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What is the worst-case time complexity of Dijkstra's algorithm when using an adj

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Question: What is the worst-case time complexity of Dijkstra\'s algorithm when using an adjacency matrix?

Options:

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

Correct Answer: O(V^2)

Solution: 

When using an adjacency matrix, the worst-case time complexity of Dijkstra\'s algorithm is O(V^2) because each vertex must be checked against all others.

What is the worst-case time complexity of Dijkstra's algorithm when using an adj

Practice Questions

Q1
What is the worst-case time complexity of Dijkstra's algorithm when using an adjacency matrix?
  1. O(V^2)
  2. O(E log V)
  3. O(V log V)
  4. O(E + V log V)

Questions & Step-by-Step Solutions

What is the worst-case time complexity of Dijkstra's algorithm when using an adjacency matrix?
  • Step 1: Understand that Dijkstra's algorithm is used to find the shortest path from a starting vertex to all other vertices in a graph.
  • Step 2: Know that an adjacency matrix is a way to represent a graph where we use a 2D array to show the connections between vertices.
  • Step 3: Realize that in an adjacency matrix, we have V rows and V columns, where V is the number of vertices in the graph.
  • Step 4: For each vertex, Dijkstra's algorithm needs to check all other vertices to find the shortest path, which means it looks at all V vertices.
  • Step 5: Since we have to do this check for each of the V vertices, the total number of checks becomes V * V, which is V^2.
  • Step 6: Therefore, the worst-case time complexity of Dijkstra's algorithm using an adjacency matrix is O(V^2).
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