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⇱ Quiz about GATE||Design Stratgies (Greedy & Dynamic) || Pyq(2010 to 2025)

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Question 1

👁 Screenshot-2025-10-15-162418
ques

Which one of the following statements is true?
GATE CSE 2021,SET1 - [2Marks] (MCQ)


  • ⌈ diam (G) / 2⌉ < diam (G 2 ) < diam(G)

  • diam(G 2 ) = diam(G)

  • diam(G) = diam(G 2 ) <= 2 diam(G)

  • diam(G 2 ) <= ⌈ diam (G) / 2 ⌉

Question 2

Let G be a weighted connected undirected graph with distinct positive edge weights. If every edge weight is increased by the same value, then which of the following statements is/are TRUE?

P : Minimum spanning tree of G does not change

Q : Shortest path between any pair of vertices does not change
GATE CSE 2016,SET1 - [1Marks] (MCQ)


  • P only

  • Q only

  • Neither P nor Q

  • Both P and Q

Question 3

Consider the following table: GATE CSE 2017,SET1 - [1Marks] (MCQ)


Algorithms


Design Paradigms

P

Kruskal

i

Divide and Conquer

Q

Quicksort

ii

Greedy

R

Floyd-Warshall

iii

Dynamic Programming

  • P-(ii), Q-(iii), R-(i)

  • P-(iii), Q-(i), R-(ii)

  • P-(ii), Q-(i), R-(iii)

  • P-(i), Q-(ii), R-(iii)

Question 4

A message is made up entirely of characters from the set X = {P,Q,R,S,T} . The table of probabilities of each character is shown below :


Character

Probability

P

0.22

Q

0.17

R

0.34

S

0.19

T

0.08

Total

1.00

A message of 100 characters over X is encoded using Huffman coding. Then the excepted length of the encoded message in bits is _____
GATE CSE 2017,SET1 - [2Marks] (NAT)

  • 225

Question 5

Consider the following undirected graph G:

👁 Screenshot-2025-05-06-102207
.

Choose a value of x that will maximize the number of minimum weight spanning trees (MWSTs) of G. The number of MWSTs of G for this value of x is ___________.
GATE CSE 2018 - [2Marks] (NAT)


  • 4

Question 6

Let G be any connected, weighted, undirected graph.

I. G has a unique minimum spanning tree, if no two edges of G have the same weight.

II. G has a unique minimum spanning tree, if, for every cut of G, there is a unique minimum-weight edge crossing the cut.

Which of the above two statements is/are TRUE?
GATE CSE 2018 - [2Marks] (MCQ)


  • I only

  • II only

  • Both I and II

  • Neither I nor II

Question 7

Let G = (V, E) be a weighted undirected graph and let T be a Minimum Spanning Tree (MST) of G maintained using adjacency lists. Suppose a new weighted edge (u,v) ∈  V × V is added to G. The worst case time complexity determining if T is still an MST of the resultant graph is
GATE CSE 2020 - [2Marks] (MCQ)


  • θ(|E| log |V|)

  • θ(|E| + |V|)

  • θ(|E| |V|)

  • θ (|V|)

Question 8

Consider a graph G = (V, E), where V = {v 1 , v 2 , …, v 100 }, E = {(v i , v j ) | 1 <= i <= j <= 100}, and weight of the edge (v i , v j ) is |i – j|. The weight of the minimum spanning tree of G is _____.
GATE CSE 2020 - [2Marks] (NAT)


  • 99

Question 9

Define Rn to be the maximum amount earned by cutting a rod of length n meters into one or more pieces of integer length and selling them. For i > 0, let p[i] denote the selling prices of a rod whose length is i meters. Consider the array of prices :

p[1] = 1, p[2] = 5, p[3] = 8, p[4] = 9, p[5] = 10, p[6] = 17, p[7] = 18

Which of the following statements is/are correct about R 7 ?
GATE CSE 2021,SET1 - [2Marks] (MSQ)



  • R7 cannot be achieved by a solution consisting of three pieces.

  • R7 = 19

  • R7 = 18

  • R7 is achieved by three different solutions.

Question 10

Consider the following undirected graph with edge weights as shown:

👁 Screenshot-2025-05-06-163408
.

The number of minimum-spanning trees of the graph is __________.
GATE CSE 2021,SET1 - [1Marks] (NAT)


  • 3

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