10.6 - Residual Graph
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Practice Questions
Test your understanding with targeted questions
What is a residual graph?
💡 Hint: Think about what happens to capacities after some flow has been sent.
What principle governs flow at intermediate nodes?
💡 Hint: Consider nodes as junctions where flow enters and exits.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What does a residual graph in network flow represent?
💡 Hint: Think about capacity adjustments.
True or False: The flow into an intermediate node can be greater than the flow out.
💡 Hint: Refer to the flow conservation principle.
3 more questions available
Challenge Problems
Push your limits with advanced challenges
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.
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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