GATE CSE 2024 Set 2 | Greedy Method Question 1 | Algorithms

GATE CSE 2024 Set 2

MCQ (More than One Correct Answer)

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Let $G$ be an undirected connected graph in which every edge has a positive integer weight. Suppose that every spanning tree in $G$ has even weight. Which of the following statements is/are TRUE for every such graph $G$?

All edges in $G$ have even weight

All edges in $G$ have even weight OR all edges in $G$ have odd weight

In each cycle $C$ in $G$, all edges in $C$ have even weight

In each cycle $C$ in $G$, either all edges in $C$ have even weight OR all edges in $C$ have odd weight

GATE CSE 2024 Set 2

Numerical

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The number of distinct minimum-weight spanning trees of the following graph is ________

GATE CSE 2024 Set 2 Algorithms - Greedy Method Question 1 English

Your input ____

GATE CSE 2021 Set 2

MCQ (Single Correct Answer)

-0.66

Consider the string abbccddeee. Each letter in the string must be assigned a binary code satisfying the following properties:

1. For any two letters, the code assigned to one letter must not be a prefix of the code assigned to the other letter.

2. For any two letters of the same frequency, the letter which occurs earlier in the dictionary order is assigned a code whose length is at most the length of the code assigned to the other letter.

Among the set of all binary code assignments which satisfy the above two properties, what is the minimum length of the encoded string?

GATE CSE 2020

MCQ (Single Correct Answer)

-0.67

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) $$ \in $$ V $$ \times $$ V is added to G. The worst case time complexity of determining if T is still an MST of the resultant graph is

$$\Theta \left( {\left| E \right| + \left| V \right|} \right)$$

$$\Theta \left( {\left| E \right|\left| V \right|} \right)$$

$$\Theta \left( {\left| E \right|\log \left| V \right|} \right)$$

$$\Theta \left( {\left| V \right|} \right)$$