Dijkstra’s Algorithm

What is Dijkstra's Algorithm used for?

• Finding the longest path in a graph

• Calculating the average of a list of numbers

• Sorting elements in an array

• Finding the shortest path in a graph

Explain the concept of Shortest Path in the context of Dijkstra's Algorithm.

• Shortest Path in Dijkstra's Algorithm is the path with the lowest total weight between two nodes in a graph.

• Shortest Path in Dijkstra's Algorithm always includes all nodes in the graph

• Shortest Path in Dijkstra's Algorithm is determined by the number of edges between nodes

• Shortest Path is the longest path between two nodes in Dijkstra's Algorithm

How does Dijkstra's Algorithm handle negative edge weights?

• Dijkstra's Algorithm does not handle negative edge weights

• Dijkstra's Algorithm treats negative edge weights as zero

• Dijkstra's Algorithm ignores negative edge weights

• Dijkstra's Algorithm can convert negative edge weights to positive values

What is the significance of Graph Theory in relation to Dijkstra's Algorithm?

• Graph Theory has no relevance to Dijkstra's Algorithm

• Dijkstra's Algorithm is not based on any mathematical concepts

• Graph Theory provides the foundation and concepts necessary for understanding and implementing Dijkstra's Algorithm.

• Graph Theory is only applicable to other algorithms, not Dijkstra's

Describe the process of Optimization in Dijkstra's Algorithm.

• Optimization requires visiting all nodes in a random order

• Optimization in Dijkstra's Algorithm involves selecting the node with the smallest distance from the source node at each step.

• Optimization in Dijkstra's Algorithm is based on random node selection

• Optimization involves selecting the node with the largest distance from the source node

What data structure is commonly used to implement Dijkstra's Algorithm?

• linked list

• hash table

• stack

• priority queue

What is the time complexity of Dijkstra's Algorithm?

• O(E log V)

• O((V + E) log V)

• O(V^2)

• O(log V)

Explain the difference between Dijkstra's Algorithm and Bellman-Ford Algorithm.

• Dijkstra's Algorithm works for non-negative edge weights, while Bellman-Ford Algorithm can handle negative edge weights and detect negative cycles.

• Dijkstra's Algorithm only works for negative edge weights

• Bellman-Ford Algorithm works for non-negative edge weights

• Dijkstra's Algorithm can handle negative edge weights and detect negative cycles

How does Dijkstra's Algorithm ensure the shortest path in a graph?

• Dijkstra's Algorithm always chooses the longest path in a graph

• Dijkstra's Algorithm randomly selects vertices to calculate the shortest path

• Dijkstra's Algorithm only considers the edge weights in the graph

• Dijkstra's Algorithm maintains a priority queue of vertices based on their current shortest distance from the source vertex and iteratively selects the vertex with the shortest distance to ensure the shortest path in a graph.

Discuss a real-world application where Dijkstra's Algorithm can be used.

• Social media analytics

• Weather forecasting

• Supermarket inventory management

• Network routing protocols