CS502 - Fundamentals of Algorithms
Quiz No.3 Dated 28-01-2013
In in-place sorting algorithm is one that uses arrays for storage :
An additional array
No additional array (Right Answer)
Both of above may be true according to algorithm
More than 3 arrays of one dimension.
The running time of quick sort depends heavily on the selection of
No of inputs
Arrangement of elements in array
Size o elements
Pivot element (Right Answer)
In stable sorting algorithm
One array is used
In which duplicating elements are not handled.
More then one arrays are required.
Duplicating elements remain in same relative position after sorting. (Right Answer)
Which sorting algorithn is faster :
O(n^2)
O(nlogn)
O(n+k) (Right Answer)
O(n^3)
In Quick sort algorithm,constants hidden in T(n lg n) are
Large
Medium
Not known
Small (Right Answer)
Quick sort is based on divide and conquer paradigm; we divide the problem on base of pivot element and:
There is explicit combine process as well to conquer the solutin. (Right Answer)
No work is needed to combine the sub-arrays, the array is already sorted
Merging the subarrays
None of above.
There is relationship between number of back edges and number of cycles in DFS
Select correct option:
Both are equal.
Cycles are half of back edges.
Cycles are one fourth of back edges.
There is no relationship between back edges and number of cycle (Right Answer)
You have an adjacency list for G, what is the time complexity to compute Graph
transpose G^T ?
Select correct option:
(V+E) (Right Answer)
V.E
V
E
Question # 3 of 10 ( Start time: 06:54:27 PM ) Total Marks: 1
You have an adjacency list for G, what is the time complexity to compute Graph
transpose G^T.?
?(V + E) Right Answer)
?(V E)
?(V)
?(V^2)
What is the time complexity to extract a vertex from the priority queue in Prim's
algorithm?
Select correct option:
log (V) (Right Answer)
V.V
E.E
log (E)
Dijkstra's algorithm :
Select correct option:
Has greedy approach to find all shortest paths
Has both greedy and Dynamic approach to find all shortest paths
Has greedy approach to compute single source shortest paths to all other vertices (Right Answer)
Has both greedy and dynamic approach to compute single source shortest paths to all other vertices.
What algorithm technique is used in the implementation of Kruskal solution for the
MST?
Greedy Technique (Right Answer)
Divide-and-Conquer Technique
Dynamic Programming Technique
The algorithm combines more than one of the above techniques
What is the time complexity to extract a vertex from the priority queue in Prim's
algorithm?
Select correct option:
O (log E)
? (V)
? (V+E)
O (log V) (Right Answer)
Which is true statement in the following.
Kruskal algorithm is multiple source technique for finding MST.
Kruskal's algorithm is used to find minimum spanning tree of a graph, time complexity of this algorithm is O(EV)
Both of above
Kruskal's algorithm (choose best non-cycle edge) is better than Prim's (choose best Tree edge) when the graph has relatively few edges ) (Right Answer)
The relationship between number of back edges and number of cycles in DFS is,
Both are equal
Back edges are half of cycles
Back edges are one quarter of cycles
There is no relationship between no. of edges and cycles (Right Answer)
Kruskal's algorithm (choose best non-cycle edge) is better than Prim's (choose best tree
edge) when the graph has relatively few edges.
True (Right Answer)
False
What is the time complexity to extract a vertex from the priority queue in Prim's
algorithm?
Select correct option:
log (V)
V.V
E.E
log (E)
Suppose that a graph G = (V,E) is implemented using adjacency lists. What is the complexity of a breadth-first traversal of G?
Select correct option:
O(|V |^2)
O(|V | |E|) (Right Answer)
O(|V |^2|E|)
O(|V | + |E|)
What is generally true of Adjacency List and Adjacency Matrix representations of graphs?
Select correct option:
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) Right Answer)
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)
What general property of the list indicates that the graph has an isolated vertex?
Select correct option:
There is Null pointer at the end of list.
The Isolated vertex is not handled in list. (not Sure)
Only one value is entered in the list.
There is at least one null list.
A dense undirected graph is:
Select correct option:
A graph in which E = O(V^2) (Right Answer)
A graph in which E = O(V)
A graph in which E = O(log V)
All items above may be used to characterize a dense undirected graph
In digraph G=(V,E) ;G has cycle if and only if
Select correct option:
The DFS forest has forward edge.
The DFS forest has back edge (Right Answer)
The DFS forest has both back and forward edge
BFS forest has forward edge
Back edge is:
Select correct option:
(u, v) where v is an ancestor of u in the tree. (Right Answer)
(u,v) where u is an ancesstor of v in the tree.
(u, v) where v is an predcessor of u in the tree.
None of above
Using ASCII standard the string "abacdaacacwe" will be encoded with __________ bits
Select correct option:
64
128 (Right Answer)
96
120
Cross edge is :
Select correct option:
(u, v) where u and v are not ancestor of one another
(u, v) where u is ancesstor of v and v is not descendent of u.
(u, v) where u and v are not ancestor or descendent of one another (Right Answer)
(u, v) where u and v are either ancestor or descendent of one another.
Which statement is true?
Select correct option:
If a dynamic-programming problem satisfies the optimal-substructure property, then a locally optimal solution is globally optimal.
If a greedy choice property satisfies the optimal-substructure property, then a locally optimal solution is globally optimal.
Both of above Right Answer)
None of above
10 If you find yourself in maze the better traversel approach will bE
A dense undirected graph is:
Select correct option:
A graph in which E = O(V^2) (Right Answer)
A graph in which E = O(V)
A graph in which E = O(log V)
All items above may be used to characterize a dense undirected graph
Which is true statement.
Select correct option:
Breadth first search is shortest path algorithm that works on un-weighted graphs (Right Answer)
Depth first search is shortest path algorithm that works on un-weighted graphs.
Both of above are true.
None of above are true.
Forward edge is:
Select correct option:
(u, v) where u is a proper descendent of v in the tree.
(u, v) where v is a proper descendent of u in the tree. (Right Answer)
(u, v) where v is a proper ancesstor of u in the tree.
(u, v) where u is a proper ancesstor of v in the tree.
Back edge is:
Select correct option:
(u, v) where v is an ancestor of u in the tree. (Right Answer)
(u,v) where u is an ancesstor of v in the tree.
(u, v) where v is an predcessor of u in the tree.
None of above
Suppose that a graph G = (V,E) is implemented using adjacency lists. What is the complexity of a breadth-first traversal of G?
Select correct option:
O(|V |^2)
O(|V | |E|) (Right Answer)
O(|V |^2|E|)
O(|V | + |E|)
In digraph G=(V,E) ;G has cycle if and only if
Select correct option:
The DFS forest has forward edge.
The DFS forest has back edge (Right Answer)
The DFS forest has both back and forward edge
BFS forest has forward edge
What general property of the list indicates that the graph has an isolated vertex?
Select correct option:
There is Null pointer at the end of list.
The Isolated vertex is not handled in list. (not Sure)
Only one value is entered in the list.
There is at least one null list.
If you find yourself in maze the better traversel approach will be :
BFS
BFS and DFS both are valid (Right Answer)
Level order
DFS
Cross edge is :
(u, v) where u and v are not ancestor of one another
(u, v) where u is ancesstor of v and v is not descendent of u.
(u, v) where u and v are not ancestor or descendent of one another (Right Answer)
(u, v) where u and v are either ancestor or descendent of one another.
What algorithm technique is used in the implementation of Kruskal solution for the MST?
Greedy Technique (Right Answer)
Divide-and-Conquer Technique
Dynamic Programming Technique
The algorithm combines more than one of the above techniques
Kruskal's algorithm (choose best non-cycle edge) is better than Prim's (choose best tree edge) when the graph has relatively few
True (Right Answer)
False
You have an adjacency list for G, what is the time complexity to compute Graph transpose G^T.?
?(V + E) Right Answer)
? (V E)
? (V)
? (V^2)
A digraph is strongly connected under what condition?
A digraph is strongly connected if for every pair of vertices u, v e V, u can reach v .
A digraph is strongly connected if for every pair of vertices u, v e V, u can reach v and vice versa. (Right Answer)
A digraph is strongly connected if for at least one pair of vertex u, v e V, u can reach v and vice versa.
A digraph is strongly connected if at least one third pair of vertices u, v e V, u can reach v and vice versa.
The relationship between number of back edges and number of cycles in DFS is,
Both are equal
Back edges are half of cycles
Back edges are one quarter of cycles
There is no relationship between no. of edges and cycles (Right Answer)
What algorithm technique is used in the implementation of Kruskal solution for the MST?
Greedy Technique (Right Answer)
Divide-and-Conquer Technique
Dynamic Programming Technique
The algorithm combines more than one of the above techniques
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