private static void BuildGraph()
{
// For each cube from the cuboid we assign two nodes in the graph
int graphNodesCount = 2 * (width * height * depth) + 2;
graph = new Graph(graphNodesCount);
// Add edges from the startNode to the top side of the cuboid
startNode = graphNodesCount - 2;
for (int w = 0; w < width; w++)
{
for (int h = 0; h < height; h++)
{
int topSideNode = CalcNodeNumber(w, h, 0, 0);
int capacity = cuboid[w, h, 0];
graph.AddEdge(startNode, topSideNode, capacity);
}
}
// Add edges between each cube and its 5 neighbors
for (int d = 0; d < depth; d++)
{
for (int w = 0; w < width; w++)
{
for (int h = 0; h < height; h++)
{
AddEdgeIfPossible(w, h, d, w + 1, h, d);
AddEdgeIfPossible(w, h, d, w - 1, h, d);
AddEdgeIfPossible(w, h, d, w, h + 1, d);
AddEdgeIfPossible(w, h, d, w, h - 1, d);
AddEdgeIfPossible(w, h, d, w, h, d + 1);
AddEdgeBetweenDoubledNode(w, h, d);
}
}
}
// Add edges from the bottom side of the cuboid the the endNode
endNode = graphNodesCount - 1;
for (int w = 0; w < width; w++)
{
for (int h = 0; h < height; h++)
{
int bottomSideNode = CalcNodeNumber(w, h, depth - 1, 1);
int capacity = cuboid[w, h, depth - 1];
graph.AddEdge(bottomSideNode, endNode, capacity);
}
}
}
private static int GetPathCapacity(Graph g, List<int> path)
{
int pathCapacity = int.MaxValue;
for (int i = 0; i < path.Count - 1; i++)
{
int fromNode = path[i];
int toNode = path[i + 1];
int edgeCapacity = g.Capacities[fromNode, toNode];
if (edgeCapacity < pathCapacity)
{
pathCapacity = edgeCapacity;
}
}
return pathCapacity;
}
private static void AugmentPath(Graph g, List<int> path, int minCapacity)
{
for (int i = 0; i < path.Count - 1; i++)
{
int fromNode = path[i];
int toNode = path[i + 1];
g.Capacities[fromNode, toNode] -= minCapacity;
g.Capacities[toNode, fromNode] += minCapacity;
}
}
private static List<int> FindAugumentingPathBFS(Graph g, int startNode, int endNode)
{
int?[] prevNode = new int?[g.NodesCount];
Queue<int> queue = new Queue<int>();
bool[] visited = new bool[g.NodesCount];
visited[startNode] = true;
queue.Enqueue(startNode);
while (queue.Count > 0)
{
int currentNode = queue.Dequeue();
if (currentNode == endNode)
{
// Build the path by using prevNode[]
List<int> path = new List<int>();
int? node = endNode;
while (node != null)
{
path.Add(node.Value);
node = prevNode[node.Value];
}
path.Reverse();
return path;
}
// Append all possible child nodes to the queue
foreach (var childNode in g.ChildNodes[currentNode])
{
var capacity = g.Capacities[currentNode, childNode];
if (capacity > 0 && !visited[childNode])
{
prevNode[childNode] = currentNode;
visited[childNode] = true;
queue.Enqueue(childNode);
}
}
}
return null;
}
public static int MaxFlow(Graph g, int sourceNode, int terminalNode)
{
int maxFlow = 0;
while (true)
{
List<int> augumentingPath = FindAugumentingPathBFS(g, sourceNode, terminalNode);
if (augumentingPath == null)
{
// No more augumenting paths --> max flow is found
break;
}
int pathCapacity = GetPathCapacity(g, augumentingPath);
AugmentPath(g, augumentingPath, pathCapacity);
maxFlow += pathCapacity;
}
return maxFlow;
}