Practice Problem Motivation (2.1) - Minimum Cost Spanning Trees - Design & Analysis of Algorithms - Vol 2

Practice: Problem Motivation

Lesson 2.1Minimum Cost Spanning Trees

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8 questions

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6 sample questions

Question 1.
Define a spanning tree.
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Look for the main properties of trees.
Question 2.
Why do we need to minimize costs in Minimum Cost Spanning Trees?
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Think about government budgets after disasters.
3Question 3.
What is a Minimum Cost Spanning Tree?
- A tree that connects all vertices without loops
- The most expensive tree
- Any tree in a graph
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Recall the definition we discussed.
4Question 4.
True or False: A spanning tree can have cycles.
- True
- False
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Think about the properties of trees.
Question 5.
Given a tree with six vertices connected with edges weighted as follows: A-B (10), A-C (15), B-D (5), B-E (10), and C-F (20). Calculate the minimum cost spanning tree.
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Start with the smallest weights but remember to maintain connectivity.
Question 6.
Design a spanning tree connecting five locations in a park with the following distances (weights): A-B (2), A-C (6), B-C (3), B-D (9), C-E (5). What's the least costly way to connect all?
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Work systematically from the lowest weights, ensuring no cycles.

4 more questions in this section. Enroll free to practise them all.