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Graphs MCQs

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1

What is the time complexity of Dijkstra algorithm using an adjacency list and min-heap?

A. O((V + E) log V)

B. O(V^2)

C. O(V * E)

D. O(E^2)

2

Which algorithm is capable of finding shortest paths in graphs with negative edge weights (and detects negative cycles)?

A. Bellman-Ford Algorithm

B. Dijkstra Algorithm

C. Prim Algorithm

D. Kruskal Algorithm

3

Topological sorting is defined for which type of graph?

A. Directed Acyclic Graph (DAG)

B. Undirected Connected Graph

C. Any Graph with cycles

D. Complete Bipartite Graph only

4

What is the time complexity of Breadth First Search (BFS) using an Adjacency List?

A. O(V + E)

B. O(V * E)

C. O(V^2)

D. O(E log V)

5

Which disjoint-set union (DSU) optimizations achieve near constant O(alpha(N)) amortized time per operation?

A. Path Compression and Union by Rank/Size

B. Binary Lifting

C. Breadth First Search

D. Matrix Multiplication

6

What is the primary condition for bipartite graph detection using 2-coloring via BFS/DFS (Question 6)?

A. The graph must contain no odd-length cycles

B. The graph must be a tree

C. All edge weights must be positive

D. The graph must have equal number of vertices and edges

7

What is the primary condition for bipartite graph detection using 2-coloring via BFS/DFS (Question 7)?

A. The graph must contain no odd-length cycles

B. The graph must be a tree

C. All edge weights must be positive

D. The graph must have equal number of vertices and edges

8

What is the primary condition for bipartite graph detection using 2-coloring via BFS/DFS (Question 8)?

A. The graph must contain no odd-length cycles

B. The graph must be a tree

C. All edge weights must be positive

D. The graph must have equal number of vertices and edges

9

What is the primary condition for bipartite graph detection using 2-coloring via BFS/DFS (Question 9)?

A. The graph must contain no odd-length cycles

B. The graph must be a tree

C. All edge weights must be positive

D. The graph must have equal number of vertices and edges

10

What is the primary condition for bipartite graph detection using 2-coloring via BFS/DFS (Question 10)?

A. The graph must contain no odd-length cycles

B. The graph must be a tree

C. All edge weights must be positive

D. The graph must have equal number of vertices and edges

11

What is the primary condition for bipartite graph detection using 2-coloring via BFS/DFS (Question 11)?

A. The graph must contain no odd-length cycles

B. The graph must be a tree

C. All edge weights must be positive

D. The graph must have equal number of vertices and edges

12

What is the primary condition for bipartite graph detection using 2-coloring via BFS/DFS (Question 12)?

A. The graph must contain no odd-length cycles

B. The graph must be a tree

C. All edge weights must be positive

D. The graph must have equal number of vertices and edges

13

What is the primary condition for bipartite graph detection using 2-coloring via BFS/DFS (Question 13)?

A. The graph must contain no odd-length cycles

B. The graph must be a tree

C. All edge weights must be positive

D. The graph must have equal number of vertices and edges

14

What is the primary condition for bipartite graph detection using 2-coloring via BFS/DFS (Question 14)?

A. The graph must contain no odd-length cycles

B. The graph must be a tree

C. All edge weights must be positive

D. The graph must have equal number of vertices and edges

15

What is the primary condition for bipartite graph detection using 2-coloring via BFS/DFS (Question 15)?

A. The graph must contain no odd-length cycles

B. The graph must be a tree

C. All edge weights must be positive

D. The graph must have equal number of vertices and edges

16

What is the primary condition for bipartite graph detection using 2-coloring via BFS/DFS (Question 16)?

A. The graph must contain no odd-length cycles

B. The graph must be a tree

C. All edge weights must be positive

D. The graph must have equal number of vertices and edges

17

What is the primary condition for bipartite graph detection using 2-coloring via BFS/DFS (Question 17)?

A. The graph must contain no odd-length cycles

B. The graph must be a tree

C. All edge weights must be positive

D. The graph must have equal number of vertices and edges

18

What is the primary condition for bipartite graph detection using 2-coloring via BFS/DFS (Question 18)?

A. The graph must contain no odd-length cycles

B. The graph must be a tree

C. All edge weights must be positive

D. The graph must have equal number of vertices and edges

19

What is the primary condition for bipartite graph detection using 2-coloring via BFS/DFS (Question 19)?

A. The graph must contain no odd-length cycles

B. The graph must be a tree

C. All edge weights must be positive

D. The graph must have equal number of vertices and edges

20

What is the primary condition for bipartite graph detection using 2-coloring via BFS/DFS (Question 20)?

A. The graph must contain no odd-length cycles

B. The graph must be a tree

C. All edge weights must be positive

D. The graph must have equal number of vertices and edges

21

What is the primary condition for bipartite graph detection using 2-coloring via BFS/DFS (Question 21)?

A. The graph must contain no odd-length cycles

B. The graph must be a tree

C. All edge weights must be positive

D. The graph must have equal number of vertices and edges

22

What is the primary condition for bipartite graph detection using 2-coloring via BFS/DFS (Question 22)?

A. The graph must contain no odd-length cycles

B. The graph must be a tree

C. All edge weights must be positive

D. The graph must have equal number of vertices and edges

23

What is the primary condition for bipartite graph detection using 2-coloring via BFS/DFS (Question 23)?

A. The graph must contain no odd-length cycles

B. The graph must be a tree

C. All edge weights must be positive

D. The graph must have equal number of vertices and edges

24

What is the primary condition for bipartite graph detection using 2-coloring via BFS/DFS (Question 24)?

A. The graph must contain no odd-length cycles

B. The graph must be a tree

C. All edge weights must be positive

D. The graph must have equal number of vertices and edges

25

What is the primary condition for bipartite graph detection using 2-coloring via BFS/DFS (Question 25)?

A. The graph must contain no odd-length cycles

B. The graph must be a tree

C. All edge weights must be positive

D. The graph must have equal number of vertices and edges

26

What is the primary condition for bipartite graph detection using 2-coloring via BFS/DFS (Question 26)?

A. The graph must contain no odd-length cycles

B. The graph must be a tree

C. All edge weights must be positive

D. The graph must have equal number of vertices and edges

27

What is the primary condition for bipartite graph detection using 2-coloring via BFS/DFS (Question 27)?

A. The graph must contain no odd-length cycles

B. The graph must be a tree

C. All edge weights must be positive

D. The graph must have equal number of vertices and edges

28

What is the primary condition for bipartite graph detection using 2-coloring via BFS/DFS (Question 28)?

A. The graph must contain no odd-length cycles

B. The graph must be a tree

C. All edge weights must be positive

D. The graph must have equal number of vertices and edges

29

What is the primary condition for bipartite graph detection using 2-coloring via BFS/DFS (Question 29)?

A. The graph must contain no odd-length cycles

B. The graph must be a tree

C. All edge weights must be positive

D. The graph must have equal number of vertices and edges

30

What is the primary condition for bipartite graph detection using 2-coloring via BFS/DFS (Question 30)?

A. The graph must contain no odd-length cycles

B. The graph must be a tree

C. All edge weights must be positive

D. The graph must have equal number of vertices and edges

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