Dijkstra's Algorithm Concepts and Applications

The video tutorial introduces Dijkstra's algorithm, a method for solving the single-source shortest path problem in weighted graphs. It explains the algorithm's reliance on the greedy method, which involves solving problems in stages by selecting the shortest path at each step. The video provides a detailed example of the algorithm's application, analyzes its time complexity, and discusses its limitations, particularly with negative edge weights. The tutorial concludes by mentioning the Bellman-Ford algorithm as an alternative for handling graphs with negative edges.

What is the primary purpose of Dijkstra's algorithm?

• To detect cycles in a graph

• To sort vertices in topological order

• To solve the single-source shortest path problem

• To find the longest path in a graph

Which method does Dijkstra's algorithm use to solve optimization problems?

• Backtracking

• Greedy method

• Divide and conquer

• Dynamic programming

In Dijkstra's algorithm, what is the process of updating the shortest path estimates called?

• Expansion

• Contraction

• Relaxation

• Reduction

What is the first step in solving a graph problem using Dijkstra's algorithm?

• Select the vertex with the most edges

• Select a random vertex

• Select the vertex with the shortest path

• Select the vertex with the longest path

What is the worst-case time complexity of Dijkstra's algorithm?

• O(n log n)

• O(n^2)

• O(n)

• O(n^3)

How does Dijkstra's algorithm handle graphs with negative edge weights?

• It converts negative weights to positive

• It may not work correctly with negative edge weights

• It ignores negative edges

• It can handle them without any issues

Which algorithm is suggested as an alternative to Dijkstra's for graphs with negative weights?

• Floyd-Warshall algorithm

• Bellman-Ford's algorithm

• Prim's algorithm

• Kruskal's algorithm