Practice Residual Graph - 10.6 | 10. Network Flows | Design & Analysis of Algorithms - Vol 3
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Residual Graph

10.6 - Residual Graph

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Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What is a residual graph?

💡 Hint: Think about what happens to capacities after some flow has been sent.

Question 2 Easy

What principle governs flow at intermediate nodes?

💡 Hint: Consider nodes as junctions where flow enters and exits.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What does a residual graph in network flow represent?

Available edges for flow
Time complexity of the flow calculation
Remaining capacities and reverse paths

💡 Hint: Think about capacity adjustments.

Question 2

True or False: The flow into an intermediate node can be greater than the flow out.

True
False

💡 Hint: Refer to the flow conservation principle.

3 more questions available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Consider a directed graph with nodes A, B, C, and D. The following edges exist: A to B (capacity 5), A to C (capacity 10), B to C (capacity 15), and C to D (capacity 10). Define the residual graph after a flow of 8 from A to D. Calculate remaining capacities for each edge.

💡 Hint: Make sure to visualize the flow and adjustments.

Challenge 2 Hard

Using a real-world scenario of a delivery service with specified routes and capacities, design a model that applies the Ford-Fulkerson algorithm to identify the best path with maximum flow from supply to delivery point. Demonstrate how you would adjust the residual graph after each iteration.

💡 Hint: Focus on creating a visual representation of how capacities change.

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