private static void SolveMinCostFlow()
{
Console.WriteLine("Min Cost Flow Problem");
int numSources = 4;
int numTargets = 4;
int[,] costs = { { 90, 75, 75, 80 },
{ 35, 85, 55, 65 },
{ 125, 95, 90, 105 },
{ 45, 110, 95, 115 } };
int expectedCost = 275;
MinCostFlow minCostFlow = new MinCostFlow();
for (int source = 0; source < numSources; ++source)
{
for (int target = 0; target < numTargets; ++target)
{
minCostFlow.AddArcWithCapacityAndUnitCost(
source, /*target=*/ numSources + target, /*capacity=*/ 1,
/*flow unit cost=*/ costs[source, target]);
}
}
for (int source = 0; source < numSources; ++source)
{
minCostFlow.SetNodeSupply(source, 1);
}
for (int target = 0; target < numTargets; ++target)
{
minCostFlow.SetNodeSupply(numSources + target, -1);
}
Console.WriteLine("Solving min cost flow with " + numSources +
" sources, and " + numTargets + " targets.");
int solveStatus = minCostFlow.Solve();
if (solveStatus == MinCostFlow.OPTIMAL)
{
Console.WriteLine("total computed flow cost = " +
minCostFlow.OptimalCost() +
", expected = " + expectedCost);
}
else
{
Console.WriteLine("Solving the min cost flow problem failed." +
" Solver status: " + solveStatus);
}
}
private static void SolveMinCostFlow()
{
Console.WriteLine("Min Cost Flow Problem");
int numSources = 4;
int numTargets = 4;
int[,] costs = { { 90, 75, 75, 80 },
{ 35, 85, 55, 65 },
{ 125, 95, 90, 105 },
{ 45, 110, 95, 115 } };
int expectedCost = 275;
StarGraph graph = new StarGraph(numSources + numTargets,
numSources * numTargets);
MinCostFlow minCostFlow = new MinCostFlow(graph);
for (int source = 0; source < numSources; ++source)
{
for (int target = 0; target < numTargets; ++target)
{
int arc = graph.AddArc(source, numSources + target);
minCostFlow.SetArcUnitCost(arc, costs[source, target]);
minCostFlow.SetArcCapacity(arc, 1);
}
}
for (int source = 0; source < numSources; ++source)
{
minCostFlow.SetNodeSupply(source, 1);
}
for (int target = 0; target < numTargets; ++target)
{
minCostFlow.SetNodeSupply(numSources + target, -1);
}
Console.WriteLine("Solving min cost flow with " + numSources +
" sources, and " + numTargets + " targets.");
if (minCostFlow.Solve())
{
long totalFlowCost = minCostFlow.GetOptimalCost();
Console.WriteLine("total computed flow cost = " + totalFlowCost +
", expected = " + expectedCost);
}
else
{
Console.WriteLine("No solution found");
}
}
public void PrintNetworkFlowSolution(MinCostFlow networkFlowSolution)
{
long optimalCost = networkFlowSolution.OptimalCost();
Console.WriteLine("Minimum cost: " + optimalCost);
Console.WriteLine("");
Console.WriteLine(" Edge Flow / Capacity Cost");
for (int i = 0; i < numArcs; ++i)
{
long cost = networkFlowSolution.Flow(i) * networkFlowSolution.UnitCost(i);
Console.WriteLine(networkFlowSolution.Tail(i) + " -> " +
networkFlowSolution.Head(i) + " " +
string.Format("{0,3}", networkFlowSolution.Flow(i)) + " / " +
string.Format("{0,3}", networkFlowSolution.Capacity(i)) + " " +
string.Format("{0,3}", cost));
}
}
public long solve(CFMAStar.CostFunction costFunction)
{
// Independence Detection
List <List <TimedMove> > nonConflictsPaths = null;
IndependentDetection id = new IndependentDetection(this.problemInstance, this.goalState);
MAM_AgentState[] newStartPositions = id.Detect(out nonConflictsPaths);
if (newStartPositions.Length != 0)
{
this.problemInstance = problemInstance.ReplanProblem(newStartPositions);
this.reducer = new CFMAM_MCMF_Reducer(this.problemInstance, this.goalState);
reducer.reduce(costFunction);
if (reducer.outputProblem == null)
{
return(-1);
}
MinCostMaxFlow mcmfSolver = new MinCostMaxFlow(reducer.outputProblem);
timer = Stopwatch.StartNew();
solution = mcmfSolver.SolveMinCostFlow();
List <TimedMove>[] partialPlan = this.reducer.GetCFMAMSolution(this.solution, this.mcmfTime, true);
if (costFunction == CFMAStar.CostFunction.MakeSpan)
{
while (!isPathForEachAgent(partialPlan))
{
this.reducer.addNetworkLayer();
mcmfSolver = new MinCostMaxFlow(reducer.outputProblem);
solution = mcmfSolver.SolveMinCostFlow();
partialPlan = this.reducer.GetCFMAMSolution(this.solution, this.mcmfTime, true);
}
}
timer.Stop();
this.plan = mergePlans(partialPlan, nonConflictsPaths);
this.mcmfTime = timer.ElapsedMilliseconds;
this.solutionCost = calculateCost(this.plan, costFunction);
}
else
{
this.plan = nonConflictsPaths;
this.solutionCost = calculateCost(this.plan, costFunction);
}
return(this.solutionCost);
}
static object Solve()
{
var(p, q) = Read2();
var s = Array.ConvertAll(new bool[p], _ => Console.ReadLine());
var ps = Array.ConvertAll(new bool[p], _ => Read2L());
var qs = Array.ConvertAll(new bool[q], _ => Read2L());
var sv = p + q;
var ev = sv + 1;
var mf = new MinCostFlow(ev + 1);
for (int i = 0; i < p; ++i)
{
mf.AddEdge(sv, i, 1, 0);
}
for (int j = 0; j < q; ++j)
{
mf.AddEdge(p + j, ev, 1, 0);
}
for (int i = 0; i < p; ++i)
{
var pa = ps[i].a - ps[i].b;
for (int j = 0; j < q; ++j)
{
var qa = qs[j].a - qs[j].b;
if (s[i][j] == '1' && pa + qa > 0)
{
mf.AddEdge(i, p + j, 1, -pa - qa);
}
}
}
var r0 = ps.Sum(_ => _.b) + qs.Sum(_ => _.b);
var r = mf.GetMinCostForRange(sv, ev, Math.Min(p, q));
if (r == long.MaxValue)
{
r = 0;
}
return(r0 - r);
}
private static void SolveMinCostFlow()
{
Console.WriteLine("Min Cost Flow Problem");
int numSources = 4;
int numTargets = 4;
int[,] costs = { {90, 75, 75, 80},
{35, 85, 55, 65},
{125, 95, 90, 105},
{45, 110, 95, 115} };
int expectedCost = 275;
MinCostFlow minCostFlow = new MinCostFlow();
for (int source = 0; source < numSources; ++source)
{
for (int target = 0; target < numTargets; ++target) {
minCostFlow.AddArcWithCapacityAndUnitCost(
source, /*target=*/numSources + target, /*capacity=*/1,
/*flow unit cost=*/costs[source, target]);
}
}
for (int source = 0; source < numSources; ++source)
{
minCostFlow.SetNodeSupply(source, 1);
}
for (int target = 0; target < numTargets; ++target)
{
minCostFlow.SetNodeSupply(numSources + target, -1);
}
Console.WriteLine("Solving min cost flow with " + numSources +
" sources, and " + numTargets + " targets.");
int solveStatus = minCostFlow.Solve();
if (solveStatus == MinCostFlow.OPTIMAL)
{
Console.WriteLine("total computed flow cost = " +
minCostFlow.OptimalCost() +
", expected = " + expectedCost);
}
else
{
Console.WriteLine("Solving the min cost flow problem failed." +
" Solver status: " + solveStatus);
}
}
static object Solve()
{
var(n, c) = Read2();
var a = Read();
var sv = 2 * n;
var ev = sv + 1;
var mf = new MinCostFlow(ev + 1);
for (int i = 0; i < n; ++i)
{
mf.AddEdge(sv, i, 1, c);
mf.AddEdge(n + i, ev, 1, 0);
mf.AddEdge(i, n + i, 1, -max);
for (int j = i + 1; j < n; j++)
{
mf.AddEdge(n + i, j, 1, Math.Abs(a[i] - a[j]));
}
}
return(mf.GetMinCostForRange(sv, ev, n) + n * max);
}
public MinCostFlow SolveMinCostFlow()
{
// Instantiate a SimpleMinCostFlow solver.
MinCostFlow minCostFlow = new MinCostFlow();
// Add each arc.
for (int i = 0; i < numArcs; ++i)
{
int arc = minCostFlow.AddArcWithCapacityAndUnitCost(startNodes[i], endNodes[i],
capacities[i], unitCosts[i]);
if (arc != i)
{
throw new Exception("Internal error");
}
}
// Add node supplies.
for (int i = 0; i < numNodes; ++i)
{
minCostFlow.SetNodeSupply(i, supplies[i]);
}
// Find the min cost flow.
int solveStatus = (int)minCostFlow.SolveMaxFlowWithMinCost();
if (solveStatus == (int)MinCostFlow.Status.OPTIMAL)
{
//PrintNetworkFlowSolution(minCostFlow);
return(minCostFlow);
}
else
{
Console.WriteLine("Solving the min cost flow problem failed. Solver status: " +
solveStatus);
return(null);
}
}
static void Main()
{
// [START data]
// Define four parallel arrays: sources, destinations, capacities, and unit costs
// between each pair. For instance, the arc from node 0 to node 1 has a
// capacity of 15.
// Problem taken From Taha's 'Introduction to Operations Research',
// example 6.4-2.
int[] startNodes = { 0, 0, 1, 1, 1, 2, 2, 3, 4 };
int[] endNodes = { 1, 2, 2, 3, 4, 3, 4, 4, 2 };
int[] capacities = { 15, 8, 20, 4, 10, 15, 4, 20, 5 };
int[] unitCosts = { 4, 4, 2, 2, 6, 1, 3, 2, 3 };
// Define an array of supplies at each node.
int[] supplies = { 20, 0, 0, -5, -15 };
// [END data]
// [START constraints]
// Instantiate a SimpleMinCostFlow solver.
MinCostFlow minCostFlow = new MinCostFlow();
// Add each arc.
for (int i = 0; i < startNodes.Length; ++i)
{
int arc =
minCostFlow.AddArcWithCapacityAndUnitCost(startNodes[i], endNodes[i], capacities[i], unitCosts[i]);
if (arc != i)
{
throw new Exception("Internal error");
}
}
// Add node supplies.
for (int i = 0; i < supplies.Length; ++i)
{
minCostFlow.SetNodeSupply(i, supplies[i]);
}
// [END constraints]
// [START solve]
// Find the min cost flow.
MinCostFlow.Status solveStatus = minCostFlow.Solve();
// [END solve]
// [START print_solution]
if (solveStatus == MinCostFlow.Status.OPTIMAL)
{
Console.WriteLine("Minimum cost: " + minCostFlow.OptimalCost());
Console.WriteLine("");
Console.WriteLine(" Edge Flow / Capacity Cost");
for (int i = 0; i < minCostFlow.NumArcs(); ++i)
{
long cost = minCostFlow.Flow(i) * minCostFlow.UnitCost(i);
Console.WriteLine(minCostFlow.Tail(i) + " -> " + minCostFlow.Head(i) + " " +
string.Format("{0,3}", minCostFlow.Flow(i)) + " / " +
string.Format("{0,3}", minCostFlow.Capacity(i)) + " " +
string.Format("{0,3}", cost));
}
}
else
{
Console.WriteLine("Solving the min cost flow problem failed. Solver status: " + solveStatus);
}
// [END print_solution]
}
static void Main()
{
// [START solver]
// Instantiate a SimpleMinCostFlow solver.
MinCostFlow minCostFlow = new MinCostFlow();
// [END solver]
// [START data]
// Define the directed graph for the flow.
int[] teamA = { 1, 3, 5 };
int[] teamB = { 2, 4, 6 };
// Define four parallel arrays: sources, destinations, capacities, and unit costs
// between each pair.
int[] startNodes = { 0, 0, 11, 11, 11, 12, 12, 12, 1, 1, 1, 1, 2, 2, 2, 2, 3, 3,
3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 8, 9, 10 };
int[] endNodes = { 11, 12, 1, 3, 5, 2, 4, 6, 7, 8, 9, 10, 7, 8, 9, 10, 7, 8,
9, 10, 7, 8, 9, 10, 7, 8, 9, 10, 7, 8, 9, 10, 13, 13, 13, 13 };
int[] capacities = { 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1 };
int[] unitCosts = { 0, 0, 0, 0, 0, 0, 0, 0, 90, 76, 75, 70, 35, 85, 55, 65, 125, 95,
90, 105, 45, 110, 95, 115, 60, 105, 80, 75, 45, 65, 110, 95, 0, 0, 0, 0 };
int source = 0;
int sink = 13;
// Define an array of supplies at each node.
int[] supplies = { 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4 };
// [END data]
// [START constraints]
// Add each arc.
for (int i = 0; i < startNodes.Length; ++i)
{
int arc =
minCostFlow.AddArcWithCapacityAndUnitCost(startNodes[i], endNodes[i], capacities[i], unitCosts[i]);
if (arc != i)
{
throw new Exception("Internal error");
}
}
// Add node supplies.
for (int i = 0; i < supplies.Length; ++i)
{
minCostFlow.SetNodeSupply(i, supplies[i]);
}
// [END constraints]
// [START solve]
// Find the min cost flow.
MinCostFlow.Status status = minCostFlow.Solve();
// [END solve]
// [START print_solution]
if (status == MinCostFlow.Status.OPTIMAL)
{
Console.WriteLine("Total cost: " + minCostFlow.OptimalCost());
Console.WriteLine("");
for (int i = 0; i < minCostFlow.NumArcs(); ++i)
{
// Can ignore arcs leading out of source or into sink.
if (minCostFlow.Tail(i) != 0 && minCostFlow.Tail(i) != 11 && minCostFlow.Tail(i) != 12 &&
minCostFlow.Head(i) != 13)
{
// Arcs in the solution have a flow value of 1. Their start and end nodes
// give an assignment of worker to task.
if (minCostFlow.Flow(i) > 0)
{
Console.WriteLine("Worker " + minCostFlow.Tail(i) + " assigned to task " + minCostFlow.Head(i) +
" Cost: " + minCostFlow.UnitCost(i));
}
}
}
}
else
{
Console.WriteLine("Solving the min cost flow problem failed.");
Console.WriteLine("Solver status: " + status);
}
// [END print_solution]
}
public List <TimedMove>[] GetCFMAMSolution(MinCostFlow mcmfSolution, long mcmfTime, bool printPath = false)
{
Stack <NFReducerNode>[] paths = new Stack <NFReducerNode> [startPositions.Length];
Stack <NFReducerNode[]>[] nodesForEachTime = new Stack <NFReducerNode[]> [this.T + 1];
for (int i = 0; i < nodesForEachTime.Length; i++)
{
nodesForEachTime[i] = new Stack <NFReducerNode[]>();
}
// Sorting each move to it's time
for (int i = 0; i < outputProblem.numArcs; i++)
{
long cost = mcmfSolution.Flow(i) * mcmfSolution.UnitCost(i);
if (cost != 0)
{
NFReducerNode fromNode = GetNode(mcmfSolution.Tail(i));
NFReducerNode toNode = GetNode(mcmfSolution.Head(i));
if (T - fromNode.nodeTime == 0)
{
NFReducerNode[] nodesStartArray = { null, fromNode };
nodesForEachTime[0].Push(nodesStartArray);
}
NFReducerNode[] nodesArray = { fromNode, toNode };
nodesForEachTime[T - toNode.nodeTime].Push(nodesArray);
}
}
// Inserting start nodes to each agent path
int startNodesCounter = 0;
foreach (NFReducerNode[] startNode in nodesForEachTime[0])
{
paths[startNodesCounter] = new Stack <NFReducerNode>();
paths[startNodesCounter].Push(startNode[1]);
startNodesCounter++;
}
// Searching agents that started on the meeting points
for (int i = 0; i < paths.Length; i++)
{
if (paths[i] == null)
{
if (isAgentStartedOnGoalNode())
{
paths[i] = new Stack <NFReducerNode>();
paths[i].Push(new NFReducerNode(0, goalState.x, goalState.y));
}
else
{
paths = paths.Where(p => p != null).ToArray();
}
break;
}
}
// Adding each node of each agent to his path
for (int i = 1; i < nodesForEachTime.Length; i++)
{
while (nodesForEachTime[i].Count != 0)
{
NFReducerNode[] move = nodesForEachTime[i].Pop();
for (int j = 0; j < paths.Length; j++)
{
NFReducerNode lastNode = paths[j].Peek();
if (lastNode.x == move[0].x && lastNode.y == move[0].y && lastNode.nodeTime == move[0].nodeTime)
{
paths[j].Push(move[1]);
break;
}
}
}
}
List <TimedMove>[] agentPaths = new List <TimedMove> [startPositions.Length];
for (int i = 0; i < agentPaths.Length; i++)
{
agentPaths[i] = new List <TimedMove>();
}
for (int i = 0; i < paths.Length; i++)
{
int pathLength = paths[i].Count;
while (paths[i].Count != 0)
{
int nodeTime = pathLength - paths[i].Count;
NFReducerNode node = paths[i].Pop();
agentPaths[i].Insert(0, new TimedMove(node.x, node.y, Move.Direction.NO_DIRECTION, nodeTime));
}
}
return(agentPaths);
}
