Dijkstra Algorithm Questions Medium
The role of a path cost in the Dijkstra Algorithm is to determine the shortest path from a starting node to all other nodes in a weighted graph. The algorithm assigns a cost value to each node, representing the total weight of the path from the starting node to that particular node. Initially, the cost of the starting node is set to 0, and the costs of all other nodes are set to infinity.
During the execution of the algorithm, it explores the neighboring nodes of the current node and updates their costs if a shorter path is found. The path cost is updated by considering the weight of the current edge being traversed and adding it to the cost of the current node. If the updated cost is smaller than the previously assigned cost, it is updated.
By continuously updating the path costs, the Dijkstra Algorithm gradually finds the shortest path from the starting node to all other nodes in the graph. The algorithm terminates when all nodes have been visited or when the destination node has been reached.
In summary, the path cost plays a crucial role in the Dijkstra Algorithm as it helps determine the shortest path by continuously updating and comparing the costs of different paths to each node.