dijksrea 堆优化
时间: 2024-05-24 07:11:17 浏览: 4
Dijkstra's algorithm is an algorithm for finding the shortest path between two nodes in a graph. It works by assigning a tentative distance to every node, then repeatedly selecting the node with the smallest tentative distance and updating the distances of its neighbors until all nodes have been visited.
Dijkstra's algorithm can be optimized using a min-heap data structure. Instead of sorting the nodes by tentative distance each time, we can store them in a min-heap and extract the node with the smallest tentative distance in O(log n) time. This reduces the time complexity of the algorithm from O(n^2) to O(m log n), where m is the number of edges in the graph.
Here is the pseudocode for Dijkstra's algorithm with heap optimization:
1. Initialize distances to all nodes as infinity and set the distance of the start node to 0.
2. Create a min-heap and insert the start node with its tentative distance.
3. While the heap is not empty:
a. Extract the node with the smallest tentative distance from the heap.
b. For each neighbor of the node, calculate the tentative distance as the sum of the node's distance and the edge weight.
c. If the tentative distance is smaller than the current distance of the neighbor, update its distance and insert it into the heap with its new tentative distance.
4. Return the distances to all nodes.
Overall, dijkstra's algorithm with heap optimization is a powerful tool for finding the shortest path between two nodes in a graph efficiently.