Dijkstra's Algorithm

Dijkstra's algorithm, also known as single-source shortest paths, solves the problem of finding the shortest path from a point in a graph (the source) to a destination. It is a greedy algorithm and similar to Prim's algorithm. Algorithm starts at the source vertex, s, it grows a tree, T, that ultimately spans all vertices reachable from S. Vertices are added to T in order of distance i.e., first S, then the vertex closest to S, then the next closest, and so on.

private static int MinimumDistance(int[] distance, bool[] shortestPathTreeSet, int verticesCount)
{
int min = int.MaxValue;
int minIndex = 0;

for (int v = 0; v < verticesCount; ++v)
{
if (shortestPathTreeSet[v] == false && distance[v] <= min)
{
min = distance[v];
minIndex = v;
}
}

return minIndex;
}

private static void Print(int[] distance, int verticesCount)
{
Console.WriteLine("Vertex    Distance from source");

for (int i = 0; i < verticesCount; ++i)
Console.WriteLine("{0}\t  {1}", i, distance[i]);
}

public static void Dijkstra(int[,] graph, int source, int verticesCount)
{
int[] distance = new int[verticesCount];
bool[] shortestPathTreeSet = new bool[verticesCount];

for (int i = 0; i < verticesCount; ++i)
{
distance[i] = int.MaxValue;
shortestPathTreeSet[i] = false;
}

distance[source] = 0;

for (int count = 0; count < verticesCount - 1; ++count)
{
int u = MinimumDistance(distance, shortestPathTreeSet, verticesCount);
shortestPathTreeSet[u] = true;

for (int v = 0; v < verticesCount; ++v)
if (!shortestPathTreeSet[v] && Convert.ToBoolean(graph[u, v]) && distance[u] != int.MaxValue && distance[u] + graph[u, v] < distance[v])
distance[v] = distance[u] + graph[u, v];
}

Print(distance, verticesCount);
}

Example

int[,] graph = {
{ 0, 4, 0, 0, 0, 0, 0, 8, 0 },
{ 4, 0, 8, 0, 0, 0, 0, 11, 0 },
{ 0, 8, 0, 7, 0, 4, 0, 0, 2 },
{ 0, 0, 7, 0, 9, 14, 0, 0, 0 },
{ 0, 0, 0, 9, 0, 10, 0, 0, 0 },
{ 0, 0, 4, 0, 10, 0, 2, 0, 0 },
{ 0, 0, 0, 14, 0, 2, 0, 1, 6 },
{ 8, 11, 0, 0, 0, 0, 1, 0, 7 },
{ 0, 0, 2, 0, 0, 0, 6, 7, 0 }
};

Dijkstra(graph, 0, 9);

Output

Vertex    Distance from source
0         0
1         4
2         12
3         19
4         21
5         11
6         9
7         8
8         14