Update dijsktra_algorithm.py

data_structures/graphs/dijsktra_algorithm.py

@@ -0,0 +1,30 @@
+'''When iterating across nodes, always choose the smallest path with an un-visited vertex. 
+Store all distance + vertices in a min heap to automatically get the next shortest path. 
+If there is a limit on the amount of edges that can be visited (Ex: LeetCode Cheapest Flights Within K Stops), 
+maintain an array tracking the maximum edges to get to a vertex, and if the number of edges taken goes up, do not proceed with the iteration.
+
+Time complexity: O(V + E x log(V)) with min heap'''
+
+min_heap = []
+heapq.heappush(min_heap, [0, k + 1, src]) # only need 'k + 1' if max k edges requirement
+visited = set()
+edges_to_vertex = [0] * n # only needed if max k edges requirement
+
+while min_heap.peek() is not None:
+    distance, edge_count, vertex = heapq.heappop(min_heap)
+    if vertex in visited:
+        continue
+    visited.add(vertex)
+    if vertex == dst:
+        return distance
+
+    # only needed if max k edges requirement
+    if edges_to_vertex[vertex] >= edge_count:
+        continue
+    edges_to_vertex[vertex] = edge_count
+
+    if vertex in edges:
+        for edge in edges[vertex]:
+            heapq.heappush(min_heap, [distance + edge[1], edge_count - 1, edge[0]])
+
+return -1