GATE CSE

Greedy Method

Algorithms

(Past Years Questions)

Marks 1

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Let $$G$$ be a weighted connected undirected graph with distinct positive edge weights. If every edge weight is increase...
GATE CSE 2016 Set 1
Consider a weighted complete graph G on the vertex set {v1, v2, ..vn} such that the weight of the edge (vi, vj) is $$2|i...
GATE CSE 2006
To implement Dijkstra’s shortest path algorithm on unweighted graphs so that it runs in linear time, the data structure ...
GATE CSE 2006

Marks 2

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Consider the following undirected graph $$G: $$ Choose a value for $$x$$ that will maximize the number of minimum weig...
GATE CSE 2018
Consider the weights and values of items listed below. Note that there is only one unit of each item. .tg {border-col...
GATE CSE 2018
Consider the weighted undirected graph with $$4$$ vertices, where the weight of edge $$\left\{ {i,j} \right\}$$ is given...
GATE CSE 2016 Set 1
$$G = (V,E)$$ is an undirected simple graph in which each edge has a distinct weight, and e is a particular edge of G. W...
GATE CSE 2016 Set 1
A Young tableau is a $$2D$$ array of integers increasing from left to right and from top to bottom. Any unfilled entries...
GATE CSE 2015 Set 2
The graph shown below has 8 edges with distinct integer edge weights. The minimum spanning tree (MST) is of weight 36 an...
GATE CSE 2015 Set 1
Suppose P, Q, R, S, T are sorted sequences having lengths 20, 24, 30, 35, 50 respectively. They are to be merged into a ...
GATE CSE 2014 Set 2
The number of distinct minimum spanning trees for the weighted graph below is ________ ...
GATE CSE 2014 Set 2
Consider the directed graph shown in the figure below. There are multiple shortest paths between vertices S and T. Which...
GATE CSE 2012
An undirected graph G(V, E) contains n ( n > 2 ) nodes named v1 , v2 ,….vn. Two nodes vi , vj are connected if and only ...
GATE CSE 2011
An undirected graph G(V, E) contains n ( n > 2 ) nodes named v1 , v2 ,….vn. Two nodes vi , vj are connected if and only ...
GATE CSE 2011
Consider a complete undirected graph with vertex set {0, 1, 2, 3, 4}. Entry W(ij) in the matrix W below is the weight of...
GATE CSE 2010
Consider a complete undirected graph with vertex set {0, 1, 2, 3, 4}. Entry W(ij) in the matrix W below is the weight of...
GATE CSE 2010
Consider the following graph: Which one of the following is NOT the sequence of edges added to the minimum spanning tree...
GATE CSE 2009
Dijkstra's single source shortest path algorithm when run from vertex a in the above graph, computes the correct shorte...
GATE CSE 2008
Let w be the minimum weight among all edge weights in an undirected connected graph. Let e be a specific edge of weight ...
GATE CSE 2007
Suppose the letters a, b, c, d, e, f have probabilities 1/2, 1/4, 1/8, 1/16, 1/32, 1/32 respectively. Which of the follo...
GATE CSE 2007
Suppose the letters a, b, c, d, e, f have probabilities 1/2, 1/4, 1/8, 1/16, 1/32, 1/32 respectively. What is the averag...
GATE CSE 2007
In an unweighted, undirected connected graph, the shortest path from a node S to every other node is computed most effic...
GATE CSE 2007
Consider the following graph: Which one of the following cannot be the sequence of edges added, in that order, to a min...
GATE CSE 2006
Suppose we run Dijkstra’s single source shortest-path algorithm on the following edge-weighted directed graph with verte...
GATE CSE 2004
Let G=(V,E) be an undirected graph with a subgraph G1=(V1,E1). Weights are assigned to edges of G as follows. $$$w(e) = ...
GATE CSE 2003
Let G = (V, E) be a directed graph with n vertices. A path from vi to vj in G is sequence of vertices (vi, vi+1, ……., vj...
GATE CSE 2003
What is the weight of a minimum spanning tree of the following graph? ...
GATE CSE 2003
Let G be an undirected connected graph with distinct edge weight. Let emax be the edge with maximum weight and emin the ...
GATE CSE 2000
Complexity of Kruskal’s algorithm for finding the minimum spanning tree of an undirected graph containing n vertices and...
GATE CSE 1992
Kruskal’s algorithm for finding a minimum spanning tree of a weighted graph G with n vertices and m edges has the time c...
GATE CSE 1991
The weighted external path length of the binary tree in figure is ___________. ...
GATE CSE 1991

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