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How does Dijkstra's algorithm ensure that it finds the shortest path?

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Question: How does Dijkstra\'s algorithm ensure that it finds the shortest path?

Options:

  1. By exploring all possible paths
  2. By using a depth-first search
  3. By always choosing the nearest unvisited vertex
  4. By backtracking to previous nodes

Correct Answer: By always choosing the nearest unvisited vertex

Solution: 

Dijkstra\'s algorithm ensures it finds the shortest path by always choosing the nearest unvisited vertex, which is a key aspect of its greedy approach.

How does Dijkstra's algorithm ensure that it finds the shortest path?

Practice Questions

Q1
How does Dijkstra's algorithm ensure that it finds the shortest path?
  1. By exploring all possible paths
  2. By using a depth-first search
  3. By always choosing the nearest unvisited vertex
  4. By backtracking to previous nodes

Questions & Step-by-Step Solutions

How does Dijkstra's algorithm ensure that it finds the shortest path?
  • Step 1: Start with a graph that has nodes (vertices) and edges (connections between nodes).
  • Step 2: Choose a starting node and set its distance to 0 (since it's the starting point).
  • Step 3: Set the distance to all other nodes to infinity (meaning they are initially unreachable).
  • Step 4: Mark all nodes as unvisited.
  • Step 5: While there are unvisited nodes, do the following:
  • Step 5a: Select the unvisited node with the smallest distance (this is the nearest node).
  • Step 5b: Mark this node as visited.
  • Step 5c: Update the distances to its neighboring unvisited nodes. If the new calculated distance is smaller than the current distance, update it.
  • Step 6: Repeat Step 5 until all nodes are visited.
  • Step 7: The algorithm finishes when all nodes are visited, and the shortest path to each node is determined.
  • Greedy Algorithm – Dijkstra's algorithm uses a greedy approach by selecting the nearest unvisited vertex to ensure the shortest path is found.
  • Graph Theory – The algorithm operates on weighted graphs, where edges have non-negative weights.
  • Priority Queue – Dijkstra's algorithm utilizes a priority queue to efficiently select the next vertex to process.
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