// The main function that constructs Minimum Spanning Tree (MST)
// using Prim's algorithm
void PrimMST(struct Graph* graph)
{
int V = graph->V;// Get the number of vertices in graph
int parent[V]; // Array to store constructed MST
int key[V]; // Key values used to pick minimum weight edge in cut
// minHeap represents set E
struct MinHeap* minHeap = createMinHeap(V);
// Initialize min heap with all vertices. Key value of
// all vertices (except 0th vertex) is initially infinite
for (int v = 1; v < V; ++v)
{
parent[v] = -1;
key[v] = INT_MAX;
minHeap->array[v] = newMinHeapNode(v, key[v]);
minHeap->pos[v] = v;
}
// Make key value of 0th vertex as 0 so that it
// is extracted first
key[0] = 0;
minHeap->array[0] = newMinHeapNode(0, key[0]);
minHeap->pos[0] = 0;
// Initially size of min heap is equal to V
minHeap->size = V;
// In the followin loop, min heap contains all nodes
// not yet added to MST.
while (!isEmpty(minHeap))
{
// Extract the vertex with minimum key value
struct MinHeapNode* minHeapNode = extractMin(minHeap);
int u = minHeapNode->v; // Store the extracted vertex number
// Traverse through all adjacent vertices of u (the extracted
// vertex) and update their key values
struct AdjListNode* pCrawl = graph->array[u].head;
while (pCrawl != NULL)
{
int v = pCrawl->dest;
// If v is not yet included in MST and weight of u-v is
// less than key value of v, then update key value and
// parent of v
if (isInMinHeap(minHeap, v) && pCrawl->weight < key[v])
{
key[v] = pCrawl->weight;
parent[v] = u;
decreaseKey(minHeap, v, key[v]);
}
pCrawl = pCrawl->next;
}
}
// print edges of MST
printArr(parent, V);
}
// The main function that calulates distances of shortest paths from src to all
// vertices. It is a O(ELogV) function
void dijkstra(struct Graph* graph, int src)
{
int V = graph->V;// Get the number of vertices in graph
int dist[V]; // dist values used to pick minimum weight edge in cut
// minHeap represents set E
struct MinHeap* minHeap = createMinHeap(V);
// Initialize min heap with all vertices. dist value of all vertices
for (int v = 0; v < V; ++v)
{
dist[v] = INT_MAX;
minHeap->array[v] = newMinHeapNode(v, dist[v]);
minHeap->pos[v] = v;
}
// Make dist value of src vertex as 0 so that it is extracted first
minHeap->array[src] = newMinHeapNode(src, dist[src]);
minHeap->pos[src] = src;
dist[src] = 0;
decreaseKey(minHeap, src, dist[src]);
// Initially size of min heap is equal to V
minHeap->size = V;
// In the followin loop, min heap contains all nodes
// whose shortest distance is not yet finalized.
while (!isEmpty(minHeap))
{
// Extract the vertex with minimum distance value
struct MinHeapNode* minHeapNode = extractMin(minHeap);
int u = minHeapNode->v; // Store the extracted vertex number
// Traverse through all adjacent vertices of u (the extracted
// vertex) and update their distance values
struct AdjListNode* pCrawl = graph->array[u].head;
while (pCrawl != NULL)
{
int v = pCrawl->dest;
// If shortest distance to v is not finalized yet, and distance to v
// through u is less than its previously calculated distance
if (isInMinHeap(minHeap, v) && dist[u] != INT_MAX &&
pCrawl->weight + dist[u] < dist[v])
{
dist[v] = dist[u] + pCrawl->weight;
// update distance value in min heap also
decreaseKey(minHeap, v, dist[v]);
}
pCrawl = pCrawl->next;
}
}
// print the calculated shortest distances
printArr(dist, V);
}
int dijkstra(PWDG graph, int src, int dst) {
int V = graph->count;
int dist[V];
// Clone node:
if (src == dst) {
wdg_clone(graph, src);
dst = V; V++;
}
pMinHeap minHeap = createMinHeap(V);
for (int v=0; v<V; ++v) {
dist[v] = INT_MAX;
minHeap->array[v] = newMinHeapNode(v, dist[v]);
minHeap->pos[v] = v;
}
dist[src] = 0;
decreaseKey(minHeap, src, dist[src]);
minHeap->size = V;
while (!isEmpty(minHeap)) {
pMinHeapNode minHeapNode = extractMin(minHeap);
int u = minHeapNode->v;
if (u == dst) {
wdg_unclone(graph);
return dist[u];
}
PNODE pCrawl = graph->list[u].head;
while (pCrawl != NULL) {
int v = pCrawl->dst;
if (isInMinHeap(minHeap, v) && dist[u] != INT_MAX && pCrawl->wgt + dist[u] < dist[v]) {
dist[v] = dist[u] + pCrawl->wgt;
decreaseKey(minHeap, v, dist[v]);
}
pCrawl = pCrawl->next;
}
}
#ifdef DEBUG
printArr(dist, V, src);
#endif
wdg_unclone(graph);
return -1;
}
// The main function that constructs Minimum Spanning Tree (MST)
// using Prim's algorithm
void PrimMST(Graph* graph)
{
int MSTWeight = 0;
int V = graph->V;// Get the number of vertices in graph
int E = graph->E;// Get the number of edges in graph
int parent[V]; // Array to store constructed MST
int key[V]; // Key values used to pick minimum weight edge in cut
// minHeap represents set E
MinHeap* minHeap = createMinHeap(V);
// Initialize min heap with all vertices. Key value of
// all vertices (except 0th vertex) is initially infinite
// print edges of MST
printf("===============================================\n");
printf("Following are the edges in the constructed MST\n");
for (int v = 1; v < V; ++v)
{
parent[v] = -1;
key[v] = INT_MAX;
minHeap->array[v] = newMinHeapNode(v, key[v]);
minHeap->pos[v] = v;
}
// Make key value of 0th vertex as 0 so that it
// is extracted first
key[0] = 0;
minHeap->array[0] = newMinHeapNode(0, key[0]);
minHeap->pos[0] = 0;
// Initially size of min heap is equal to V
minHeap->size = V;
// In the followin loop, min heap contains all nodes
// not yet added to MST.
while (!isEmpty(minHeap))
{
// Extract the vertex with minimum key value
MinHeapNode* minHeapNode = extractMin(minHeap);
int u = minHeapNode->v; // Store the extracted vertex number
// Traverse through all adjacent vertices of u (the extracted
// vertex) and update their key values
int i;
int* adjList = findAdjList(graph,u);
int size = findAdjListCount(graph, u, NULL, 0);
//printf("%d->%d\n",adjList[0],adjList[1]);
//printf("%d\n",size);
for (i=1;i<size;i++)
{
int v = adjList[i];
// printf("%d\n",v);
// If v is not yet included in MST and weight of u-v is
// less than key value of v, then update key value and
// parent of v
if (isInMinHeap(minHeap, v) && findWeight(graph,u,v) < key[v])
{
key[v] = findWeight(graph,u,v);
parent[v] = u;
decreaseKey(minHeap, v, key[v]);
}
}
MSTWeight += minHeapNode->key;
}
int n;
for (n=1;n<V;n++) {
printf("Edge: %d -- %d (Weight: %d)\n",parent[n],n,key[n]);
}
printf("Total Weight: %d\n", MSTWeight);
printf("===============================================\n");
}
