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What is the time complexity of Dijkstra's algorithm using a priority queue imple

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Question: What is the time complexity of Dijkstra\'s algorithm using a priority queue implemented with a binary heap?

Options:

  1. O(V^2)
  2. O(E log V)
  3. O(V log V)
  4. O(E + V)

Correct Answer: O(E log V)

Solution: 

Dijkstra\'s algorithm has a time complexity of O(E log V) when using a priority queue implemented with a binary heap, where E is the number of edges and V is the number of vertices.

What is the time complexity of Dijkstra's algorithm using a priority queue imple

Practice Questions

Q1
What is the time complexity of Dijkstra's algorithm using a priority queue implemented with a binary heap?
  1. O(V^2)
  2. O(E log V)
  3. O(V log V)
  4. O(E + V)

Questions & Step-by-Step Solutions

What is the time complexity of Dijkstra's algorithm using a priority queue implemented with a binary heap?
  • Step 1: Understand what Dijkstra's algorithm does. It finds the shortest path from a starting vertex to all other vertices in a graph.
  • Step 2: Identify the components of the graph. A graph consists of vertices (V) and edges (E). Vertices are the points, and edges are the connections between them.
  • Step 3: Recognize that Dijkstra's algorithm uses a priority queue to efficiently get the next vertex with the smallest distance.
  • Step 4: Know that a binary heap is a common way to implement a priority queue. It allows for efficient insertion and extraction of the minimum element.
  • Step 5: Determine how many times Dijkstra's algorithm processes each vertex. It processes each vertex once, which is O(V).
  • Step 6: Understand that for each vertex processed, the algorithm examines all its edges. The total number of edges examined is O(E).
  • Step 7: Each time an edge is examined, the algorithm may need to update the priority queue. This operation takes O(log V) time in a binary heap.
  • Step 8: Combine the steps: For each of the E edges, the algorithm performs an O(log V) operation. Therefore, the total time complexity is O(E log V).
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