Скачать или смотреть 27 Dijkstra algorithm Greedy Method

Dijkstra's algorithm is a widely used graph traversal and pathfinding algorithm that finds the shortest paths from a source vertex to all other vertices in a weighted graph. It was developed by Dutch computer scientist Edsger W. Dijkstra in 1956. The algorithm works for both directed and undirected graphs, but it requires that the graph's edges have non-negative weights.

The basic idea of Dijkstra's algorithm is to iteratively explore the vertices of the graph while keeping track of the shortest distances discovered so far from the source vertex to each vertex. The algorithm maintains two main data structures:

Priority Queue (Min Heap): This data structure is used to keep track of the vertices that need to be visited next. Vertices are stored in the priority queue based on their current tentative distance from the source vertex. The vertex with the smallest tentative distance is always removed from the queue first.

Distance Array: This array stores the shortest distance found so far from the source vertex to each vertex in the graph.

Here's a high-level overview of the algorithm:

Initialize the distance array with a large value for all vertices except the source vertex, which is set to 0.
Insert the source vertex into the priority queue.
While the priority queue is not empty:
a. Remove the vertex with the smallest tentative distance from the queue.
b. For each neighboring vertex of the current vertex:
Calculate the distance to the neighboring vertex through the current vertex.
If the calculated distance is smaller than the stored distance in the distance array, update the distance array.
Insert the neighboring vertex into the priority queue (if not already present).
Once the priority queue is empty, the distance array contains the shortest distances from the source vertex to all other vertices.
Dijkstra's algorithm is greedy in nature, always selecting the vertex with the smallest tentative distance to visit next. This property makes it work well for finding shortest paths in non-negative weighted graphs, but it won't work correctly if negative weights are present (use Bellman-Ford algorithm for such cases).

It's important to note that Dijkstra's algorithm doesn't work on graphs with negative edge weights because it assumes that shorter paths are found by visiting vertices in order of increasing distance from the source vertex. If a negative-weight edge is encountered, it might cause the algorithm to produce incorrect results.

Overall, Dijkstra's algorithm is a fundamental tool in computer science, used in various applications such as network routing, transportation systems, and more.
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