1
GATE CSE 2011
+1
-0.3
An algorithm to find the length of the longest monotonically increasing sequence of numbers in an array A[0:n−1] is given below.

Let Li, denote the length of the longest monotonically increasing sequence starting at index i in the array. Initialize Ln−1=1.

For all i such that $$0 \leq i \leq n-2$$

$$L_i = \begin{cases} 1+ L_{i+1} & \quad\text{if A[i] < A[i+1]} \\ 1 & \quad\text{Otherwise}\end{cases}$$

Finally, the length of the longest monotonically increasing sequence is max(L0, L1,…,Ln−1)
Which of the following statements is TRUE?
A
The algorithm uses dynamic programming paradigm
B
The algorithm has a linear complexity and uses branch and bound paradigm
C
The algorithm has a non-linear polynomial complexity and uses branch and bound paradigm
D
The algorithm uses divide and conquer paradigm
2
GATE CSE 2011
+2
-0.6
Four matrices M1, M2, M3 and M4 of dimensions p $$\times$$ q, q $$\times$$ r, r $$\times$$ s and s $$\times$$ t respectively can be multiplied is several ways with different number of total scalar multiplications. For example, when multiplied as ((M1 $$\times$$ M2) $$\times$$ (M3 $$\times$$ M4)), the total number of multiplications is pqr + rst + prt. When multiplied as (((M1 $$\times$$ M2) $$\times$$ M3) $$\times$$ M4), the total number of scalar multiplications is pqr + prs + pst.

If p = 10, q = 100, r = 20, s = 5 and t = 80, then the number of scalar multiplications needed is:
A
248000
B
44000
C
19000
D
25000
3
GATE CSE 2011
+1
-0.3
In a compiler, keywords of a language are recognized during
A
parsing of the program
B
the code generation
C
the lexical analysis of the program
D
dataflow analysis
4
GATE CSE 2011
+2
-0.6
Consider a network with five nodes, N1 to N5, as shown below.

The network uses a Distance Vector Routing protocol. Once the routes have stabilized, the distance vectors at different nodes are as following

N1 : ( 0, 1, 7, 8, 4 )
N2 : ( 1, 0, 6, 7, 3 )
N3 : ( 7, 6, 0, 2, 6 )
N4 : ( 8, 7, 2, 0, 4 )
N5 : ( 4, 3, 6, 4, 0 )

Each distance vector is the distance of the best known path at that instance to nodes, N1 to N5, where the distance to itself is 0. Also, all links are symmetric and the cost is identical in both directions. In each round, all nodes exchange their distance vectors with their respective neighbors. Then all nodes update their distance vectors. In between two rounds, any change in cost of a link will cause the two incident nodes to change only that entry in their distance vectors

After the update in the previous question, the link N1-N2 goes down. N2 will reflect this change immediately in its distance vector as cost, $$\infty$$. After the NEXT ROUND of update, what will be the cost to N1 in the distance vector of N3?

A
3
B
9
C
10
D
$$\infty$$
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