Master Shortest Path Algorithms in Advanced Data Structures

Question 1

In a weighted, directed graph, which algorithm is greedy and finds the shortest path from a source vertex to all other vertices?

Accepted Answer

Dijkstra's

Answer

Floyd-Warshall

Answer

Bellman-Ford

Answer

Prim's

Question 2

Explain the practical significance of shortest path algorithms and provide real-world examples from different fields.

Accepted Answer

One practical application of shortest path algorithms is optimizing routes in transportation systems, such as finding the fastest delivery routes.

Answer

Shortest path algorithms are mainly used for theoretical purposes in computer science.

Answer

Shortest path algorithms have no real-world applications and are only used for academic research.

Answer

Shortest path algorithms are only applicable to finding the shortest paths in social networks.

Question 3

Which of the following algorithms finds the shortest path from a single source vertex to all other vertices in a graph?

Accepted Answer

Dijkstra's algorithm

Answer

Floyd-Warshall algorithm

Answer

Bellman-Ford algorithm

Answer

Prim's algorithm

Question 4

Which data structure is used to implement the priority queue in Dijkstra's algorithm?

Accepted Answer

Heap

Answer

Array

Answer

Linked list

Answer

Queue

Question 5

Floyd-Warshall algorithm is used to find the shortest paths:

Accepted Answer

Between all pairs of vertices in a graph

Answer

From a single source vertex to all other vertices in a graph

Answer

Between two specific vertices in a graph

Answer

Between all vertices in a tree

Question 6

What is the time complexity of Floyd-Warshall algorithm for a graph with V vertices?

Accepted Answer

O(V^3)

Answer

O(V)

Answer

O(V log V)

Answer

O(E^2)

Question 7

Which of the following is a key difference between Dijkstra's and Floyd-Warshall algorithms?

Accepted Answer

Dijkstra's algorithm finds the shortest path from a single source vertex while Floyd-Warshall algorithm finds the shortest paths between all pairs of vertices

Answer

Dijkstra's algorithm is greedy while Floyd-Warshall algorithm is dynamic programming

Answer

Dijkstra's algorithm can handle negative edge weights while Floyd-Warshall algorithm cannot

Answer

Floyd-Warshall algorithm is more efficient for large graphs while Dijkstra's algorithm is more efficient for sparse graphs

Question 8

Which algorithm is specifically designed to find the shortest path between two nodes in a directed graph?

Accepted Answer

Dijkstra's algorithm

Answer

Floyd-Warshall algorithm

Answer

Prim's algorithm

Answer

Bellman-Ford algorithm

Question 9

In Dijkstra's algorithm, which data structure is used to efficiently manage the set of unvisited nodes?

Accepted Answer

Priority queue

Answer

Hash table

Answer

Stack

Answer

Linked list

Question 10

What is the time complexity of the Floyd-Warshall algorithm for finding all-pairs shortest paths in a graph with 'n' nodes?

Accepted Answer

O(n³)

Answer

O(n²)

Answer

O(n log n)

Answer

O(2^n)

Question 11

Which of the following accurately describes the practical applications of shortest path algorithms?

Accepted Answer

They can be used to optimize routing and solve network optimization problems.

Answer

They are exclusively applicable to directed graphs.

Answer

They always find the shortest path, regardless of the graph's size.

Question 12

In a weighted graph, what does the weight assigned to an edge represent?

Accepted Answer

The cost or distance associated with traversing that edge.

Answer

The direction of the edge.

Answer

The number of nodes connected by the edge.

Question 13

For a graph with negative edge weights, which algorithm is suitable for finding the shortest path?

Accepted Answer

Bellman-Ford algorithm

Answer

Dijkstra's algorithm

Answer

Prim's algorithm

Question 14

Which technique can be employed to detect negative cycles in a graph?

Accepted Answer

Bellman-Ford algorithm with a relaxation criterion.

Answer

Floyd-Warshall algorithm with a negative weight check.

Answer

Dijkstra's algorithm with a negative weight check.

Question 15

In a directed acyclic graph (DAG), what approach can be used to find the longest path?

Accepted Answer

Topological sort followed by a relaxation step.

Answer

Bellman-Ford algorithm with a longest path modification.

Answer

Floyd-Warshall algorithm with a longest path modification.

Answer

Dijkstra's algorithm with reversed edge weights.

Question 16

Provide an example of a real-world application where shortest path algorithms are utilized.

Accepted Answer

Optimizing network routing to minimize latency

Answer

Translating languages

Answer

Predicting weather patterns

Answer

Detecting fraud in financial transactions

Question 17

Which of the following is NOT a characteristic of Dijkstra's algorithm?

Accepted Answer

It can identify the shortest path in graphs with negative edge weights.

Answer

It utilizes a priority queue to determine the next vertex to traverse.

Answer

It operates using a greedy approach.

Answer

It determines the shortest path from a specified starting vertex to all other vertices.

Question 18

What is the computational complexity of the Floyd-Warshall algorithm for finding the shortest paths between all pairs of vertices in a graph with 'n' vertices?

Accepted Answer

O(n^3)

Answer

O(n * log n)

Answer

O(n)

Answer

O(n^2)

Question 19

Which data structure is the most efficient choice for implementing Dijkstra's algorithm?

Accepted Answer

Priority Queue

Answer

Linked List

Answer

Hash Table

Answer

Stack

Question 20

In which real-world application are shortest path algorithms commonly employed?

Accepted Answer

Routing in computer networks

Answer

Clustering

Answer

Natural language processing

Answer

Image segmentation

Question 21

Consider a weighted graph with both positive and negative edge weights. Which algorithm should be used to find the shortest path from a single source vertex to all others?

Accepted Answer

Bellman-Ford

Answer

Dijkstra's

Answer

Floyd-Warshall

Question 22

Which concept plays a significant role in shortest path algorithms?

Accepted Answer

Relaxation

Answer

Backtracking

Answer

Heuristic

Answer

Pruning

Question 23

Consider the following weighted graph:
    A --2-- B --1-- C
    What is the shortest path from A to C using Dijkstra's algorithm?

Accepted Answer

A -> B -> C

Answer

B -> A -> C

Answer

A -> C

Answer

B -> C

Question 24

In Dijkstra's algorithm, which data structure is used to store the tentative distances to all unvisited vertices?

Accepted Answer

Priority Queue

Answer

Queue

Answer

Stack

Answer

Hash Table

Question 25

Which step in the Floyd-Warshall algorithm is crucial for finding all-pairs shortest paths?

Accepted Answer

Iterative update of shortest paths through intermediate vertices

Answer

Dynamic programming to compute all possible paths

Answer

Greedy selection of shortest paths

Answer

Depth-first traversal to identify shortest paths

Question 26

For a weighted graph with non-negative edge weights, which algorithm is guaranteed to find the shortest path between two vertices?

Accepted Answer

Dijkstra's algorithm

Answer

Breadth-First Search (BFS)

Answer

Kruskal's algorithm

Answer

Prim's algorithm

Question 27

What property of a graph is essential for Dijkstra's algorithm to produce accurate shortest paths?

Accepted Answer

Non-negative edge weights

Answer

Undirected edges

Answer

Acyclic edges

Answer

Complete edges

Question 28

In a graph with both positive and negative edge weights, which algorithm can be employed to find the shortest path?

Accepted Answer

Bellman-Ford algorithm

Answer

Prim's algorithm

Answer

Floyd-Warshall algorithm

Answer

Dijkstra's algorithm

Question 29

Which real-world scenario demonstrates a practical application of shortest path algorithms?

Accepted Answer

Calculating the shortest route on a map

Answer

Clustering high-dimensional data points

Answer

Predicting user preferences

Answer

Detecting anomalies in time series data

Question 30

What is the time complexity of the Floyd-Warshall algorithm for a graph with V vertices?

Accepted Answer

O(V^3)

Answer

O(E log V)

Answer

O(V log V)

Answer

O(E)

Question 31

How does the Floyd-Warshall algorithm differ from the Dijkstra algorithm?

Accepted Answer

Floyd-Warshall computes all-pairs shortest paths, while Dijkstra finds the shortest path from a single source to all others

Answer

Floyd-Warshall requires non-negative edge weights, while Dijkstra does not

Answer

Floyd-Warshall has a lower time complexity than Dijkstra

Answer

Floyd-Warshall is a greedy algorithm, while Dijkstra is not

Question 32

In the context of shortest path algorithms, what is the purpose of the 'relax' operation?

Accepted Answer

Updating the tentative distance to a vertex if a shorter path is found

Answer

Removing an edge from the graph

Answer

Adding a vertex to the visited set

Answer

Calculating the edge weights

Question 33

Which data structure is most suitable for representing a graph when implementing shortest path algorithms?

Accepted Answer

Adjacency list

Answer

Edge list

Answer

Incidence matrix

Answer

Adjacency matrix

Question 34

Which algorithm is most suitable for finding the shortest path between two nodes in a directed or undirected graph with non-negative edge weights?

Accepted Answer

Dijkstra's algorithm

Answer

Bellman-Ford algorithm

Answer

Prim's algorithm

Question 35

In the context of shortest path algorithms, which data structure is commonly used to manage the set of nodes that have been visited or are still being considered?

Accepted Answer

Queue or Priority queue

Answer

Hash table

Answer

Adjacency list

Answer

Binary search tree

Question 36

Consider a graph G with n vertices and m edges. What is the time complexity of the Floyd-Warshall algorithm for finding the shortest path between all pairs of vertices in G?

Accepted Answer

O(n^3)

Answer

O(m * log n)

Answer

O(n^2 * log n)

Answer

O(n * m)

Question 37

Which of the following conditions must a graph satisfy for Dijkstra's algorithm to find the shortest path correctly?

Accepted Answer

Non-negative edge weights

Answer

Absence of cycles

Answer

All vertices connected

Answer

Directed edges

Question 38

Given a graph G represented as an adjacency matrix, how can the Floyd-Warshall algorithm be used to determine the shortest path between two vertices u and v in G?

Accepted Answer

By examining the value in the cell [u][v] of the resulting matrix.

Answer

By traversing the matrix column-wise.

Answer

By traversing the matrix row-wise.

Question 39

Which property of a graph ensures that the shortest path between two nodes will be unique?

Accepted Answer

Absence of cycles and non-negative edge weights

Answer

Negative edge weights

Answer

All vertices connected

Answer

Directed edges

Question 40

Consider the following graph: A --> B (5) --> C (2), A --> C (1), C --> D (3). What is the shortest path from A to D?

Accepted Answer

A --> C --> D

Answer

A --> B --> C --> D

Answer

A --> C --> B --> D

Answer

A --> B --> D

Question 41

How does Bellman-Ford algorithm handle negative edge weights?

Accepted Answer

It can handle negative edge weights and detect negative weight cycles.

Answer

It ignores negative edge weights.

Answer

It assigns negative values to distances.

Question 42

Which algorithm is specifically designed to find the shortest path from a specified source node to all other nodes in a weighted, directed graph?

Accepted Answer

Dijkstra's algorithm

Answer

Floyd-Warshall algorithm

Answer

Kruskal's algorithm

Answer

Bellman-Ford algorithm

Question 43

For a weighted, directed graph, which algorithm is optimal for efficiently determining the shortest paths between all pairs of nodes?

Accepted Answer

Floyd-Warshall algorithm

Answer

Dijkstra's algorithm

Answer

Prim's algorithm

Answer

Kruskal's algorithm

Question 44

In Dijkstra's algorithm, which data structure is employed to efficiently manage the tentative shortest distances to each node?

Accepted Answer

Priority queue

Answer

Stack

Answer

Queue

Answer

Linked list

Question 45

Identify the limitation of Dijkstra's algorithm:

Accepted Answer

Inability to handle negative edge weights

Answer

High time complexity

Answer

Applicability only to directed graphs

Answer

Unsuitability for large graphs

Question 46

Determine the time complexity of the Floyd-Warshall algorithm for a graph with 'n' nodes:

Accepted Answer

Θ(n^3)

Answer

Θ(n log n)

Answer

Θ(n^2)

Question 47

Provide an example of a practical application of shortest path algorithms:

Accepted Answer

Routing in computer networks

Answer

Data compression

Answer

Collision detection

Answer

Image processing

Question 48

In Dijkstra's algorithm, when starting from node 'A' in a weighted graph with non-negative edge weights, which node is prioritized for shortest path computation?

Accepted Answer

Node with the smallest weight edge connected to 'A'

Answer

Node with the largest weight edge connected to 'A'

Answer

Randomly selected node from the graph

Question 49

In Floyd-Warshall algorithm, the value stored in cell (i, j) of the distance matrix after the kth iteration represents:

Accepted Answer

Shortest path from node 'i' to node 'j' using intermediate nodes from 1 to k

Answer

Weight of the edge between nodes 'i' and 'j'

Answer

Shortest path from node 'i' to node 'j' using only node 'k' as an intermediate node

Question 50

Envision a scenario where you need to find the shortest path between two nodes in a graph representing a road network. Which algorithm would be most appropriate for this task?

Accepted Answer

Dijkstra's algorithm

Answer

Kruskal's algorithm

Answer

Prim's algorithm

Answer

Bellman-Ford algorithm