1
GATE CSE 2022
Numerical
+1
-0.33

Let G(V, E) be a directed graph, where V = {1, 2, 3, 4, 5} is the set of vertices and E is the set of directed edges, as defined by the following adjacency matrix A.

$$A[i][j] = \left\{ {\matrix{ {1,} & {1 \le j \le i \le 5} \cr {0,} & {otherwise} \cr } } \right.$$

A[i][j] = 1 indicates a directed edge from node i to node j. A directed spanning tree of G, rooted at r $$\in$$ V, is defined as a subgraph T of G such that the undirected version of T is a tree, and T contains a directed path from r to every other vertex in V. The number of such directed spanning trees rooted at vertex 5 is _____________.

2
GATE CSE 2016 Set 2
+1
-0.3
The Floyd-Warshall algorithm for all-pair shortest paths computation is based on
A
B
C
D
neither Greedy nor Divide-and-Conquer nor Dynamic Programming paradigm.
3
GATE CSE 2015 Set 1
+1
-0.3
Match the following:

List 1

(P) Prim’s algorithm for minimum spanning tree
(Q) Floyd-Warshall algorithm for all pairs shortest paths
(R) Mergesort
(S) Hamiltonian circuit

List 2

(i) Backtracking
(ii) Greedy method
(iii) Dynamic programming
(iv) Divide and conquer
A
P - iii, Q - ii, R - iv, S - i
B
P - i, Q - ii, R - iv, S - iii
C
P - ii, Q - iii, R - iv, S - i
D
P - ii, Q - i, R - iii, S - iv
4
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
GATE CSE Subjects
EXAM MAP
Medical
NEET