Practice Introduction To The Problem Domain (3.1) - Spanning Trees: Prim’s Algorithm

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10 questions

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6 sample questions

Question 1.
What is a spanning tree?
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Think about how trees connect branches without forming loops.
Question 2.
How many edges does a spanning tree have?
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Consider a scenario with three vertices.
3Question 3.
What does Prim's algorithm aim to find in a graph?
- Shortest path
- Minimum spanning tree
- Maximum flow
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Think about the trees in graph theory.
4Question 4.
Prim's algorithm is a type of which algorithm?
- Greedy
- Dynamic Programming
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Recall the definitions of different algorithm types.
Question 5.
Given a connected graph with vertices A, B, C, D, and edges with weights, determine the minimum spanning tree using Prim's algorithm. Provide a visual representation.
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List out edges by weight to start.
Question 6.
Prove that Prim's algorithm will always yield an optimal solution. Reference the minimum separator lemma in your proof.
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Explore the implications of making improper edge selections.

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