void dijkstra(MGraph *G, int s)
{
int i, *set, u, v;
MinQueue queue;
initialize_single_source(G, s);
set = malloc(sizeof(int)*G->numVertexes);
queue.size = G->numVertexes;
queue.heap = malloc(sizeof(int)*(G->numVertexes+1));
//初始化集合S为空
for(i=0;i<G->numVertexes;i++)
{
set[i] = 0;
}
set[s] = 1;
//初始化队列为空
for(i=0;i<G->numVertexes;i++)
{
queue.heap[i+1] = i;
}
//逐步添加最小权值边
while(queue.size>0)
{
build_min_heap(&queue);
u = extract_min(&queue);
set[u] = 1;
for(i=0;i<G->numVertexes;i++)
{
if(G->edges[u][i] != INFINITY)
{
relax(u,i, G->edges[u][i]);
}
}
}
}
void dijkstra_normal(MGraph *G, int s)
{
printf("This is dijkstra O(n2)\n");
int i ,j, u, *set, min;
initialize_single_source(G, s);
set = malloc(sizeof(int)*G->numVertexes);
for(i=0;i<G->numVertexes;i++)
{
set[i] = 0;
}
for(i=0;i<G->numVertexes;i++)
{
min = INFINITY;
for(j=0;j<G->numVertexes;j++)
{
if((set[j]==0) && d[j] < min)
{
u = j;
min = d[j];
}
}
set[u] = 1;
for(j=0;j<G->numVertexes;j++)
{
if(G->edges[u][j] != INFINITY)
{
if(d[j] > d[u] +G->edges[u][j])
{
d[j] = d[u] + G->edges[u][j];
p[j] = u;
}
}
}
}
}
// 将d[]拷贝到优先队列中，在优先队列中对d进行修改(decreace_key)
// 处理完成后，再拷贝出来
// 假定graph，d[]，parent[]均已分配内存
void dijkstra(AdjList* graph, int numVertices, int s, int d[], int parent[])
{
int i;
AdjListNodePtr v;
FibHeap h = make_fib_heap();
FibHeapNodePtr fpnArray[numVertices];
initialize_single_source(graph, numVertices, s, d, parent);
construct_queue(graph, numVertices, d, h, fpnArray);
fib_heap_root_print(h->min);
while(h->min != NIL)
{
FibHeapNodePtr u = fib_heap_extract_min(h);
printf("extract_min: %d\n", u->ref);
// 指示顶点u已不再优先队列中
u->inq = FALSE;
v = graph[u->ref];
// 对以u->ref为顶点的每条边进行松弛
while(v)
{
// 有无代码依赖于parent[]的修改？
// 循环的下一次迭代依赖于优先队列中关键字域的修改
dijkstra_relax(u->ref, v->vertex, v->weight, parent, fpnArray, h);
v = v->next;
}
}
// 将队列中关键字的值拷贝回d中，利用fpnArray[]
for (i = 0; i < numVertices; i++) {
d[i] = fpnArray[i]->key;
}
// 释放优先队列中的内存...
}
/* Run the Bellman-Ford algorithm from vertex s. Fills in arrays d
and pi. */
int bellman_ford(int first[], int node[], int next[], double w[], double d[],
int pi[], int s, int n) {
int u, v, i, j;
initialize_single_source(d, pi, s, n);
for (i = 1; i <= n-1; ++i) {
for (u = 1; u <= n; ++u) {
j = first[u];// pour chaque sommet
while (j > 0) {
v = node[j];
relax(u, v, w[j], d, pi);
j = next[j];
}
}
}
for (u = 1; u <= n; ++u) {
j = first[u];
while (j > 0) {
v = node[j];
if (d[v] > d[u] + w[j])
return 0;
j = next[j];
}
}
return 1;
}
/**
* @brief Dijkstra's shortest path algorithm
*
* @param[in] g The graph to operate on
* @param[in] s The starting vertex
* @param[in] cb The function to call when a shortest spath vertex is determined.
*/
void sp_dijkstra (GRAPH_T* g, unsigned long s, SP_DJ_FP_T cb)
{
HEAP_T* h;
VTX_D_T* u = NULL;
VTX_D_T* v;
unsigned long key, no;
char* ctx = NULL;
EDGE_T* e;
void* p;
initialize_single_source (g, s);
h = heap_create (DS_HEAP_MIN, GRAPH_NO_VERTICES(g));
while (NULL != (u = graph_vertex_next_get (g, u)))
{
heap_min_insert (h, D_SP_AUX_SPEST(u), u, &D_SP_AUX_I(u));
}
while (HEAP_SIZE(h))
{
heap_extract_min (h, &p, &key);
u = (VTX_D_T*)p;
ctx = NULL;
no = ((VTX_D_T*)u)->no;
while (no)
{
e = graph_vertex_next_edge_get (g, u, &ctx);
if (e->v1 == u)
v = e->v2;
else
v = e->v1;
if (v->id.iid == s)
{
no--;
continue;
}
DEBUG_PRINT ("Relaxing v=%lu (OLD weight: %lu; NEW weight: u=%lu w=%lu)\n",
v->id.iid, D_SP_AUX_SPEST(v), u->id.iid, e->weight);
relax (g, u, v, e->weight);
heap_decrease_key (h, D_SP_AUX_I(v), D_SP_AUX_SPEST(v));
no--;
}
}
if (cb)
{
v = NULL;
while (NULL != (v = graph_vertex_next_get (g, v)))
{
cb (v);
//fprintf (stderr, "vid = %lu sp=%lu\n", v->id.iid, D_SP_AUX_SPEST(v));
}
}
}
/*Caminhos mínimos por Bellman-Ford: */
void BellmanFord (Graph *G, int source) {
int i, u;
int pai[G->V]; /*Árvore de caminhos mínimos.*/
int dist[G->V]; /*Distâncias mínimas.*/
Queue *Q = criar_queue (G->V);
initialize_single_source (source, pai, dist, Q, G->V);
/*****************************/
/*FAZER: termine o algoritmo!*/
/*****************************/
Node *v;
/*Variável para percorrer a lista de adjacência do vértice {u}*/
for(i = 0; i< G->V - 1; i++)
{
int u;
for(u = 0; u < G->V; u++)
{
for(v = G->listadj[u]; v != NULL; v = v->proximo)
{
relax (u, v->id, G, pai, dist);
}
}
}
for(u = 0; u < G->V; u++)
{
for(v = G->listadj[u]; v != NULL; v = v->proximo)
{
if(dist[v->id] > dist[u] + v->id)
{
printf("Falso\n");
printf("Tem solução\n");
exit(0);
}
printf("Verdadeiro");
exit(1);
}
}
}
/*Caminhos mínimos por Dijkstra: */
void Dijkstra (Graph *G, int source) {
int pai[G->V]; /*Árvore de caminhos mínimos.*/
int dist[G->V]; /*Distâncias mínimas.*/
Queue *Q = criar_queue (G->V);
initialize_single_source (source, pai, dist, Q, G->V);
while (!vazio_queue(Q)) {
int u = extract_min (Q, dist, G->V);
Node *v; /*Variável para percorrer a lista de adjacência do vértice {u}*/
for (v = G->listadj[u]; v != NULL; v = v->proximo) {
relax (u, v->id, G, pai, dist);
}
printf("Nó = %d (predecessor = %d), caminho mínimo do nó %d até o nó %d = %d\n", u, pai[u], source, u, dist[u]);
}
}
/* Run Dijkstra's algorithm from vertex s. Fills in arrays d and pi. */
void dijkstra(int first[], int node[], int next[], double w[], double d[],
int pi[], int s, int n, int handle[], int heap_index[]) {
int size = n;
int u, v, i;
initialize_single_source(d, handle, heap_index, pi, s, n);
while (size > 0) {
u = handle[1];
extract_min(d, handle, heap_index, size);
--size;
i = first[u];
while (i > 0) {
v = node[i];
relax(u, v, w[i], d, handle, heap_index, size, pi);
i = next[i];
}
}
}
void dag_shortest_path(AdjList* graph, int length, int s, int d[], int parent[])
{
AdjListNodePtr adjNode;
List list = NULL, x = NULL;
// toplogically sort the vertices of G
toplogical_sort(graph, length, &list);
initialize_single_source(graph, length, s, d, parent);
x = list;
while(x->value != s){
x = x->next;
}
while(x)
{
adjNode = graph[x->value];
while(adjNode)
{
relax(x->value, adjNode->vertex, adjNode->weight ,d, parent);
adjNode = adjNode->next;
}
x = x->next;
}
free_list(list);
}