我正在研究Kruskal的算法。使用qsort函数的排序部分会创建一个奇怪的节点行为:它按权重正确排序,但会更改每个节点的父节点。当程序执行FIND-SET(X)
函数时,这种行为导致堆栈溢出。
这是我的代码:
#include <iostream>
/*
*DISJOINT
*SETS
*/
typedef struct NODE {
int rank;
int data;
struct NODE *parent;
} NODE;
//MAKE-SET(x)
void makeSet(NODE *node) {
node->parent = node;
node->rank = 0;
}
//FIND-SET(x)
NODE *findSet(NODE *node) {
if (node != node->parent) {
node->parent = findSet(node->parent);
}
return node->parent;
}
//LINK(x, y)
void link(NODE *nodeX, NODE *nodeY) {
if (nodeX->rank > nodeY->rank) {
nodeY->parent = nodeX;
} else {
nodeX->parent = nodeY;
if (nodeX->rank == nodeY->rank) {
nodeY->rank += 1;
}
}
}
//UNION(x, y)
void unionSet(NODE *nodeX, NODE *nodeY) {
link(findSet(nodeX), findSet(nodeY));
}
/*
*GRAPH
*/
typedef struct EDGE {
NODE source;
NODE destination;
int weight;
} EDGE;
typedef struct GRAPH {
int V; //Number of vertices/nodes
int E; //Number of edges
EDGE *edge; //Array of edges
} GRAPH;
GRAPH *newGraph(int allocatedNumberOfVertices, int allocatedNumberOfEdges) {
GRAPH *graph = (GRAPH *)malloc(sizeof(GRAPH));
graph->E = 0; // intial state: no edges
graph->V = allocatedNumberOfVertices;
graph->edge = (EDGE *)malloc((allocatedNumberOfEdges) * sizeof(EDGE));
return graph;
}
void addEdge(GRAPH *graph, NODE srcNode, NODE dstNode, int weight) {
graph->edge[graph->E].source = srcNode;
graph->edge[graph->E].destination = dstNode;
graph->edge[graph->E].weight = weight;
graph->E += 1;
}
int compareEdges(const void *first, const void *second) {
const EDGE *firstEdge = (const EDGE *)first;
const EDGE *secondEdge = (const EDGE *)second;
if (firstEdge->weight == secondEdge->weight) {
return 0;
} else if (firstEdge->weight > secondEdge->weight) {
return 1;
} else {
return -1;
}
}
/*Kruskal's algorithm - returns an array of least weighted edges*/
EDGE *getMinimumSpanningTree(GRAPH *graph) {
int V = graph->V;
int E = graph->E;
int resultE = 0;
EDGE *result = (EDGE *)malloc(E * (sizeof(EDGE)));
//create a disjoint-set for every node
for (int e = 0; e < E; e++) {
makeSet(&(graph->edge[e].source));
makeSet(&(graph->edge[e].destination));
}
//sort edges of graph into nondecreasing order by weight
qsort(graph->edge, graph->E, sizeof(struct EDGE), compareEdges);
//finds a safe edge to add to the growing forest
for (int e = 0; e < E; e++) {
if (findSet(&(graph->edge[e].source))->data != findSet(&(graph->edge[e].destination))->data) {
result[resultE++] = *graph->edge;
unionSet(&(graph->edge[e].source), &(graph->edge[e].destination));
}
}
return result;
}
void KruskalDemo() {
GRAPH *graph = newGraph(6, 9);
NODE node[6];
for (int i = 0; i < 6; i++) {
node[i].data = i;
}
addEdge(graph, node[0], node[1], 3);
addEdge(graph, node[1], node[2], 1);
addEdge(graph, node[2], node[3], 1);
addEdge(graph, node[3], node[0], 1);
addEdge(graph, node[3], node[1], 3);
addEdge(graph, node[3], node[4], 6);
addEdge(graph, node[4], node[2], 5);
addEdge(graph, node[4], node[5], 2);
addEdge(graph, node[5], node[2], 4);
EDGE *MST = getMinimumSpanningTree(graph);
//we expect to have 5 vertices
for (int i = 0; i < 5; i++) {
printf("weight(%d, %d) = %d\n", MST->source.data, MST->destination.data, MST->weight);
}
}
int main() {
KruskalDemo();
return 0;
}