[Minimum tree structure of a directed graph-zhu liu algorithm] Template

Find a learning URL for the tree in the smallest tree, like ~ Http://acm.nudt.edu.cn /~ The Minimum Spanning Tree of twcourse/tree.html undirected graphs can use prim. Algorithm Or the krusual algorithm, and the Minimum Spanning Tree of the directed graph is also called the Minimum Spanning Tree. It first fixes a root and then obtains the tree embedding template with the smallest weight.

# Define n 1005 # define type int # define Max int_maxstruct edge {int U, V; type cost;} e [40005]; int pre [N], Id [N], vis [N]; Type in [N]; int n, m; Type Zhuliu (INT root, int NV, int ne) {// root, number of knots, number of edges type ret = 0; while (true) {// 1. find the smallest inbound edge for (INT I = 0; I <NV; I ++) in [I] = max; For (INT I = 0; I <ne; I ++) {int u = E [I]. u; int v = E [I]. v; If (E [I]. cost <in [v] & U! = V) {// In this step, you can cut off the self-ring and find the smallest inbound edge of each vertex pre [v] = u; in [v] = E [I]. cost ;}}for (INT I = 0; I <NV; I ++) {if (I = root) continue; If (in [I] = max) return-1; // if there is no inbound edge except the heel, the root cannot reach it} // 2. int cntnode = 0; memset (ID,-1, sizeof (ID); memset (VIS,-1, sizeof (VIS); in [root] = 0; for (INT I = 0; I <NV; I ++) {// mark each ring RET + = in [I]; int v = I; while (vis [v]! = I & ID [v] =-1 & V! = Root) {vis [v] = I; // vis is used to mark each node in the ring as the vertex with an inbound edge, for example, to mark 1, 2, 3, 4, 5, 6 are marked as 1 V = pre [v];} If (V! = Root & ID [v] =-1) {for (INT u = pre [v]; u! = V; u = pre [u]) {ID [u] = cntnode;} ID [v] = cntnode ++ ;}} if (cntnode = 0) break; // For (INT I = 0; I <NV; I ++) if (ID [I] =-1) {ID [I] = cntnode ++ ;} // 3. scale down, re-mark, adjust the weight of the edge entering the ring, so that the minimum inbound edge can be found in the next cycle (INT I = 0; I <ne; I ++) {int v = E [I]. v; E [I]. U = ID [E [I]. u]; E [I]. V = ID [E [I]. v]; If (E [I]. u! = E [I]. v) {e [I]. Cost-= in [v] ;}} NV = cntnode; root = ID [root];} return ret ;}