Dijkstra's Algorithm and Single Source Shortest Paths

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What is a key characteristic of the greedy technique in algorithm design?

Making locally optimal choices at each step (correct)

Always leading to a suboptimal solution

Allowing changes to previous choices

Considering all possible future steps

What is the primary goal of the prove optimality step in the greedy technique?

To determine the edge weights in a graph

To demonstrate that locally optimal choices lead to the best possible outcome (correct)

To identify the minimum spanning tree

To find the shortest path in a graph

Which algorithm is used to solve the single-source shortest-paths problem in the general case with negative edge weights?

Prim's Algorithm

Dijkstra's Algorithm

Topological Sort

Bellman-Ford Algorithm (correct)

What is the purpose of the iterative process in the greedy technique?

To apply the chosen strategy iteratively, making locally optimal choices Signup and view all the answers

Which of the following is NOT a characteristic of the greedy technique?

Allowing changes to previous choices Signup and view all the answers

What is the primary focus of the strategy identification step in the greedy technique?

Understanding the problem and determining a strategy Signup and view all the answers

What is the purpose of Prim's Algorithm?

To find the minimum cost spanning tree Signup and view all the answers

What is the result of applying Huffman coding to a set of symbols?

A more efficient encoding scheme Signup and view all the answers

What is the running time of the implementation of Prim's Algorithm?

Polynomial in the number of nodes Signup and view all the answers

What is the main difference between Prim's Algorithm and Kruskal's Algorithm?

The method of computing the minimum spanning tree Signup and view all the answers

What is the purpose of Step 1 in Huffman's Algorithm?

To create a separate tree for each symbol in the alphabet Signup and view all the answers

What is the goal of finding the minimum spanning tree in a graph?

To minimize the total weight of the tree Signup and view all the answers

What is a requirement for Dijkstra's algorithm to solve the single-source shortest-paths problem?

All edge weights are nonnegative Signup and view all the answers

What is the primary function of the EXTRACT_MIN operation in Dijkstra's algorithm?

To select the vertex with the minimum shortest-path estimate Signup and view all the answers

What is the definition of a spanning tree in an undirected connected graph?

A connected acyclic subgraph that contains all vertices Signup and view all the answers

What is the purpose of the set S in Dijkstra's algorithm?

To store the vertices whose final shortest-path weights have been determined Signup and view all the answers

What is the purpose of the priority queue Q in Dijkstra's algorithm?

To store the vertices, keyed by their d values Signup and view all the answers

What is the difference between Dijkstra's algorithm and Prim's algorithm?

Dijkstra's algorithm finds the shortest path, while Prim's algorithm finds the minimum spanning tree Signup and view all the answers

Dijkstra's Algorithm and Single Source Shortest Paths

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