def dijkstra_heap(graph,source,stress = False):
n_nodes = len(graph)
Q = [True] * n_nodes
dist = [MAX_INT] * n_nodes #distance from source to v
prev = [None] * n_nodes #previous node in optimal path
dist[source] = 0
S = Heap()
for node,distance in enumerate(dist):
S.insert((distance,node))
while S.size != 0:
#find vertex with minimum distance
dist_u , u = S.pop() #instead of finding the minimum we just grab it. O(logn) vs O(n)
Q[u] = False
weights = graph[u]
for v,edge in enumerate(weights):
# can I find a way to relate this to the decrease priority?
# yes. we need to iterate the heap itself and not the weight array
if edge != MAX_INT and Q[v]: #v is in Q and is neighbor
#we need some way of relating this to the heap
alt = dist_u + edge #alternative path
if alt < dist[v]: #alternative path is better
dist[v] = alt
prev[v] = u
S.decrease_priority(v,alt)
if stress:
#progress tracker - to be removed
print(str(S.size)+'\r',end = '')
return (dist,prev)
