Several families are planning a shared car trip on scenic drives in New Hampshire's White Mountains. To minimize the possibility of any quarrels, they want to assign individuals to cars so that no two members of a family are in the same car. Explain how to formulate this problem as a network flow problem.

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Explanation:

Build a spring, sink, vertices, and vertices for each car for a household. Every unit in the stream is a human. Attach the source from each vertical of a family with such a capacity line equivalent to the family size; this sets the number of members in each household. Attach every car vertices to the sink with the edge of the car's passenger belt; this assures the correct number of people for every vehicle. Connecting every vertex in your household to any vertex in your vehicle with a capacity 1 border guarantees that one family member joins a single car. The link between both the acceptable allocation of people to vehicles as well as the maximum flow inside the graph seems clear to notice.

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