Podcast
Questions and Answers
What is an intractable problem in computer science?
What is an intractable problem in computer science?
- A problem for which it is unlikely that a polynomial time algorithm solution exists (correct)
- A problem with a solution that can be found by an exponential time algorithm
- A problem for which a solution can be found in constant time
- A problem with a solution that can be found by a polynomial time algorithm
What does it mean when an algorithm is said to be of polynomial time?
What does it mean when an algorithm is said to be of polynomial time?
- The algorithm cannot handle large inputs
- The algorithm's running time is exponential
- The algorithm always takes the same amount of time to execute
- The algorithm's running time is upper bounded by a polynomial expression in the size of the input (correct)
Which of the following is an example of an intractable problem?
Which of the following is an example of an intractable problem?
- Traveling Salesman Problem (correct)
- Linear Regression
- Binary Search
- Bubble Sort
What are some common examples of intractable problems?
What are some common examples of intractable problems?
What are some common data structures used to model intractable problems?
What are some common data structures used to model intractable problems?
What does a graph illustrate?
What does a graph illustrate?
What is the formal definition of a graph G?
What is the formal definition of a graph G?
What does a vertex represent in the context of this graph?
What does a vertex represent in the context of this graph?
Which type of graph has all its edges directed?
Which type of graph has all its edges directed?
What is the number of edges in a complete directed graph with n vertices?
What is the number of edges in a complete directed graph with n vertices?
In adjacency matrix representation, what does A(i,j) = 1 indicate?
In adjacency matrix representation, what does A(i,j) = 1 indicate?
What is the space requirement for an adjacency matrix?
What is the space requirement for an adjacency matrix?
What does the adjacency list representation involve?
What does the adjacency list representation involve?
What does null in an adjacency list represent?
What does null in an adjacency list represent?
What is the time complexity of the adjacency list representation?
What is the time complexity of the adjacency list representation?
"What is a complete graph?"
"What is a complete graph?"
What are the two types of directed and undirected edges mentioned in the text?
What are the two types of directed and undirected edges mentioned in the text?
How does a complete undirected graph differ from a complete directed graph in terms of its edges?
How does a complete undirected graph differ from a complete directed graph in terms of its edges?
Study Notes
Intractable Problems
- An intractable problem in computer science is a problem that cannot be solved in a reasonable amount of time (e.g., within seconds, minutes, or hours) due to its computational complexity.
Algorithm Time Complexity
- An algorithm is said to be of polynomial time if its running time increases polynomially (e.g., O(n), O(n^2), O(n^3)) with the size of the input.
Examples of Intractable Problems
- The traveling salesman problem is an example of an intractable problem.
Graph Theory
- A graph illustrates relationships between objects or nodes.
- The formal definition of a graph G is G = (V, E), where V is the set of vertices and E is the set of edges.
Graph Components
- A vertex represents a node in the graph.
- A graph with all its edges directed is called a directed graph.
- The number of edges in a complete directed graph with n vertices is n(n-1).
Graph Representations
- In adjacency matrix representation, A(i,j) = 1 indicates that there is an edge from vertex i to vertex j.
- The space requirement for an adjacency matrix is O(n^2).
- Adjacency list representation involves storing edges as lists of vertices that are connected to each vertex.
- Null in an adjacency list represents the absence of an edge.
Graph Types
- A complete graph is a graph in which every vertex is connected to every other vertex.
Edge Types
- The two types of edges are directed edges and undirected edges.
- A complete undirected graph differs from a complete directed graph in that it has two edges between each pair of vertices (one in each direction), whereas a complete directed graph has only one edge between each pair of vertices (in one direction).
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Description
Test your understanding of intractable problems in computer science with this review quiz. Explore the classification of problems as tractable or intractable, and learn about polynomial time algorithms and their upper bound running time. This quiz is designed to help you reinforce your knowledge of algorithmic complexity.
