·With pilot
meaning of the title
A group of pilots, a group of co-pilots. Some pilots can fly with the co-pilot. Ask how many planes can fly at most.
answer
Bipartite graph maximum matching model.
The super source goes to all the sides with a capacity of 1 for the pilot, and all the co-pilots go to the side with a capacity of 1 for the super sink. The pilots and co-pilots who can fly together are connected to a side with a capacity of 1. Running the maximum flow is the maximum matching of the bipartite graph.
· Space flight program
meaning of the title
m experiments, n instruments. Each experiment requires several instruments. There is a cost to activate each instrument, and each experiment has a value. Ask which instruments are most profitable to activate.
answer
The maximum weight closed subgraph problem. It can be transformed into a minimum cut problem.
The super source is connected to all experiments to the side whose capacity is the profit, and the instrument is connected to the super sink to the side whose capacity is the cost.
The maximum weight closed graph problem can be transformed into a minimum cut problem, and then solved by maximum flow.