shipment
Public Sub New(q As Double, cpu As Double, rv As Integer, cv As Integer)
Quantity = q
CostPerUnit = cpu
R = rv
C = cv
End Sub
 
Public ReadOnly Property CostPerUnit() As Double
 
Public Property Quantity() As Double
 
Public ReadOnly Property R As Integer
 
Public ReadOnly Property C As Integer
 
Public Shared Operator =(s1 As Shipment, s2 As Shipment) As Boolean
Return s1.CostPerUnit = s2.CostPerUnit _
AndAlso s1.Quantity = s2.Quantity _
AndAlso s1.R = s2.R _
AndAlso s1.C = s2.C
End Operator
 
Public Shared Operator <>(s1 As Shipment, s2 As Shipment) As Boolean
Return s1.CostPerUnit <> s2.CostPerUnit _
OrElse s1.Quantity <> s2.Quantity _
OrElse s1.R <> s2.R _
OrElse s1.C <> s2.C
End Operator
End Class
 
Class Program
Private demand() As Integer
Private supply() As Integer
Private costs(,) As Double
Private matrix(,) As Shipment
 
Sub Init(filename As String)
Dim file = My.Computer.FileSystem.OpenTextFileReader(filename)
Dim line = file.ReadLine
Dim numArr = line.Split
Dim numSources = Integer.Parse(numArr(0))
Dim numDestinations = Integer.Parse(numArr(1))
 
Dim src As New List(Of Integer)
Dim dst As New List(Of Integer)
 
line = file.ReadLine
numArr = line.Split
For i = 1 To numSources
src.Add(Integer.Parse(numArr(i - 1)))
Next
 
line = file.ReadLine
numArr = line.Split
For i = 1 To numDestinations
dst.Add(Integer.Parse(numArr(i - 1)))
Next
 
REM fix imbalance
Dim totalSrc = src.Sum
Dim totalDst = dst.Sum
If totalSrc > totalDst Then
dst.Add(totalSrc - totalDst)
ElseIf totalDst > totalSrc Then
src.Add(totalDst - totalSrc)
End If
 
supply = src.ToArray
demand = dst.ToArray
 
ReDim costs(supply.Length - 1, demand.Length - 1)
ReDim matrix(supply.Length - 1, demand.Length - 1)
 
For i = 1 To numSources
line = file.ReadLine
numArr = line.Split
For j = 1 To numDestinations
costs(i - 1, j - 1) = Integer.Parse(numArr(j - 1))
Next
Next
End Sub
 
Sub NorthWestCornerRule()
Dim northwest = 1
For r = 1 To supply.Length
For c = northwest To demand.Length
Dim quantity = Math.Min(supply(r - 1), demand(c - 1))
If quantity > 0 Then
matrix(r - 1, c - 1) = New Shipment(quantity, costs(r - 1, c - 1), r - 1, c - 1)
 
supply(r - 1) -= quantity
demand(c - 1) -= quantity
 
If supply(r - 1) = 0 Then
northwest = c
Exit For
End If
End If
Next
Next
End Sub
 
Sub SteppingStone()
Dim maxReduction = 0.0
Dim move() As Shipment = Nothing
Dim leaving As Shipment = Nothing
 
FixDegenerateCase()
 
For r = 1 To supply.Length
For c = 1 To demand.Length
If Not IsNothing(matrix(r - 1, c - 1)) Then
Continue For
End If
 
Dim trial As New Shipment(0, costs(r - 1, c - 1), r - 1, c - 1)
Dim path = GetClosedPath(trial)
 
Dim reduction = 0.0
Dim lowestQuanity = Integer.MaxValue
Dim leavingCandidate As Shipment = Nothing
 
Dim plus = True
For Each s In path
If plus Then
reduction += s.CostPerUnit
Else
reduction -= s.CostPerUnit
If s.Quantity < lowestQuanity Then
leavingCandidate = s
lowestQuanity = s.Quantity
End If
End If
plus = Not plus
Next
If reduction < maxReduction Then
move = path
leaving = leavingCandidate
maxReduction = reduction
End If
Next
Next
 
If Not IsNothing(move) Then
Dim q = leaving.Quantity
Dim plus = True
For Each s In move
s.Quantity += If(plus, q, -q)
matrix(s.R, s.C) = If(s.Quantity = 0, Nothing, s)
plus = Not plus
Next
SteppingStone()
End If
End Sub
 
Sub FixDegenerateCase()
Const eps = Double.Epsilon
If supply.Length + demand.Length - 1 <> MatrixToList().Count Then
For r = 1 To supply.Length
For c = 1 To demand.Length
If IsNothing(matrix(r - 1, c - 1)) Then
Dim dummy As New Shipment(eps, costs(r - 1, c - 1), r - 1, c - 1)
If GetClosedPath(dummy).Length = 0 Then
matrix(r - 1, c - 1) = dummy
Return
End If
End If
Next
Next
End If
End Sub
 
Function MatrixToList() As List(Of Shipment)
Dim newList As New List(Of Shipment)
For Each item In matrix
If Not IsNothing(item) Then
newList.Add(item)
End If
Next
Return newList
End Function
 
Function GetClosedPath(s As Shipment) As Shipment()
Dim path = MatrixToList()
path.Add(s)
 
REM remove (and keep removing) elements that do not have a veritcal AND horizontal neighbor
Dim before As Integer
Do
before = path.Count
path.RemoveAll(Function(ship)
Dim nbrs = GetNeighbors(ship, path)
Return IsNothing(nbrs(0)) OrElse IsNothing(nbrs(1))
End Function)
Loop While before <> path.Count
 
REM place the remaining elements in the correct plus-minus order
Dim stones = path.ToArray
Dim prev = s
For i = 1 To stones.Length
stones(i - 1) = prev
prev = GetNeighbors(prev, path)((i - 1) Mod 2)
Next
Return stones
End Function
 
Function GetNeighbors(s As Shipment, lst As List(Of Shipment)) As Shipment()
Dim nbrs() As Shipment = {Nothing, Nothing}
For Each o In lst
If o <> s Then
If o.R = s.R AndAlso IsNothing(nbrs(0)) Then
nbrs(0) = o
ElseIf o.C = s.C AndAlso IsNothing(nbrs(1)) Then
nbrs(1) = o
End If
If Not IsNothing(nbrs(0)) AndAlso Not IsNothing(nbrs(1)) Then
Exit For
End If
End If
Next
Return nbrs
End Function
 
Sub PrintResult(filename As String)
Console.WriteLine("Optimal solution {0}" + vbNewLine, filename)
Dim totalCosts = 0.0
 
For r = 1 To supply.Length
For c = 1 To demand.Length
Dim s = matrix(r - 1, c - 1)
If Not IsNothing(s) AndAlso s.R = r - 1 AndAlso s.C = c - 1 Then
Console.Write(" {0,3} ", s.Quantity)
totalCosts += (s.Quantity * s.CostPerUnit)
Else
Console.Write(" - ")
End If
Next
Console.WriteLine()
Next
Console.WriteLine(vbNewLine + "Total costs: {0}" + vbNewLine, totalCosts)
End Sub
End Class
 
Sub Main()
For Each filename In {"input1.txt", "input2.txt", "input3.txt"}
Dim p As New Program
p.Init(filename)
p.NorthWestCornerRule()
p.SteppingStone()
p.PrintResult(filename)
Next
End Sub
 
End Module</syntaxhighlight>
{{out}}
<pre>Optimal solution input1.txt
 
20 - 5
- 30 5
 
Total costs: 180
 
Optimal solution input2.txt
 
- - - 12
20 - 10 10
- 30 - 3
 
Total costs: 130
 
Optimal solution input3.txt
 
- - - 14
- 9 - 1
10 - 5 -
- 5 7 -
- 1 - -
 
Total costs: 1000</pre>
 
=={{header|Wren}}==
{{trans|Java}}
{{libheader|Wren-dynamic}}
{{libheader|Wren-ioutil}}
{{libheader|Wren-math}}
{{libheader|Wren-seq}}
{{libheader|Wren-fmt}}
<syntaxhighlight lang="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"])
 
class Transport {
construct new(filename) {
var lines = FileUtil.readLines(filename)
var split = lines[0].split(" ")
var numSources = Num.fromString(split[0])
var numDests = Num.fromString(split[1])
var src = List.filled(numSources, 0)
var dst = List.filled(numDests, 0)
split = lines[1].split(" ")
for (i in 0...numSources) src[i] = Num.fromString(split[i])
split = lines[2].split(" ")
for (i in 0...numDests) dst[i] = Num.fromString(split[i])
 
// fix imbalance
var totalSrc = Nums.sum(src)
var totalDst = Nums.sum(dst)
if (totalSrc > totalDst) {
dst.add(totalSrc - totalDst)
} else if (totalDst > totalSrc) {
src.add(totalDst - totalSrc)
}
_supply = src
_demand = dst
_costs = List.filled(_supply.count, null)
_matrix = List.filled(_supply.count, null)
for (i in 0..._supply.count) {
_costs[i] = List.filled(_demand.count, 0)
_matrix[i] = List.filled(_demand.count, null)
}
for (i in 0...numSources) {
split = lines[i + 3].split(" ")
for (j in 0...numDests) _costs[i][j] = Num.fromString(split[j])
}
_filename = filename
}
 
northWestCornerRule() {
var northwest = 0
for (r in 0..._supply.count) {
var c = northwest
while (c < _demand.count) {
var quantity = _supply[r].min(_demand[c])
if (quantity > 0) {
_matrix[r][c] = Shipment.new(quantity, _costs[r][c], r, c)
_supply[r] = _supply[r] - quantity.floor
_demand[c] = _demand[c] - quantity.floor
if (_supply[r] == 0) {
northwest = c
break
}
}
c = c + 1
}
}
}
 
steppingStone() {
var maxReduction = 0
var move = null
var leaving = null
fixDegenerateCase_()
 
for (r in 0..._supply.count) {
for (c in 0..._demand.count) {
if (_matrix[r][c] != null) continue
var trial = Shipment.new(0, _costs[r][c], r, c)
var path = getClosedPath_(trial)
var reduction = 0
var lowestQuantity = Num.maxSafeInteger
var leavingCandidate = null
var plus = true
for (s in path) {
if (plus) {
reduction = reduction + s.costPerUnit
} else {
reduction = reduction - s.costPerUnit
if (s.quantity < lowestQuantity) {
leavingCandidate = s
lowestQuantity = s.quantity
}
}
plus = !plus
}
if (reduction < maxReduction) {
move = path
leaving = leavingCandidate
maxReduction = reduction
}
}
}
 
if (move) {
var q = leaving.quantity
var plus = true
for (s in move) {
s.quantity = s.quantity + ((plus) ? q : -q)
_matrix[s.r][s.c] = (s.quantity == 0) ? null : s
plus = !plus
}
steppingStone()
}
}
 
matrixToList_() { Lst.flatten(_matrix).where { |s| s != null }.toList }
 
getClosedPath_(s) {
var path = matrixToList_()
path.insert(0, s)
// remove (and keep removing) elements that do not have a
// vertical AND horizontal neighbor
while (true) {
var removals = 0
for (e in path) {
var nbrs = getNeighbors_(e, path)
if (nbrs[0] == null || nbrs[1] == null) {
path.remove(e)
removals = removals + 1
}
}
if (removals == 0) break
}
 
// place the remaining elements in the correct plus-minus order
var stones = List.filled(path.count, null)
var prev = s
for (i in 0...stones.count) {
stones[i] = prev
prev = getNeighbors_(prev, path)[i % 2]
}
return stones
}
 
getNeighbors_(s, lst) {
var nbrs = List.filled(2, null)
for (o in lst) {
if (o != s) {
if (o.r == s.r && nbrs[0] == null) {
nbrs[0] = o
} else if (o.c == s.c && nbrs[1] == null) {
nbrs[1] = o
}
if (nbrs[0] != null && nbrs[1] != null) break
}
}
return nbrs
}
 
fixDegenerateCase_() {
var eps = Num.smallest
if (_supply.count + _demand.count - 1 != matrixToList_().count) {
for (r in 0..._supply.count) {
for (c in 0..._demand.count) {
if (_matrix[r][c] == null) {
var dummy = Shipment.new(eps, _costs[r][c], r, c)
if (getClosedPath_(dummy).count == 0) {
_matrix[r][c] = dummy
return
}
}
}
}
}
}
 
printResult() {
var text = File.read(_filename)
System.print("%(_filename)\n\n%(text)")
System.print("Optimal solution %(_filename)\n")
var totalCosts = 0
for (r in 0..._supply.count) {
for (c in 0..._demand.count) {
var s = _matrix[r][c]
if (s != null && s.r == r && s.c == c) {
Fmt.write(" $3d ", s.quantity.floor)
totalCosts = totalCosts + s.quantity * s.costPerUnit
} else System.write(" - ")
}
System.print()
}
System.print("\nTotal costs: %(totalCosts)\n")
}
}
 
var filenames = ["input1.txt", "input2.txt", "input3.txt"]
for (filename in filenames) {
var t = Transport.new(filename)
t.northWestCornerRule()
t.steppingStone()
t.printResult()
}</syntaxhighlight>
 
{{out}}
<pre>
input1.txt
 
2 3
25 35
20 30 10
3 5 7
3 2 5
 
Optimal solution input1.txt
 
20 - 5
- 30 5
 
Total costs: 180
 
input2.txt
 
3 3
12 40 33
20 30 10
3 5 7
2 4 6
9 1 8
 
Optimal solution input2.txt
 
- - - 12
20 - 10 10
- 30 - 3
 
Total costs: 130
 
input3.txt
 
4 4
14 10 15 12
10 15 12 15
10 30 25 15
20 15 20 10
10 30 20 20
30 40 35 45
 
Optimal solution input3.txt
 
- - - 14
- 9 - 1
10 - 5 -
- 5 7 -
- 1 - -
 
Total costs: 1000
</pre>
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