How do you check if a path exists between two nodes?

How do you check if a path exists between two nodes?

Approach: Either Breadth First Search (BFS) or Depth First Search (DFS) can be used to find path between two vertices. Take the first vertex as source in BFS (or DFS), follow the standard BFS (or DFS). If the second vertex is found in our traversal, then return true else return false.

How do you test whether a graph is strongly connected or not?

A simple solution is to perform Depth–first search (DFS) or Breadth–first search (BFS) starting from every vertex in the graph. If each DFS/BFS call visits every other vertex in the graph, then the graph is strongly connected.

Which of the following algorithm will you use to find a simple path containing as few edges as possible in a graph from vertex u to v?

We can use the Breadth–first search (BFS) algorithm to check the connectivity between any two vertices in the graph efficiently. The idea is to start the BFS routine from the source vertex and check if the destination vertex is reached during the traversal.

Which algorithm will you use to determine the shortest path between the nodes in a graph?

Dijkstra’s algorithm
Dijkstra’s algorithm can be used to determine the shortest path from one node in a graph to every other node within the same graph data structure, provided that the nodes are reachable from the starting node. Dijkstra’s algorithm can be used to find the shortest path.

How much time is required to test if a graph is strongly connected?

This algorithm takes O(V*(V+E)) time which can be same as transitive closure for a dense graph. A better idea can be Strongly Connected Components (SCC) algorithm. We can find all SCCs in O(V+E) time. If number of SCCs is one, then graph is strongly connected.

What is an efficient algorithm for determining strong connectivity in a directed graph?

The problem of determining whether two vertices in a graph are connected can be solved efficiently using a search algorithm, such as breadth-first search.

Does BFS run in linear time?

For a directed graph, the sum of the sizes of the adjacency lists of all the nodes is E. So, the time complexity in this case is O(V) + O(E) = O(V + E). For an undirected graph, each edge appears twice. Once in the adjacency list of either end of the edge.

What is the time complexity of DFS algorithm?

The time complexity of DFS if the entire tree is traversed is O(V) where V is the number of nodes. If the graph is represented as adjacency list: Here, each node maintains a list of all its adjacent edges.

Which algorithm is not used for finding the optimal spanning tree?

9. Which of the following is not the algorithm to find the minimum spanning tree of the given graph? Explanation: The Boruvka’s algorithm, Prim’s algorithm and Kruskal’s algorithm are the algorithms that can be used to find the minimum spanning tree of the given graph.

Which algorithm can be used to find out shortest path to each vertex from vertex 2 in the following graph?

Bellman Ford’s algorithm is used to find the shortest paths from the source vertex to all other vertices in a weighted graph.

How do you calculate the average case of an algorithm?

Average case= arithmetic mean. Run the algorithm many times, using many different inputs of size nthat come from some distribution that generates these inputs (in the simplest case, all the possible inputs are equally likely), compute the total running time (by adding the individual times), and divide by the number of trials.

What does the running time of an algorithm depend on?

The running time of an algorithm depends on the size and “complexity” of the input. For example the best case running time of insertion sort on an input of some size n is proportional to n, i.e. c * n time units for some constant c which depends on the cost (time) of comparison, arithmetic, of your computing model.

What is the difference between best case and worst case algorithms?

Best case = fastest time to complete, with optimal inputs chosen. For example, the best case for a sorting algorithm would be data that’s already sorted. Worst case = slowest time to complete, with pessimal inputs chosen.

What is the worst case time complexity of linear search?

Therefore, the worst case time complexity of linear search would be Θ (n). Average Case Analysis (Sometimes done) In average case analysis, we take all possible inputs and calculate computing time for all of the inputs. Sum all the calculated values and divide the sum by total number of inputs.