void Kruskal(Graph& G, Edge* &MST) {
ParTree<int> A(G.verticesNum()); //等价类
minHeap<Edge> H(G.edgesNum()); //最小值堆（minheap）
MST=new Edge[G.verticesNum()-1]; //最小支撑树
int MSTtag=0; //最小支撑树边的标号
for(int i=0; i<G.verticesNum(); i++) //将图的所有边插入最小值堆H中
for(Edge e= G. firstEdge(i); G.isEdge(e);e=G. nextEdge(e))
if(G.fromVertex(e)< G.toVertex(e)) //因为是无向图，所以应防止重复插入
H.insert(e);
int EquNum=G.verticesNum(); //开始时有|V|个等价类
while(EquNum>1) { //合并等价类
Edge e=H.removeMin(); //获得下一条权最小的边
if(e.weight==INFINITE) {
std::cout << "不存在最小支撑树." <<std::endl;
delete [] MST; //释放空间
MST=NULL; //MST是空数组
return;
}
int from=G.fromVertex(e); //记录该条边的信息
int to= G.toVertex(e);
if(A.Different(from,to)) { //如果边e的两个顶点不在一个等价类
A.Union(from,to); //将边e的两个顶点所在的两个等价类合并为一个
AddEdgetoMST(e,MST,MSTtag++); //将边e加到MST
EquNum--; //将等价类的个数减1
}
}
}
// Prim's MST algorithm: priority queue version
void Prim(Graph* G, int* D, int s) {
int i, v, w; // "v" is current vertex
int V[G->n()]; // V[I] stores I's closest neighbor
DijkElem temp;
DijkElem E[G->e()]; // Heap array with lots of space
temp.distance = 0; temp.vertex = s;
E[0] = temp; // Initialize heap array
heap<DijkElem, DDComp> H(E, 1, G->e()); // Create heap
for (i=0; i<G->n(); i++) { // Now build MST
do {
if(H.size() == 0) return; // Nothing to remove
temp = H.removefirst();
v = temp.vertex;
} while (G->getMark(v) == VISITED);
G->setMark(v, VISITED);
if (v != s) AddEdgetoMST(V[v], v); // Add edge to MST
if (D[v] == INFINITY) return; // Ureachable vertex
for (w=G->first(v); w<G->n(); w = G->next(v,w))
if (D[w] > G->weight(v, w)) { // Update D
D[w] = G->weight(v, w);
V[w] = v; // Update who it came from
temp.distance = D[w]; temp.vertex = w;
H.insert(temp); // Insert new distance in heap
}
}
}
void Kruskel(Graph* G) { // Kruskal's MST algorithm
ParPtrTree A(G->n()); // Equivalence class array
KruskElem E[G->e()]; // Array of edges for min-heap
int i;
int edgecnt = 0;
for (i=0; i<G->n(); i++) // Put the edges on the array
for (int w=G->first(i); w<G->n(); w = G->next(i,w)) {
E[edgecnt].distance = G->weight(i, w);
E[edgecnt].from = i;
E[edgecnt++].to = w;
}
// Heapify the edges
heap<KruskElem, Comp> H(E, edgecnt, edgecnt);
int numMST = G->n(); // Initially n equiv classes
for (i=0; numMST>1; i++) { // Combine equiv classes
KruskElem temp;
temp = H.removefirst(); // Get next cheapest edge
int v = temp.from; int u = temp.to;
if (A.differ(v, u)) { // If in different equiv classes
A.UNION(v, u); // Combine equiv classes
AddEdgetoMST(temp.from, temp.to); // Add edge to MST
numMST--; // One less MST
}
}
}
