Fundamentals of Algorithms (CS502)

1. 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

2. 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

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

   1. True
   2. False

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

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

   1. True
   2. False

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

   1. True
   2. False

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

   1. True
   2. False

9. 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

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

    1. True
    2. False

11. 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

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

    1. True
    2. False
    3. Unknown

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

    1. True
    2. False

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

    1. True
    2. False

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

    1. True
    2. False

16. The Huffman algorithm finds an exponential solution

    1. True
    2. False

17. 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

18. 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

19. 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

20. 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)

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

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

22. 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

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

    1. 
    2. 
    3. 
    4. 

24. A graph may contain ________.

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

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

    1. True
    2. False

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

    1. True
    2. False

27. 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

28. 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

29. 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

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

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

31. 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

32. 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

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

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

34. The Huffman algorithm finds a polynomial solution.

    1. True
    2. False

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

    1. True
    2. False

36. 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

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

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

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

    1. True
    2. False

39. Adding an edge to a free tree creates.

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

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

    1. True
    2. False

41. 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

42. 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

43. 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

44. 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

45. 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

46. 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

47. 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)

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

    1. True
    2. False

49. 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

50. 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

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