What does Dijkstra's algorithm guarantee when it is applied to a graph?Select one:a. It finds all possible paths from one vertex to another in the shortest time.b. It calculates the maximum capacity of flow from source to sink in a network.c. It finds the shortest path from a single source to all other vertices in a graph with non-negative weights.d. It identifies whether a graph is bipartite or not

How does Dijkstra's algorithm find the shortest path in a graph?A) By brute force checking all possible pathsB) By maintaining a priority queue of nodes and their tentative distances from the start nodeC) By calculating the average distance between nodesD) By finding the maximum flow in a graph

What is a crucial requirement for Dijkstra’s algorithm (for finding shortest path) to work correctly?Select one:a. All edge weights in the graph must be equal.b. The graph must be fully connected.c. The graph must be a tree.d. The graph must not contain any negative edge weights.

• Analyze the time complexity of Dijkstra's algorithm and discuss how it changes with different graph representations.

Dijkstra's algorithm

Suppose you implemented Dijkstra's algorithm using a priority queue which supports each operations with the following worst-case performance, where n is the number of items in the priority queue:search: O(1)insert: O(loglog(n))delete: O(1)extractMin: O(loglog(n))decreaseKey: O(sqrt(n))isEmpty: O(1)You are given a connected, directed, weighted graph G with non-negative weights and a specified source.  G has n nodes and m edges.  What is the running time of Dijkstra's Algorithm on G using this new priority queue?  (There are no other changes made to Dijkstra's Algorithm.)