From 0 to 1 Data Structures & Algorithms in Java - Dealing With Negative Cycles In The Bellman Ford Algorithm

The video tutorial explains the concept of negative cycles in graphs and their impact on shortest path calculations. It introduces the Bellman Ford algorithm, which can handle graphs with negative weighted edges. The tutorial provides an example of a negative cycle and demonstrates how it affects path calculations. It also explains how to detect negative cycles using the Bellman Ford algorithm and discusses the algorithm's complexity in terms of edge and vertex traversal.

What is a negative cycle in a graph?

• A cycle with all positive edge weights

• A cycle with no edges

• A cycle with equal positive and negative edge weights

• A cycle with a total negative edge weight

Why is it difficult to find the shortest path in a graph with a negative cycle?

• Because negative cycles make the graph disconnected

• Because negative cycles allow for infinitely decreasing path lengths

• Because negative cycles increase the path length

• Because negative cycles create multiple shortest paths

How does the Bellman-Ford algorithm detect a negative cycle?

• By comparing the graph to a known cycle-free graph

• By counting the number of edges in the graph

• By performing an additional iteration after V-1 relaxations

• By checking if all vertices have been visited

What happens if a vertex's distance is updated after V-1 iterations in Bellman-Ford?

• The graph is acyclic

• The graph has a negative cycle

• The graph has a positive cycle

• The graph is disconnected

What is the time complexity of the Bellman-Ford algorithm using adjacency lists?

• O(EV)

• O(E^2)

• O(V^2)

• O(V^3)

How does the time complexity change when using an adjacency matrix?

• It becomes O(E^2)

• It remains O(EV)

• It becomes O(V^3)

• It becomes O(V^2)

Why is E equal to V^2 in an adjacency matrix?

• Because the graph is a cycle

• Because the graph is a tree

• Because there are no edges in the graph

• Because every vertex is connected to every other vertex