public static bool hamiltonianCycleUtil(GraphAM graph, int[] path, int pSize, int[] added)
{
// Base case full length path is found this last check can be modified to make it a path.
if (pSize == graph.count)
{
if (graph.adj[path[pSize - 1], path[0]] == 1)
{
path[pSize] = path[0];
return(true);
}
else
{
return(false);
}
}
for (int vertex = 0; vertex < graph.count; vertex++)
{
// there is a path from last element and next vertex
if (pSize == 0 || (graph.adj[path[pSize - 1], vertex] == 1 && added[vertex] == 0))
{
path[pSize++] = vertex;
added[vertex] = 1;
if (hamiltonianCycleUtil(graph, path, pSize, added))
{
return(true);
}
// backtracking
pSize--;
added[vertex] = 0;
}
}
return(false);
}
public static bool hamiltonianPathUtil(GraphAM graph, int[] path, int pSize, int[] added)
{
// Base case full length path is found
if (pSize == graph.count)
{
return(true);
}
for (int vertex = 0; vertex < graph.count; vertex++)
{
// there is a path from last element and next vertex
// and next vertex is not already included in path.
if (pSize == 0 || (graph.adj[path[pSize - 1], vertex] == 1 && added[vertex] == 0))
{
path[pSize++] = vertex;
added[vertex] = 1;
if (hamiltonianPathUtil(graph, path, pSize, added))
{
return(true);
}
// backtracking
pSize--;
added[vertex] = 0;
}
}
return(false);
}
public static void dijkstra(GraphAM gph, int source)
{
int[] previous = new int[gph.count];
int[] dist = new int[gph.count];
bool[] visited = new bool[gph.count];
for (int i = 0; i < gph.count; i++)
{
previous[i] = -1;
dist[i] = int.MaxValue; // infinite
visited[i] = false;
}
dist[source] = 0;
previous[source] = -1;
PriorityQueue <Edge> queue = new PriorityQueue <Edge>();
Edge node = new Edge(source, 0);
queue.add(node);
while (queue.isEmpty() != true)
{
node = queue.peek();
queue.remove();
source = node.dest;
visited[source] = true;
for (int dest = 0; dest < gph.count; dest++)
{
int cost = gph.adj[source, dest];
if (cost != 0)
{
int alt = cost + dist[source];
if (dist[dest] > alt && visited[dest] == false)
{
dist[dest] = alt;
previous[dest] = source;
node = new Edge(dest, alt);
queue.add(node);
}
}
}
}
int count = gph.count;
for (int i = 0; i < count; i++)
{
if (dist[i] == int.MaxValue)
{
Console.WriteLine(" \n node id " + i + " prev " + previous[i] + " distance : Unreachable");
}
else
{
Console.WriteLine(" node id " + i + " prev " + previous[i] + " distance : " + dist[i]);
}
}
}
public static void Main(string[] args)
{
GraphAM graph = new GraphAM(4);
graph.addUndirectedEdge(0, 1, 1);
graph.addUndirectedEdge(0, 2, 1);
graph.addUndirectedEdge(1, 2, 1);
graph.addUndirectedEdge(2, 3, 1);
graph.print();
}
public static void main2(string[] args)
{
int count = 5;
GraphAM graph = new GraphAM(count);
int[,] adj = new int[, ]
{
{ 0, 1, 0, 1, 0 },
{ 1, 0, 1, 1, 0 },
{ 0, 1, 0, 0, 1 },
{ 1, 1, 0, 0, 1 },
{ 0, 1, 1, 1, 0 }
};
for (int i = 0; i < count; i++)
{
for (int j = 0; j < count; j++)
{
if (adj[i, j] == 1)
{
graph.addDirectedEdge(i, j, 1);
}
}
}
Console.WriteLine("hamiltonianPath : " + hamiltonianPath(graph));
Console.WriteLine("hamiltonianCycle : " + hamiltonianCycle(graph));
GraphAM graph2 = new GraphAM(count);
int[,] adj2 = new int[, ]
{
{ 0, 1, 0, 1, 0 },
{ 1, 0, 1, 1, 0 },
{ 0, 1, 0, 0, 1 },
{ 1, 1, 0, 0, 0 },
{ 0, 1, 1, 0, 0 }
};
for (int i = 0; i < count; i++)
{
for (int j = 0; j < count; j++)
{
if (adj2[i, j] == 1)
{
graph2.addDirectedEdge(i, j, 1);
}
}
}
Console.WriteLine("hamiltonianPath : " + hamiltonianPath(graph2));
Console.WriteLine("hamiltonianCycle : " + hamiltonianCycle(graph2));
}
public static bool hamiltonianCycle(GraphAM graph)
{
int[] path = new int[graph.count + 1];
int[] added = new int[graph.count];
if (hamiltonianCycleUtil(graph, path, 0, added))
{
Console.WriteLine("Hamiltonian Cycle found :: ");
for (int i = 0; i <= graph.count; i++)
{
Console.Write(" " + path[i]);
}
return(true);
}
Console.WriteLine("Hamiltonian Cycle not found");
return(false);
}
public static void main41(string[] args)
{
GraphAM gph = new GraphAM(9);
gph.addUndirectedEdge(0, 2, 1);
gph.addUndirectedEdge(1, 2, 5);
gph.addUndirectedEdge(1, 3, 7);
gph.addUndirectedEdge(1, 4, 9);
gph.addUndirectedEdge(3, 2, 2);
gph.addUndirectedEdge(3, 5, 4);
gph.addUndirectedEdge(4, 5, 6);
gph.addUndirectedEdge(4, 6, 3);
gph.addUndirectedEdge(5, 7, 1);
gph.addUndirectedEdge(6, 7, 7);
gph.addUndirectedEdge(7, 8, 17);
gph.print();
prims(gph);
dijkstra(gph, 1);
}
public static void main40(string[] args)
{
GraphAM gph = new GraphAM(9);
gph.addUndirectedEdge(0, 1, 4);
gph.addUndirectedEdge(0, 7, 8);
gph.addUndirectedEdge(1, 2, 8);
gph.addUndirectedEdge(1, 7, 11);
gph.addUndirectedEdge(2, 3, 7);
gph.addUndirectedEdge(2, 8, 2);
gph.addUndirectedEdge(2, 5, 4);
gph.addUndirectedEdge(3, 4, 9);
gph.addUndirectedEdge(3, 5, 14);
gph.addUndirectedEdge(4, 5, 10);
gph.addUndirectedEdge(5, 6, 2);
gph.addUndirectedEdge(6, 7, 1);
gph.addUndirectedEdge(6, 8, 6);
gph.addUndirectedEdge(7, 8, 7);
gph.print();
prims(gph);
dijkstra(gph, 0);
}
