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# VU CS502- Fundamentals Of Algorithms (Session – 4) FinalTerm Solved Unsolved Past Papers Spring 2010

FINALTERM  EXAMINATION

Spring 2010

CS502- Fundamentals of Algorithms (Session – 4)

Time: 90 min

Marks: 58

Question No: 1    ( Marks: 1 )    – Please choose one

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

► Not a solution

► An algorithm

► Good solution

► The best solution

Question No: 2    ( Marks: 1 )    – Please choose one

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.

► True

► False

Question No: 3    ( Marks: 1 )    – Please choose one

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

► True

► False

► unknown

Question No: 4    ( Marks: 1 )    – Please choose one

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

► Lists require less space than matrices but take longer to find the weight of an edge (v1,v2)

► Lists require less space than matrices and they are faster to find the weight of an edge (v1,v2)

► Lists require more space than matrices and they take longer to find the weight of an edge (v1,v2)

► Lists require more space than matrices but are faster to find the weight of an edge (v1,v2)

Question No: 5    ( Marks: 1 )    – Please choose one

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

► v edges.

► v – e + 5 edges

►  v + e edges.

► None of these

Question No: 6    ( Marks: 1 )    – Please choose one

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

► True

► False

Question No: 7    ( Marks: 1 )    – Please choose one

The Huffman algorithm finds a (n) _____________ solution.

► Optimal

► Non-optimal

► Exponential

► Polynomial

Question No: 8    ( Marks: 1 )    – Please choose one

The Huffman algorithm finds an exponential solution

► True

► False

Question No: 9    ( Marks: 1 )    – Please choose one

The Huffman algorithm finds a polynomial solution

► True

► False

Question No: 10    ( Marks: 1 )    – Please choose one

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

► True

► False

Question No: 11    ( Marks: 1 )    – Please choose one

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

► True

► False

Question No: 12    ( Marks: 1 )    – Please choose one

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

► True

► False

Question No: 13    ( Marks: 1 )    – Please choose one

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

► True

► False

Question No: 14    ( Marks: 1 )    – Please choose one

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

► True

► False

Question No: 15    ( Marks: 1 )    – Please choose one

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

► True

► False

Question No: 16    ( Marks: 1 )    – Please choose one

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

► True

► False

Question No: 17    ( Marks: 1 )    – Please choose one

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

► True

► False

Question No: 18    ( Marks: 1 )    – Please choose one

Dijkstra’s algorithm is operates by maintaining a subset of vertices

► True

► False

Question No: 19    ( Marks: 1 )    – Please choose one

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

► True

► False

Question No: 20    ( Marks: 1 )    – Please choose one

Which of the following graph(s) describe(s) the above adjacency list?

►

Question No: 21    ( Marks: 1 )    – Please choose one

We do sorting to,

► keep elements in random positions

► keep the algorithm run in linear order

► keep the algorithm run in (log n) order

► keep elements in increasing or decreasing order

Question No: 22    ( Marks: 1 )    – Please choose one

After partitioning array in Quick sort, pivot is placed in a position such that

► Values smaller than pivot are on left and larger than pivot are on right

► Values larger than pivot are on left and smaller than pivot are on right

► Pivot is the first element of array

► Pivot is the last element of array

Question No: 23    ( Marks: 1 )    – Please choose one

Merge sort is stable sort, but not an in-place algorithm

► True  (p#54)

► False

Question No: 24    ( Marks: 1 )    – Please choose one

In counting sort, once we know the ranks, we simply _________ numbers to their final positions in an output array.

► Delete

► copy (p#57)

► Mark

► arrange

Question No: 25    ( Marks: 1 )    – Please choose one

Dynamic programming algorithms need to store the results of intermediate sub-problems.

► True   p#75)

► False

Question No: 26    ( Marks: 1 )    – Please choose one

A p × q matrix A can be multiplied with a q × r matrix B. The result will be a p × r matrix C. There are (p . r) total entries in C and each takes _________ to compute.

► O (q) (p= 84)

► O (1)

► O (n2)

► O (n3)

Question No: 27    ( Marks: 2 )

Give a detailed example for 2-d maxima problem.

Question No: 28    ( Marks: 2 )

Differentiate between back edge and forward edge.

Question No: 29    ( Marks: 2 )

How the generic greedy algorithm operates in minimum spanning tree?

Question No: 30    ( Marks: 2 )

What are two cases for computing  assuming we already have the previous matrix  using Floyed-Warshall algorithm?

Question No: 31    ( Marks: 3 )

Describe Minimum Spanning Trees Problem with examples.

Question No: 32    ( Marks: 3 )

What is decision problem, also explain with example?

Question No: 33    ( Marks: 3 )

Prove that the generic TRAVERSE (S) marks every vertex in any connected graph exactly once and the set of edges (v, parent (v)) with parent (v) ¹F form a spanning tree of the graph.

Question No: 34    ( Marks: 5 )

Suppose you could reduce an NP-complete problem to a polynomial time problem in polynomial time. What would be the consequence?

Question No: 35    ( Marks: 5 )

Prove the following lemma,

Lemma: Given a digraph G = (V, E), consider any DFS forest of G and consider any edge (u, v) ∈ E. If this edge is a tree, forward or cross edge, then f[u] > f[v]. If this edge is a back edge, then f[u] ≤ f[v]

Question No: 36    ( Marks: 5 )

What is the cost of the following graph?