How is the time complexity of BFS affected when the graph is represented using an adjacency matrix?
A. It becomes O(V log V).
B. It becomes O(E log V).
C. It remains O(V2 ).
D. It becomes O(V + E).
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Which of the following properties is essential for the efficient implementation of Dijkstra's algorithm?
A. An adjacency matrix for fast access.
B. A stack to keep track of visited nodes.
C. A hash table for node storage.
D. A priority queue or min-heap to extract the minimum distance.
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In a graph with weights, which algorithm helps in constructing a Minimum Spanning Tree (MST)?
A. Prim's Algorithm or Kruskal's Algorithm
B. Dijkstra's Algorithm
C. Bellman-Ford Algorithm
D. Floyd-Warshall Algorithm
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Which traversal algorithm can be used to check if a graph is bipartite?
A. Neither BFS nor DFS
B. DFS
C. BFS
D. Both BFS and DFS
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What is a characteristic feature of a Biconnected Graph?
A. It has exactly two connected components.
B. It has no cycles.
C. It remains connected even after removing any single vertex.
D. It contains multiple paths between nodes.
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Prim's algorithm can be efficiently implemented using . . . . . . . . for graphs with greater density.
A. d-ary heap
B. linear search
C. fibonacci heap
D. binary search
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Which of the following is the most commonly used data structure for implementing Dijkstra's Algorithm?
A. Max priority queue
B. Stack
C. Circular queue
D. Min priority queue
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Time Complexity of DFS is? (V - number of vertices, E - number of edges)
A. O(V + E)
B. O(V)
C. O(E)
D. O(V*E)
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Who proposed the modern formulation of Floyd-Warshall Algorithm as three nested loops?
A. Robert Floyd
B. Stephen Warshall
C. Bernard Roy
D. Peter Ingerman
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Which of the following branch and bound strategy leads to breadth first search?
A. LIFO branch and bound
B. FIFO branch and bound
C. Lowest cost branch and bound
D. Highest cost branch and bound
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Which data structure is most suitable for implementing best first branch and bound strategy?
A. stack
B. queue
C. priority queue
D. linked list
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The time taken to compute the transitive closure of a graph is Theta(n2 ).
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In BFS, how many times a node is visited?
A. Once
B. Twice
C. Equivalent to number of indegree of the node
D. Thrice
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Consider the graph M with 3 vertices. Its adjacency matrix is shown below. Which of the following is true?
{\text{M}} = \left[ {\begin{array}{*{20}{c}}
0&1&1 \\
1&0&1 \\
1&1&0
\end{array}} \right]
A. Graph M has no minimum spanning tree
B. Graph M has a unique minimum spanning trees of cost 2
C. Graph M has 3 distinct minimum spanning trees, each of cost 2
D. Graph M has 3 spanning trees of different costs
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Which of the following is not a branch and bound strategy to generate branches?
A. LIFO branch and bound
B. FIFO branch and bound
C. Lowest cost branch and bound
D. Highest cost branch and bound
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Complete the program.
n=rows[W]
D(0)=W
for k=1 to n
do for i=1 to n
do for j=1 to n
do ___________ return D(n)A. dij(k)=min(dij(k-1), dik(k-1) - dkj(k-1))
B. dij(k)=max(dij(k-1), dik(k-1) - dkj(k-1))
C. dij(k)=min(dij(k-1), dik(k-1) + dkj(k-1))
D. dij(k)=max(dij(k-1), dik(k-1) + dkj(k-1))
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Which of the following is false?
A. The spanning trees do not have any cycles
B. MST have n - 1 edges if the graph has n edges
C. Edge e belonging to a cut of the graph if has the weight smaller than any other edge in the same cut, then the edge e is present in all the MSTs of the graph
D. Removing one edge from the spanning tree will not make the graph disconnected
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What approach is being followed in Floyd Warshall Algorithm?
A. Linear Programming
B. Backtracking
C. Greedy technique
D. Dynamic Programming
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What is the basic principle behind Bellmann Ford Algorithm?
A. Interpolation
B. Extrapolation
C. Regression
D. Relaxation
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Which of the following is not the algorithm to find the minimum spanning tree of the given graph?
A. Boruvka's algorithm
B. Prim's algorithm
C. Kruskal's algorithm
D. Bellman-Ford algorithm
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