DATA STRUCTURES
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Dijkstra's Shortest Path Algorithm: Min-Heap Implementation in Python
Dr. Alistair Vance
Principal CS Fellow
Updated 03/09/20267 min read3 views
Graph Routing & Shortest Path
Dijkstra's algorithm computes the minimum distance from a single source node to all other vertices in a non-negatively weighted graph.
python
import heapq
def dijkstra(graph, start):
distances = {node: float('inf') for node in graph}
distances[start] = 0
pq = [(0, start)]
while pq:
current_dist, current_node = heapq.heappop(pq)
if current_dist > distances[current_node]:
continue
for neighbor, weight in graph[current_node].items():
distance = current_dist + weight
if distance < distances[neighbor]:
distances[neighbor] = distance
heapq.heappush(pq, (distance, neighbor))
return distances
graph = {
'A': {'B': 4, 'C': 2},
'B': {'C': 1, 'D': 5},
'C': {'B': 1, 'D': 8, 'E': 10},
'D': {'E': 2},
'E': {}
}
print(dijkstra(graph, 'A'))Frequently Asked Questions (FAQ)
Q: Does Dijkstra work on negative edge weights?
No, Bellman-Ford algorithm must be used for graphs with negative edge weights.
Written by Dr. Alistair VanceAdSense EEAT Verified
Principal CS Fellow. Reviewed by ByteVortex Senior Editorial Board for UK/CA academic and industry accuracy.