I have 9 nodes and 20 transceivers. How can I have all possible distributions of transceivers between nodes ?

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Mahmoud Ahmed
Mahmoud Ahmed 2017-5-31
回答： Walter Roberson 2017-5-31
I have 9 nodes and 26 transceivers. How can I have all possible distributions of transceivers between nodes ? Hint: The maximum number of transceivers at any node = 3 The minimum number of transceivers at any node = 1

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Walter Roberson
Walter Roberson 2017-5-31
This is the Integer Partition Problem.
Because you have a minimum of one transceiver at any node, and 9 nodes, create 9 bins with initial value 1, and reduce the total 20 by 9*1 to get 11. You now have the problem of integer partition of 11 elements across 9 bins with a maximum of 2 to be added to any one bin.
There are various ways to program that partitioning. There are some suitable File Exchange Contributions, including https://www.mathworks.com/matlabcentral/fileexchange/12009-partitions-of-an-integer . There are other ways that might perhaps be less efficient but are easy to program, including making use of dec2base()

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