How does Dijkstra's algorithm find the shortest path in a graph?A) By brute force checking all possible pathsB) By maintaining a priority queue of nodes and their tentative distances from the start nodeC) By calculating the average distance between nodesD) By finding the maximum flow in a graph

The correct answer is B) By maintaining a priority queue of nodes and their tentative distances from the start node.

Dijkstra's algorithm works by visiting vertices in the graph starting with the object's start vertex. It selects the vertex with the smallest tentative distance to visit first. Here are the steps:

1. Mark all nodes unvisited. Create a set of all the unvisited nodes called the unvisited set.
2. Assign to every node a tentative distance value: set it to zero for our initial node and to infinity for all other nodes. Set the initial node as current.
3. For the current node, consider all of its unvisited neighbors and calculate their tentative distances through the current node. Compare the newly calculated tentative distance to the current assigned value and assign the smaller one.
4. When we are done considering all of the unvisited neighbors of the current node, mark the current node as visited and remove it from the unvisited set. A visited node will never be checked again.
5. If the destination node has been marked visited (when planning a route between two specific nodes) or if the smallest tentative distance among the nodes in the unvisited set is infinity (when planning a complete traversal; occurs when there is no connection between the initial node and remaining unvisited nodes), then stop. The algorithm has finished.
6. Otherwise, select the unvisited node that is marked with the smallest tentative distance, set it as the new "current node", and go back to step 3.