Fundamentals of Algorithms (CS502)

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

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

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

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

3. 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

4. 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

5. 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)

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

   1. True
   2. False

7. 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

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

   1. True
   2. False

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

   1. True
   2. False

10. 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

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

    1. True
    2. False

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

    1. True
    2. False

13. The Huffman algorithm finds a polynomial solution.

    1. True
    2. False

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

    1. True
    2. False
    3. Unknown

15. 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

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

    1. True
    2. False

17. 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

18. 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

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

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

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

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

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

    1. True
    2. False

22. 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

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

    1. True
    2. False

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

    1. True
    2. False

25. 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

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

    1. True
    2. False

27. The Huffman algorithm finds an exponential solution

    1. True
    2. False

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

    1. True
    2. False

29. 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

30. Adding an edge to a free tree creates.

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

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

    1. 
    2. 
    3. 
    4. 

32. 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

33. 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

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

    1. True
    2. False

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. A graph may contain ________.

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

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

    1. True
    2. False

38. 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

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

    1. True
    2. False

40. 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

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

    1. True
    2. False

42. 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

43. 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

44. 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

45. 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

46. 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

47. 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

48. 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)

49. 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

50. 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)

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