Fundamentals of Algorithms (CS502)

1. The term “coloring” came form the original application which was in architectural design.

   1. True
   2. False

2. In the clique cover problem, for two vertices to be in the same group, they must be adjacent to each other.

   1. True
   2. False

3. If a problem is in NP, it must also be in P.

   1. True
   2. False
   3. Unknown

4. Although it requires more complicated data structures, Prim's algorithm for a minimum spanning tree is better than Kruskal's when the graph has a large number of vertices.

   1. True
   2. False

5. Consider the following adjacency list:
   
   Which of the following graph(s) describe(s) the above adjacency list?

   1. 
   2. 
   3. 
   4. 

6. Dijkstra’s algorithm is operated by maintaining a subset of vertices.

   1. True
   2. False

7. The difference between Prim’s algorithm and Dijkstra’s algorithm is that Dijkstra’s algorithm uses a different key.

   1. True
   2. False

8. Shortest path problems can be solved efficiently by modeling the road map as a graph.

   1. True
   2. False

9. Dijkestra’s single source shortest path algorithm works if all edges weights are non-negative and there are negative cost cycles.

   1. True
   2. False

10. Bellman-Ford allows negative weights edges and negative cost cycles.

    1. True
    2. False

11. Maximum number of vertices in a Directed Graph may be |V2|

    1. True
    2. False

12. What is generally true of Adjacency List and Adjacency Matrix representations of graphs?

    1. Lists require less space than matrices but take longer to find the weight of an edge (v1,v2)
    2. Lists require less space than matrices and they are faster to find the weight of an edge (v1,v2)
    3. Lists require more space than matrices and they take longer to find the weight of an edge (v1,v2)
    4. Lists require more space than matrices but are faster to find the weight of an edge (v1,v2)

13. If a graph has v vertices and e edges then to obtain a spanning tree we have to delete

    1. v edges.
    2. v – e + 5 edges
    3. v + e edges.
    4. None of the given

14. The Huffman algorithm finds a(n) ________ solution.

    1. Optimal
    2. Non-optimal
    3. Exponential
    4. Polynomial

15. The Huffman algorithm finds an exponential solution

    1. True
    2. False

16. The Huffman algorithm finds a polynomial solution.

    1. True
    2. False

17. The greedy part of the Huffman encoding algorithm is to first find two nodes with larger frequency.

    1. True
    2. False

18. The codeword assigned to characters by the Huffman algorithm have the property that no codeword is the postfix of any other.

    1. True
    2. False

19. Huffman algorithm uses a greedy approach to generate a postfix code T that minimizes the expected length B(T) of the encoded string.

    1. True
    2. False

20. An optimization problem is one in which you want to find,

    1. Not a solution
    2. An algorithm
    3. Good solution
    4. The best solution

21. Which is true statement.

    1. Breadth first search is shortest path algorithm that works on un-weighted graphs
    2. Depth first search is shortest path algorithm that works on un-weighted graphs.
    3. Both of above are true.
    4. None of the given

22. We say that two vertices u and v are mutually ________ if u can reach v and vice versa.

    1. Crossed
    2. Forward
    3. Reachable
    4. Nor Reachable

23. Adding an edge to a free tree creates.

    1. A cycle
    2. A complete MST
    3. A partial MST
    4. A shortest path

24. Networks are ________ in the sense that is possible from any location in the network to reach any other location in the digraph.

    1. Complete
    2. Incomplete
    3. Not graphs
    4. Transportation

25. Diagraphs are not used in communication and transportation networks.

    1. True
    2. False

26. In strong components algorithm, first of all DFS is run for computing finish times of vertices.

    1. True
    2. False

27. According to parenthesis lemma. vertex u is a descendent of v vertex if and only if,

    1. [d[u], f[u]] ⊆ [d[v], f[v]]
    2. [d[u], f[u]] ⊇ [d[v], f[v]]
    3. Unrelated
    4. Disjoint

28. A free tree with n vertices have exactly n+1 edges.

    1. True
    2. False

29. Strongly connected components are not affected by reversal of all edges in terms of vertices reachability.

    1. True
    2. False

30. We say that two vertices u and v are mutually not reachable if u can reach v and vice versa.

    1. True
    2. False

31. You have an adjacency list for G, what is the time compexity to compute Graph transpose G^T.?

    1. ? (V + E)
    2. ? (V E)
    3. ?(V)
    4. ?(v^2)

32. In strong components algorithm, first of all DFS is run for getting ________ times of vertices.

    1. Start
    2. Finish
    3. Both start & finish
    4. None of the given

33. By breaking any edge on cycle created in free tree, the free ________ is restored.

    1. Edge
    2. Tree
    3. Cycle
    4. Vertex

34. In ________ algorithm, at any time, the subset of edges A forms a single tree.

    1. Kruskal's
    2. Prim's
    3. Both Kruskal's and Prim's
    4. None of the given

35. In kruskal's algorithm, the next edge is added to viable set A, if its adding does not induce a cycle.

    1. True
    2. False

36. The ________ given by DFS allow us to determine whether the graph contains any cycles.

    1. Order
    2. Time stamps
    3. BFS traversing
    4. Topological sort

37. Kruskal's algorithm (choose best non-cycle edge) is better than Prim's (choose best free edge) when the gaph has relatively few edges.

    1. True
    2. False

38. A graph may contain ________.

    1. Exactly one MST
    2. Maximum one MST
    3. NO MST
    4. More than one MST

39. In Prim's algorithm, we start with the root vertex r; it can be any vertex.

    1. True
    2. False

40. You have an adjacency list for G, what is the time compexity to compute Graph transpose G^T?

    1. (V+E)
    2. V.E
    3. V
    4. E

41. Chain matrix multiplication problem can be solved through ________ strategy.

    1. Dynamic programming
    2. Greedy
    3. Divide and conquer
    4. Sorting

42. Counting sort assumes that the numbers to be sorted are in the range ________.

    1. k to n where n is large
    2. 1 to k where k is small
    3. k to n where k is small
    4. k to n where n is small

43. In Dynamic Programming approach, we do not store the solution to each sub-problem in case if it reappears.

    1. True
    2. False

44. In Dynamic Programming, our approach is to ________.

    1. Develop the solution in a top-down fashion
    2. Express the problem non-recursively
    3. Build the solution in a bottom-up fashion
    4. Input several sub-problems simultaneously

45. Heap sort is a/an ________ and ________ sorting algorithm.

    1. Not in-place, not stable one
    2. In-place, stable one
    3. In-place, not stable one
    4. Not in-place, stable one

46. If there are Θ (n²) entries in edit distance matrix then each entry E (i, j) takes ________ time to compute.

    1. Θ (n)
    2. Θ (n²)
    3. Θ (1)
    4. Θ (n log n)

47. Radix sort is not a non-comparative integer sorting algorithm.

    1. True
    2. False

48. Dynamic Programming is a problem-solving approach in which ________.

    1. Problem is solved in Zero time
    2. Solution is developed only at final stage
    3. Both are correct
    4. Both are incorrect

49. Consider three matrices X, Y, Z of dimensions 1 × 2, 2 × 3, 3 × 4 respectively. The number of multiplications of X(YZ) is:

    1. 16
    2. 23
    3. 26
    4. 32

50. We can use the optimal substructure property to devise a ________ formulation of the edit distance problem.

    1. Selective
    2. Optimum
    3. Iterative
    4. Recursive

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