Graphs and Algorithms Quiz

Questions and Answers

What is the time complexity of the Floyd-Warshall algorithm?

$O(n^3)$

Which type of problems does the Floyd-Warshall algorithm address?

All pairs shortest path problems

What is a key feature of the Floyd-Warshall algorithm compared to Dijkstra's algorithm?

Supports negative edge-weights

In what form can an edge-weighted graph be represented for the Floyd-Warshall algorithm?

Adjacency matrix Signup and view all the answers

What is a limitation of Dijkstra's algorithm compared to the Floyd-Warshall algorithm?

Doesn't work with negative-weight edges Signup and view all the answers

What is a random variable?

A function that associates each element in the sample space with a real number Signup and view all the answers

When is a random variable called discrete?

When its set of possible values is countable Signup and view all the answers

What does the notation $X : S → R$ denote?

The association of each element in the sample space with a real number Signup and view all the answers

What are the possible values of the random variable X in the given example?

{0, 1, 2} Signup and view all the answers

In a statistical experiment, what is often important regarding outcomes?

Allocating numerical values to the outcomes Signup and view all the answers

Study Notes

Algorithmic Complexity

The time complexity of the Floyd-Warshall algorithm is O(n^3).

Graph Problems

The Floyd-Warshall algorithm addresses all-pairs shortest path problems in weighted graphs.

Comparison to Dijkstra's Algorithm

A key feature of the Floyd-Warshall algorithm is that it can handle negative edge weights, unlike Dijkstra's algorithm.

Graph Representation

An edge-weighted graph can be represented as an adjacency matrix for the Floyd-Warshall algorithm.

Limitations of Dijkstra's Algorithm

A limitation of Dijkstra's algorithm is that it cannot handle negative edge weights, unlike the Floyd-Warshall algorithm.

Random Variables

A random variable is a variable whose possible values are determined by chance.

Discrete Random Variables

A random variable is called discrete if it can only take on specific, distinct values.

Notation

The notation $X : S → R$ denotes a random variable X with a sample space S and a range of real numbers R.

Random Variable Values

In the given example, the possible values of the random variable X are the values in the sample space S.

Statistical Experiments

In a statistical experiment, what is often important regarding outcomes is the probability of each outcome occurring.