In a graph, if there are multiple paths to a node, how does Dijkstra's algorithm

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Question: In a graph, if there are multiple paths to a node, how does Dijkstra\'s algorithm determine which path to take?

Options:

Correct Answer: It chooses the path with the least weight

Solution:

Dijkstra\'s algorithm always chooses the path with the least cumulative weight to ensure the shortest path is found.

In a graph, if there are multiple paths to a node, how does Dijkstra's algorithm determine which path to take?

In a graph, if there are multiple paths to a node, how does Dijkstra's algorithm determine which path to take?

Step 1: Start at the initial node and set its distance to 0.
Step 2: Set the distance to all other nodes as infinity.
Step 3: Mark the initial node as the current node.
Step 4: Look at all the neighbors of the current node and calculate their cumulative weights (distance from the start node).
Step 5: If the cumulative weight to a neighbor is less than its current known weight, update the neighbor's weight.
Step 6: Once all neighbors are checked, mark the current node as visited.
Step 7: Choose the unvisited node with the smallest cumulative weight as the new current node.
Step 8: Repeat steps 4 to 7 until all nodes are visited or the destination node is reached.
Step 9: The path to the destination node with the least cumulative weight is the shortest path.

Dijkstra's Algorithm – A graph search algorithm that finds the shortest path from a starting node to all other nodes by exploring paths with the least cumulative weight.
Cumulative Weight – The total weight of a path, which is the sum of the weights of all edges in that path.
Path Selection – The process by which Dijkstra's algorithm evaluates multiple paths to a node and selects the one with the least cumulative weight.