1

GATE CSE 2016 Set 1

Numerical

+2

-0

Consider the weighted undirected graph with $$4$$ vertices, where the weight of edge $$\left\{ {i,j} \right\}$$ is given by the entry $${W_{ij}}$$ in the matrix $$W.$$
$$$W = \left[ {\matrix{
0 & 2 & 8 & 5 \cr
2 & 0 & 5 & 8 \cr
8 & 5 & 0 & X \cr
5 & 8 & X & 0 \cr
} } \right]$$$

The largest possible integer value of $$x,$$ for which at least one shortest path between some pair of vertices will contain the edge with weight $$x$$ is _________________.

Your input ____

2

GATE CSE 2015 Set 2

Numerical

+2

-0

A Young tableau is a $$2D$$ array of integers increasing from left to right and from top to bottom. Any unfilled entries are marked with $$\infty ,$$ and hence there cannot be any entry to the right of, or below a $$\infty .$$ The following Young tableau consists of unique entries.

1 | 2 | 5 | 14 |
---|---|---|---|

3 | 4 | 6 | 23 |

10 | 12 | 18 | 25 |

31 | ∞ |
∞ | ∞ |

When an element is removed from a Young tableau, other elements should be moved into its place so that the resulting table is still a Young tableau (unfilled entries may be filled in with a $$\infty $$). The minimum number of entries (other than $$1$$) to be shifted, to remove $$1$$ from the given Young tableau is ______________.

Your input ____

3

GATE CSE 2015 Set 1

Numerical

+2

-0

The graph shown below has 8 edges with distinct integer edge weights. The minimum spanning tree (MST) is of weight 36 and contains the edges: {(A, C), (B, C), (B, E), (E, F), (D, F)}. The edge weights of only those edges which are in the MST are given in the figure shown below. The minimum possible sum of weights of all 8 edges of this graph is ___________.

Your input ____

4

GATE CSE 2014 Set 2

Numerical

+2

-0

Suppose P, Q, R, S, T are sorted sequences having lengths 20, 24, 30, 35, 50 respectively. They are to be merged into a single sequence by merging together two sequences at a time. The number of comparisons that will be needed in the worst case by the optimal algorithm for doing this is ____.

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Questions Asked from Greedy Method (Marks 2)

Number in Brackets after Paper Indicates No. of Questions

GATE CSE 2024 Set 2 (2)
GATE CSE 2020 (2)
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GATE CSE 2016 Set 1 (2)
GATE CSE 2015 Set 2 (1)
GATE CSE 2015 Set 1 (1)
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GATE CSE 2007 (4)
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GATE CSE 2003 (3)
GATE CSE 2000 (1)
GATE CSE 1992 (1)
GATE CSE 1991 (2)

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Discrete Mathematics

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