C Language algorithm

This problem has been examined in cases 1-2 and 1-3. Because each spanning tree of the N-vertex-free network g has exactly the n-1 edge, the problem is to select the n-1 edge in some way so that they form the minimum spanning tree of G. At least three different greedy strategies can be used to select this n-1 edge. The three greedy algorithm strategies for minimizing spanning trees are: K r u S k a l algorithm, P r i m algorithm and s o l l n algorithm.

1.Kruskal algorithm

(1) Algorithm idea

K r u S k a l algorithm to select the n-1 edge each time, the greedy rule is: from the remaining side of the selection of a loop does not produce a minimum cost of the edge to join the selected edge of the collection. Note that if the selected edge produces a loop, it is impossible to form a spanning tree. K r u S k a l algorithm is divided into e-step, where E is the number of edges in the network. Consider this e-edge in an incremental order, considering one side at a time. When you consider an edge, if you add it to the collection of the selected edges, the loop appears, discard it, or select it.

Explore the network in Figure 1-12a. No edges are selected at the beginning. Figure 13-12b shows the current state of each node. The Edge (1,6) is the first selected edge, which is added to the build tree to be built, with figure 1 3-1 2 C. Next select the Edge (3,4) and add it to the tree (as shown in Figure 1 3-1 2 D). Then consider the Edge (2,7), add it to the tree does not produce a loop, so you get Figure 1 3-1 2 E. Next consider the edge (2,3) and add it to the tree (as shown in Figure 1 3-1 2 f). On the other side that has not yet been considered, (7,4) has a minimum cost, so consider it first, add it to the tree you are creating and create a loop, so discard it. The Edge (5,4) is then added to the tree, and the resulting tree is shown in Figure 13-12g. The next consideration is the Edge (7,5), which is discarded because it produces a loop. Finally, consider the Edge (6,5) and add it to the tree to produce a spanning tree, which consumes 9 9. Fig. 1-1 3 shows the pseudo code of K r u S k a l algorithm.

//Find a minimum spanning tree in a network with n vertices

Make T a collection of the selected edges, initialize the t=

Make e a collection of edges in the network

W h i l e (e≠) && (| T |≠n-1) {

Order (U,V) is the least expensive edge in E e=e-{(u,v)}//Remove Edge from E

I f ((u,v) does not produce loops in T) will (U,V) be added T

}

I f (| T |==n-1) T is the minimum cost spanning tree

E L S E Networks are not interconnected and cannot find the spanning tree

Graph 13-13 Kruskao algorithm pseudo-code