What data structures are commonly used in the implementation of the Dijkstra Algorithm?

The Dijkstra Algorithm, also known as Dijkstra's Shortest Path Algorithm, is a popular algorithm used to find the shortest path between two nodes in a graph. In its implementation, several data structures are commonly used to efficiently store and manipulate the graph's information. The main data structures used in the implementation of the Dijkstra Algorithm are:

1. Priority Queue: A priority queue is used to store the vertices of the graph based on their tentative distances from the source node. It allows efficient retrieval of the vertex with the minimum distance, which is crucial for the algorithm's operation. The priority queue can be implemented using a binary heap, Fibonacci heap, or other suitable data structures.

2. Adjacency List: An adjacency list is used to represent the graph's structure efficiently. It stores each vertex's neighbors and the corresponding edge weights. This data structure allows quick access to the adjacent vertices of a given vertex, enabling efficient exploration of the graph during the algorithm's execution.

3. Distance Array: A distance array is used to keep track of the tentative distances from the source node to each vertex in the graph. Initially, all distances are set to infinity except for the source node, which is set to zero. As the algorithm progresses, the distances are updated based on the shortest paths found so far.

4. Visited Array: A visited array is used to keep track of the vertices that have been visited by the algorithm. It helps in avoiding unnecessary revisits to already processed vertices, improving the algorithm's efficiency.

5. Predecessor Array: A predecessor array is used to store the previous vertex on the shortest path from the source node to each vertex. It is updated during the algorithm's execution to keep track of the optimal path found so far.

These data structures work together to efficiently implement the Dijkstra Algorithm and find the shortest path in a graph. By utilizing a priority queue to select the vertex with the minimum distance, an adjacency list to explore the graph's structure, and arrays to store and update the necessary information, the algorithm can effectively find the shortest path from the source node to all other nodes in the graph.