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 L_i, denote the length of the longest monotonically increasing sequence starting at index i in the array. Initialize L_n−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,…,L_n−1)
Which of the following statements is TRUE?

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:

In a compiler, keywords of a language are recognized during

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

The cost of link N2 - N3 reduces to 2 in (both directions). After the next round of updates, what will be the new distance vector at node, N3?