Graph traversal algorithms are algorithms that visit each vertex (node) in a graph exactly once. The traversal algorithms are used to search and explore the graph, and they can be used to find specific vertices, determine the connectivity of vertices or to solve different problems that are modeled as graphs.
Here are some examples of graph traversal algorithms:
Example: Imagine you want to find the shortest distance between two cities on a map, BFS algorithm can be used to explore all possible routes from the starting city to the destination city, and find the shortest path.
Example: Imagine you have a maze and you want to find all the possible paths from one end to another. DFS algorithm can be used to search each possible path, and keep track of all paths that reach the end.
Example: Imagine you have a road network between cities with different distances, Dijkstra’s Algorithm can be used to find the shortest distance to travel from one city to another.
These are just a few examples of graph traversal algorithms, there are other algorithms such as A* algorithm, Kruskal’s algorithm, and Prim’s algorithm that can be used based on the problem to be solved.
What is the difference between BFS and DFS in terms of the order in which they explore a graph?
Answer: BFS explores a graph in breadth-first order, i.e. visiting all nodes at a given depth before moving on to nodes at the next depth, while DFS explores a graph in depth-first order, i.e. visiting every node connected to a given starting node before moving on to the next unexplored starting node.
How does a Dijkstra’s algorithm determine the shortest path between two nodes in a weighted graph?
Answer: Dijkstra’s algorithm works by calculating the shortest path from a starting node to all other nodes in the graph, one node at a time, using a priority queue to keep track of the next unvisited node with the smallest calculated path so far. At each iteration, the algorithm updates the distance to each of the adjacent nodes of the current node, using the weight of the edge connecting them, and adds them to the priority queue if they haven’t been visited yet.
What is a backtracking algorithm, and how is it used in graph traversal?
Answer: A backtracking algorithm is a type of algorithm that tries out different solutions to a problem by incrementally building a candidate solution and undoing any partial solutions that fail to meet certain criteria. Backtracking algorithms can be used in graph traversal to find all possible paths between two nodes, by exploring each possible connection from the starting node until reaching the destination node, and backtracking when no more paths are available.
What is the time complexity of a BFS algorithm for a graph with V vertices and E edges?
Answer: The time complexity of BFS is O(V + E), since it visits each vertex and each of its neighbors exactly once. In the worst-case scenario, where the graph is completely connected and every vertex has E - 1 neighbors, the algorithm will take O(V + VE) time, which can be simplified to O(VE).
How does a Topological Sort algorithm work, and what is it used for?
Answer: A Topological Sort algorithm is used to sort the nodes of a directed acyclic graph (DAG) in such a way that every directed edge goes from a lower-ranked node to a higher-ranked node. The algorithm works by repeatedly finding a node with no incoming edges, removing it from the graph, and adding it to the sorted list. If the graph is not a DAG, the algorithm will fail to find a valid sorting order. The time complexity of a Topological Sort is O(V + E), the same as BFS.