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

Practice Questions

Q1
In a graph, if there are multiple paths to a node, how does Dijkstra's algorithm determine which path to take?
  1. It chooses the path with the most edges
  2. It chooses the path with the least weight
  3. It randomly selects a path
  4. It chooses the first path it encounters

Questions & Step-by-Step Solutions

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.
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