Top MCQs on Graph Traversals with Answers Graph traversal is a fundamental operation in graph theory and computer science that involves visiting all the vertices (nodes) of a graph in a systematic way. There are two main methods for graph traversal: depth-first traversal and breadth-first traversal. More On Depth First Search… More On Breadth First Search… Graph Traversal Top MCQs on Graph Traversals with Answers Please wait while the activity loads. If this activity does not load, try refreshing your browser. Also, this page requires javascript. Please visit using a browser with javascript enabled. If loading fails, click here to try again Question 1 Which of the following algorithms can be used to most efficiently determine the presence of a cycle in a given graph ? Depth First Search Breadth First Search Prim\'s Minimum Spanning Tree Algorithm Kruskal\' Minimum Spanning Tree Algorithm Top MCQs on Graph Traversals with Answers Discuss itQuestion 1-Explanation: To find cycle in a graph we can use the Depth First Traversal (DFS) technique. It is based on the idea that there is a cycle in a graph only if there is a back edge [i.e., a node points to one of its ancestors] present in the graph. To detect a back edge, we need to keep track of the nodes visited till now and the nodes that are in the current recursion stack [i.e., the current path that we are visiting]. If during recursion, we reach a node that is already in the recursion stack, there is a cycle present in the graph. Hence Option (A) is the correct answer. Question 2 Traversal of a graph is different from tree because There can be a loop in graph so we must maintain a visited flag for every vertex DFS of a graph uses stack, but inorder traversal of a tree is recursive BFS of a graph uses queue, but a time efficient BFS of a tree is recursive. All of the above Top MCQs on Graph Traversals with Answers Discuss itQuestion 2-Explanation: Depth First Traversal (or DFS) for a graph is similar to Depth First Traversal of a tree. The only catch here is, that, unlike trees, graphs may contain cycles (a node may be visited twice). To avoid processing a node more than once, use a boolean visited array. A graph can have more than one DFS traversal. Hence Option (A) is the correct answer. Question 3 What are the appropriate data structures for following algorithms? 1) Breadth-First Search 2) Depth First Search 3) Prim's Minimum Spanning Tree 4) Kruskal' Minimum Spanning Tree Stack QueuePriority QueueUnion FindQueueStackPriority QueueUnion FindStackQueueUnion FindPriority Queue Priority QueueQueueStackUnion FindTop MCQs on Graph Traversals with Answers Discuss itQuestion 3-Explanation: Breadth First Search uses Queue Depth First Search uses Stack Prim\'s Minimum Spanning Tree uses Priority Queue. Kruskal\' Minimum Spanning Tree uses Union Find. Hence Option(B) is the correct answer. Question 4 The Breadth First Search algorithm has been implemented using the queue data structure. One possible order of visiting the nodes of the following graph is MNOPQR NQMPOR QMNPRO QMNPOR Top MCQs on Graph Traversals with Answers Discuss itQuestion 4-Explanation: Option (A) is MNOPQR. It cannot be a BFS as the traversal starts with M, but O is visited before N and Q. In BFS all adjacent must be visited before adjacent of adjacent. Option (B) is NQMPOR. It also cannot be BFS, because here, P is visited before O. (C) and (D) match up to QMNP. We see that M was added to the queue before N and P (because M comes before NP in QMNP). Because R is M\'s neighbor, it gets added to the queue before the neighbor of N and P (which is O). Thus, R is visited before O. Hence (C) is the correct answer. Question 5 Let G be an undirected graph. Consider a depth-first traversal of G, and let T be the resulting depth-first search tree. Let u be a vertex in G and let v be the first new (unvisited) vertex visited after visiting u in the traversal. Which of the following statements is always true? (GATE CS 2000) {u,v} must be an edge in G, and u is a descendant of v in T {u,v} must be an edge in G, and v is a descendant of u in T If {u,v} is not an edge in G then u is a leaf in T If {u,v} is not an edge in G then u and v must have the same parent in T Top MCQs on Graph Traversals with Answers Discuss itQuestion 5-Explanation: In DFS, if \'v\' is visited after \'u\', then one of the following is true. 1) (u, v) is an edge. u / \\ v w / / \\ x y z 2) \'u\' is a leaf node. w / \\ x v / / \\ u y z In DFS, after visiting a node, we first recur for all unvisited children. If there are no unvisited children (u is leaf), then control goes back to parent and parent then visits next unvisited children. Hence (C) is the correct answer. Question 6Consider the following graph, Among the following sequences: (I) a b e g h f (II) a b f e h g (III) a b f h g e (IV) a f g h b e Which are depth first traversals of the above graph? I, II and IV only I and IV only II, III and IV only I, III and IV only Top MCQs on Graph Traversals with Answers Discuss itQuestion 6-Explanation: We can check all DFSs for following properties. In DFS, if a vertex \'v\' is visited after \'u\', then one of the following is true. 1) (u, v) is an edge. u / \\ v w / / \\ x y z 2) \'u\' is a leaf node. w / \\ x v / / \\ u y z In DFS, after visiting a node, we first recur for all unvisited children. If there are no unvisited children (u is leaf), then control goes back to parent and parent then visits next unvisited children.Question 7 Make is a utility that automatically builds executable programs and libraries from source code by reading files called makefiles which specify how to derive the target program. Which of the following standard graph algorithms is used by Make. Strongly Connected Components Topological Sorting Breadth First Search Dijkstra\'s Shortest Path Top MCQs on Graph Traversals with Answers Discuss itQuestion 7-Explanation: Make can decide the order of building software using topological sorting. Topological sorting produces the order considering all dependencies provide by makefile. See following for details. Topological Sorting Hence Option(B) is the correct answer. Question 8 Given two vertices in a graph s and t, which of the two traversals (BFS and DFS) can be used to find if there is path from s to t? Only BFS Only DFS Both BFS and DFS Neither BFS nor DFS Top MCQs on Graph Traversals with Answers Discuss itQuestion 8-Explanation: We can use both traversals to find if there is a path from s to t. Hence Option(C) is the correct answer. Question 9 Which of the following condition is sufficient to detect cycle in a directed graph? There is an edge from currently being visited node to an already visited node. There is an edge from currently being visited node to an ancestor of currently visited node in DFS forest. Every node is seen twice in DFS. None of the above Top MCQs on Graph Traversals with Answers Discuss itQuestion 9-Explanation: To find cycle in a directed graph we can use the Depth First Traversal (DFS) technique. It is based on the idea that there is a cycle in a graph only if there is a back edge [i.e., a node points to one of its ancestors] present in the graph. To detect a back edge, we need to keep track of the nodes visited till now and the nodes that are in the current recursion stack [i.e., the current path that we are visiting]. If during recursion, we reach a node that is already in the recursion stack, there is a cycle present in the graph. If the graph is disconnected then get the DFS forest and check for a cycle in individual trees by checking back edges. Hence Option(B) is the correct answer. Question 10 Is following statement true/false If a DFS of a directed graph contains a back edge, any other DFS of the same graph will also contain at least one back edge. True False Top MCQs on Graph Traversals with Answers Discuss itQuestion 10-Explanation: A back edge means a cycle in graph. So if there is a cycle, all DFS traversals would contain at least one back edge. 123 There are 30 questions to complete. You have completed questions question Your accuracy is Correct Wrong Partial-Credit You have not finished your quiz. If you leave this page, your progress will be lost. Correct Answer You Selected Not Attempted Final Score on Quiz Attempted Questions Correct Attempted Questions Wrong Questions Not Attempted Total Questions on Quiz Question Details Results Date Score Hint Time allowed minutes seconds Time used Answer Choice(s) Selected Question Text All doneNeed more practice!Keep trying!Not bad!Good work!Perfect! 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