TMA 01 Part 2: Collections, Algorithms, and Coding Style

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What is the common way to represent a graph in computer science?

Using a tree data structure

Using a list of vertices and edges

Using a matrix of adjacencies (correct)

Using a set of nodes and a set of edges

Which graph traversal algorithm is used to visit all reachable nodes from a given starting node?

Dijkstra's algorithm

Depth-First Search (DFS)

Breadth-First Search (BFS) (correct)

Kruskal's algorithm

What is the time complexity of Breadth-First Search (BFS) on a graph with $V$ vertices and $E$ edges?

$O(E)$

$O(V + E)$ (correct)

$O(V)$

$O(V^2)$

Which graph data structure is used to represent a tree?

Rooted tree Signup and view all the answers

What is the purpose of Kruskal's algorithm in graph theory?

To find the minimum spanning tree of a weighted graph Signup and view all the answers

What topic does the section 'Undirected graph components' in the text fall under?

Graphs Signup and view all the answers

Which section in the text mentions 'Minimum spanning tree'?

Graphs Signup and view all the answers

In which part of the text would you expect to find information about 'Topological sort'?

Graphs Signup and view all the answers

Which part of the text discusses 'Jousting' and 'Dot product'?

Graphs Signup and view all the answers

'Longest common subsequence' and 'Knapsack' are topics found in which part of the text?

Dynamic Programming Signup and view all the answers

'Borrow a book' and 'Levenshtein distance' are mentioned in which part of the text?

Complexity classes Signup and view all the answers

What is the purpose of the adjacency matrix representation of a graph?

To represent the connectivity between nodes in a graph Signup and view all the answers

Which graph traversal algorithm is used to visit all reachable nodes from a given starting node?

Depth-First Search (DFS) Signup and view all the answers

What is the purpose of Topological Sort in graph theory?

To order the nodes of a directed graph based on their dependencies Signup and view all the answers

What is the purpose of the adjacency list representation of a graph?

To allow for fast lookups of node degrees Signup and view all the answers

What is the purpose of Kruskal's algorithm in graph theory?

To find the minimum spanning tree of a graph Signup and view all the answers

What is the purpose of the edge list representation of a graph?

To efficiently store the edges of a sparse graph Signup and view all the answers

What is the most common way to represent a graph in computer science?

Adjacency list Signup and view all the answers

Which graph traversal algorithm is used to visit all reachable nodes from a given starting node?

Breadth-First Search (BFS) Signup and view all the answers

What is the time complexity of Breadth-First Search (BFS) on a graph with $V$ vertices and $E$ edges?

$O(V + E)$ Signup and view all the answers

Which graph data structure is used to represent a tree?

Rooted tree Signup and view all the answers

What is the purpose of Kruskal's algorithm in graph theory?

To find the minimum spanning tree of a graph Signup and view all the answers

What is the purpose of Prim's algorithm in graph theory?

To find the minimum spanning tree of a graph Signup and view all the answers

What is the purpose of Dijkstra's algorithm in graph theory?

To find the shortest path between two nodes Signup and view all the answers

What is the purpose of Topological Sort in graph theory?

To find a linear ordering of the vertices in a directed acyclic graph (DAG) Signup and view all the answers

What is the purpose of the Strongly Connected Components (SCC) algorithm in graph theory?

To partition a directed graph into its strongly connected components Signup and view all the answers

What is the purpose of the Tarjan's algorithm in graph theory?

To find the strongly connected components of a directed graph Signup and view all the answers

What starts with an empty candidate sequence or set and extends it one item at a time?

Partial candidates Signup and view all the answers

Which technique only generates a fraction of all candidates making it more efficient than exhaustive search?

Tree traversal Signup and view all the answers

In backtracking, what core traversal is used for generating permutations and subsets?

Tree traversal Signup and view all the answers

When extending a candidate in backtracking, what does the algorithm do if it cannot lead to a solution or a better solution?

Goes back and tries a different item or candidate Signup and view all the answers

At the core of backtracking is a recursive pre-order traversal of what structure?

Tree Signup and view all the answers

Which problems in M269 are solved using backtracking on sequences of non-duplicate items or subsets of items?

Constraint satisfaction and optimization problems Signup and view all the answers

What is the purpose of the first check in a backtracking algorithm?

To check if it's worth extending the candidate with a chosen item Signup and view all the answers

What is the purpose of the second check in a backtracking algorithm?

To check if a candidate satisfies the global constraints Signup and view all the answers

How can the search space be further pruned for subset problems in a backtracking algorithm?

By sorting the items in advance and stopping when a candidate cannot be extended Signup and view all the answers

What is the purpose of the third check in a backtracking algorithm for optimization problems?

To compute the value of each solution found and update the current best Signup and view all the answers

What represents the local constraints in a backtracking algorithm?

The conditions that a partial candidate must satisfy to be extended Signup and view all the answers

In the context of backtracking algorithms, what do 'candidates' and 'extensions' represent?

Candidates are partial solutions, and extensions are the steps to complete them Signup and view all the answers

What is the primary purpose of backtracking?

To generate candidates incrementally and prune the search space Signup and view all the answers

Which condition is necessary for backtracking to be applicable?

Each solution (and candidate) is a collection of items Signup and view all the answers

What is the primary advantage of backtracking over exhaustive search?

It is more efficient because it can prune the search space substantially Signup and view all the answers

What is the primary difference between global constraints and local constraints in backtracking?

Global constraints apply to the entire solution, while local constraints apply to individual items Signup and view all the answers

In the context of backtracking, what is a partial candidate?

An incomplete candidate that satisfies all constraints so far Signup and view all the answers

What is the typical approach used by backtracking algorithms to explore the search space?

Depth-first search Signup and view all the answers

What is the primary advantage of backtracking over exhaustive search?

Backtracking can generate fewer candidates by pruning the search space Signup and view all the answers

What is the primary difference between global constraints and local constraints in backtracking?

Global constraints apply to the entire candidate solution, while local constraints apply to individual items in the candidate Signup and view all the answers

When extending a candidate in backtracking, what does the algorithm do if it cannot lead to a solution or a better solution?

The algorithm backtracks to the previous step and explores a different extension Signup and view all the answers

How can the search space be further pruned for subset problems in a backtracking algorithm?

By only considering unique items when extending the candidate Signup and view all the answers

What is the purpose of the first check in a backtracking algorithm?

To determine if the current candidate is a complete solution Signup and view all the answers

Which technique only generates a fraction of all candidates, making it more efficient than exhaustive search?

Backtracking Signup and view all the answers

What is the primary advantage of backtracking over exhaustive search?

Backtracking explores the search space more efficiently by pruning branches that do not satisfy the local constraints. Signup and view all the answers

What do the 'local constraints' represent in the context of a backtracking algorithm?

The constraints that apply to the current candidate solution, regardless of the rest of the solution. Signup and view all the answers

What is the purpose of the first check in a backtracking algorithm?

To check if extending the current candidate solution with a chosen item is worth pursuing, based on the local constraints. Signup and view all the answers

How can the search space be further pruned for subset problems in a backtracking algorithm?

By sorting the items in advance so that when one can't extend a candidate, neither can any of the subsequent items. Signup and view all the answers

What is the primary difference between global constraints and local constraints in a backtracking algorithm?

Global constraints apply to the entire candidate solution, while local constraints only apply to the current item being considered. Signup and view all the answers

What is the key ingredient that turns an exhaustive traversal into a backtracking algorithm?

The check to see if it's worth extending the current candidate solution with a chosen item, based on the local constraints. Signup and view all the answers

What is a key advantage of backtracking over exhaustive search?

Prunes vast parts of the search space Signup and view all the answers

In backtracking, where are global constraints checked?

On all candidate sequences Signup and view all the answers

What differentiates backtracking from brute-force search in terms of candidate generation?

Backtracking prunes candidate generation Signup and view all the answers

How does backtracking handle local constraints during candidate generation?

Local constraints are checked for each extension Signup and view all the answers

Why is backtracking more efficient than generating all permutations?

It prunes vast parts of the search space Signup and view all the answers

What is a distinguishing feature of backtracking compared to brute-force search regarding the search space?

'Prunes parts of the search space' Signup and view all the answers

TMA 01 Part 2: Collections, Algorithms, and Coding Style

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Questions and Answers

What is the common way to represent a graph in computer science?

Which graph traversal algorithm is used to visit all reachable nodes from a given starting node?

What is the time complexity of Breadth-First Search (BFS) on a graph with $V$ vertices and $E$ edges?

Which graph data structure is used to represent a tree?

What is the purpose of Kruskal's algorithm in graph theory?

What topic does the section 'Undirected graph components' in the text fall under?

Which section in the text mentions 'Minimum spanning tree'?

In which part of the text would you expect to find information about 'Topological sort'?

Which part of the text discusses 'Jousting' and 'Dot product'?

'Longest common subsequence' and 'Knapsack' are topics found in which part of the text?

'Borrow a book' and 'Levenshtein distance' are mentioned in which part of the text?

What is the purpose of the adjacency matrix representation of a graph?

Which graph traversal algorithm is used to visit all reachable nodes from a given starting node?

What is the purpose of Topological Sort in graph theory?

What is the purpose of the adjacency list representation of a graph?

What is the purpose of Kruskal's algorithm in graph theory?

What is the purpose of the edge list representation of a graph?

What is the most common way to represent a graph in computer science?

Which graph traversal algorithm is used to visit all reachable nodes from a given starting node?

What is the time complexity of Breadth-First Search (BFS) on a graph with $V$ vertices and $E$ edges?

Which graph data structure is used to represent a tree?

What is the purpose of Kruskal's algorithm in graph theory?

What is the purpose of Prim's algorithm in graph theory?

What is the purpose of Dijkstra's algorithm in graph theory?

What is the purpose of Topological Sort in graph theory?

What is the purpose of the Strongly Connected Components (SCC) algorithm in graph theory?

What is the purpose of the Tarjan's algorithm in graph theory?

What starts with an empty candidate sequence or set and extends it one item at a time?

Which technique only generates a fraction of all candidates making it more efficient than exhaustive search?

In backtracking, what core traversal is used for generating permutations and subsets?

When extending a candidate in backtracking, what does the algorithm do if it cannot lead to a solution or a better solution?

At the core of backtracking is a recursive pre-order traversal of what structure?

Which problems in M269 are solved using backtracking on sequences of non-duplicate items or subsets of items?

What is the purpose of the first check in a backtracking algorithm?

What is the purpose of the second check in a backtracking algorithm?

How can the search space be further pruned for subset problems in a backtracking algorithm?

What is the purpose of the third check in a backtracking algorithm for optimization problems?

What represents the local constraints in a backtracking algorithm?

In the context of backtracking algorithms, what do 'candidates' and 'extensions' represent?

What is the primary purpose of backtracking?

Which condition is necessary for backtracking to be applicable?

What is the primary advantage of backtracking over exhaustive search?

What is the primary difference between global constraints and local constraints in backtracking?

In the context of backtracking, what is a partial candidate?

What is the typical approach used by backtracking algorithms to explore the search space?

What is the primary advantage of backtracking over exhaustive search?

What is the primary difference between global constraints and local constraints in backtracking?

When extending a candidate in backtracking, what does the algorithm do if it cannot lead to a solution or a better solution?

How can the search space be further pruned for subset problems in a backtracking algorithm?

What is the purpose of the first check in a backtracking algorithm?

Which technique only generates a fraction of all candidates, making it more efficient than exhaustive search?

What is the primary advantage of backtracking over exhaustive search?

What do the 'local constraints' represent in the context of a backtracking algorithm?

What is the purpose of the first check in a backtracking algorithm?

How can the search space be further pruned for subset problems in a backtracking algorithm?

What is the primary difference between global constraints and local constraints in a backtracking algorithm?

What is the key ingredient that turns an exhaustive traversal into a backtracking algorithm?

What is a key advantage of backtracking over exhaustive search?

In backtracking, where are global constraints checked?

What differentiates backtracking from brute-force search in terms of candidate generation?

How does backtracking handle local constraints during candidate generation?

Why is backtracking more efficient than generating all permutations?

What is a distinguishing feature of backtracking compared to brute-force search regarding the search space?

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