使用Prim算法找到有向图的MST

Question

can any one plz help me how to Find the MST using the PRIM algorithm. Highlight the edges of the MST and write the sequence in which the nodes are added to the MST.. thanks

Answer 1

Quoting The Directed Minimum Spanning Tree Problem :

1. Discard the arcs entering the root if any; For each node other than the root, select the entering arc with the smallest cost; Let the selected n-1 arcs be the set S.
2. If no cycle formed, G(N,S) is a MST. Otherwise, continue.
3. For each cycle formed, contract the nodes in the cycle into a pseudo-node (k), and modify the cost of each arc which enters a node (j) in the cycle from some node (i) outside the cycle according to the following equation.
   c(i,k)=c(i,j)-(c(x(j),j)-min_{j}(c(x(j),j)) here c(x(j),j) is the cost of the arc in the cycle which enters j.
4. For each pseudo-node, select the entering arc which has the smallest modified cost; Replace the arc which enters the same real node in S by the new selected arc.
5. Go to step 2 with the contracted graph.

The key idea of the algorithm is to find the replacing arc(s) which has the minimum extra cost to eliminate cycle(s) if any. The given equation exhibits the associated extra cost.