// a *standard* implementation of Dijkstra's algorithm using a priority queue
// with a minor modification for the problem
static int GetTreeWeight(Graph graph, int hospital, int verticeCount, IEnumerable<int> hospitals)
{
var distances = new MinHeap<int>();
foreach (var adj in graph[hospital])
{
distances.TrySetPriority(adj.Item2, adj.Item1);
}
// return value
int ret = 0;
var tree = new HashSet<int>();
int housesAdded = 0;
int totalHouses = verticeCount - hospitals.Count();
while (housesAdded < totalHouses && distances.Count > 0)
{
// edge nearest to 'hospital'
var min = distances.ChopHeadWithPriority();
var weight = min.Item1;
// the new vertex in the tree
var v1 = min.Item2;
// modification of algorithm:
// sum the distance to the root of all nodes that aren't
// hospitals
if (!hospitals.Contains(v1))
{
housesAdded += 1;
ret += weight;
}
tree.Add(v1);
// update the priorities of all external neighbours of the vertex
// we've just added
foreach (var adj in graph[v1])
{
var v2 = adj.Item1;
if (v2 == hospital)
continue;
if (tree.Contains(v2))
{
continue;
}
// perhaps improve priority
distances.TrySetPriority(weight + adj.Item2, v2, false);
}
}
return ret;
}