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GATE CSE
Greedy Method
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Previous Years Questions
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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
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To implement Dijkstra’s shortest path algorithm on unweighted graphs so that it runs in linear time, the data structure ...
GATE CSE 2006
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Consider a weighted complete graph G on the vertex set {v1, v2, ..vn} such that the weight of the edge (vi, vj) is $$2|i...
GATE CSE 2006
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Marks 2
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Consider a graph G = (V, E), where V = {v1, v2, ...., v100}, E = {(vi, vj) | 1 ≤ i < j ≤ 100}, and weight of the edg...
GATE CSE 2020
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Let G = (V, E) be a weighted undirected graph and let T be a Minimum Spanning Tree (MST) of G maintained using adjacency...
GATE CSE 2020
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Consider the following undirected graph $$G: $$ Choose a value for $$x$$ that will maximize the number of minimum weig...
GATE CSE 2018
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Consider the weights and values of items listed below. Note that there is only one unit of each item. .tg {border-col...
GATE CSE 2018
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Consider the weighted undirected graph with $$4$$ vertices, where the weight of edge $$\left\{ {i,j} \right\}$$ is given...
GATE CSE 2016 Set 1
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$$G = (V,E)$$ is an undirected simple graph in which each edge has a distinct weight, and e is a particular edge of G. W...
GATE CSE 2016 Set 1
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A Young tableau is a $$2D$$ array of integers increasing from left to right and from top to bottom. Any unfilled entries...
GATE CSE 2015 Set 2
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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
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The number of distinct minimum spanning trees for the weighted graph below is ________ ...
GATE CSE 2014 Set 2
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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
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Consider the directed graph shown in the figure below. There are multiple shortest paths between vertices S and T. Which...
GATE CSE 2012
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An undirected graph G(V, E) contains n ( n > 2 ) nodes named v1 , v2 ,….vn. Two nodes vi , vj are connected if and on...
GATE CSE 2011
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An undirected graph G(V, E) contains n ( n > 2 ) nodes named v1 , v2 ,….vn. Two nodes vi , vj are connected if and on...
GATE CSE 2011
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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
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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
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Consider the following graph: Which one of the following is NOT the sequence of edges added to the minimum spanning tree...
GATE CSE 2009
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Dijkstra's single source shortest path algorithm when run from vertex a in the above graph, computes the correct shorte...
GATE CSE 2008
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In an unweighted, undirected connected graph, the shortest path from a node S to every other node is computed most effic...
GATE CSE 2007
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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
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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
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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
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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
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Suppose we run Dijkstra’s single source shortest-path algorithm on the following edge-weighted directed graph with verte...
GATE CSE 2004
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What is the weight of a minimum spanning tree of the following graph? ...
GATE CSE 2003
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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
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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
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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
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Complexity of Kruskal’s algorithm for finding the minimum spanning tree of an undirected graph containing n vertices and...
GATE CSE 1992
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The weighted external path length of the binary tree in figure is ___________. ...
GATE CSE 1991
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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
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