/*
* Time((V+E)logV), Space(V)
* can't handle negative distances; can return shortest paths from vertex 0 to all other vertice.
* 1. initialize the distance of vetex 0 to 0 and all others to INF.
* 2. add all vertice to a minimum heap based on their distances from vetex 0
* 2. loop until heap is empty, extract min from heap and update the distance of its all adjacent vertices.
*/
int[] Dijkstra(int n, IList <int[]>[] adj)
{
var dist = new int[n];
for (int i = 1; i < n; i++)
{
dist[i] = INF;
}
var heap = new HeapArray(dist);
var prev = new int[n]; // used to recover the path
for (int i = 0; i < n - 1; i++)
{
var min = heap.ExtractMin();
foreach (var e in adj[min])
{
int src = e[0], dst = e[1], w = e[2];
if (dist[dst] > dist[src] + w)
{
heap.Update(dst, dist[src] + w);
dist[dst] = dist[src] + w;
prev[dst] = src;
}
}
}
return(dist);
}