What algorithm to use to determine minimum number of actions required to get the system to “Zero” state?

Question

This is kind of more generic question, isn\'t language-specific. More about idea and algorithm to use.

The system is as follows:

It registers small loans bet

Answer 1

You should be able to solve this in O(n) by first determining how much each person owes and is owed. Transfer the debts of anyone who owes less than he is owed to his debtors (thus turning that person into an end point). Repeat until you can't transfer any more debts.