This Kata is a bit more optimized version of minimum account balancing problem.

You are given a list of transactions between people in the form of ( payer, payee, amount ) .

This means payer pays amount to payee, so that payee owes amount to payer.

Return the list of minimum number of transactions, with minimum amount of total money transferred, so that everyone pays back what they owed. Each transaction should be in the form of ( payer, payee, amount ) .

Example #1

l = [(3, 0, 7), (3, 1, 5), (3, 2, 1), (4, 2, 7)]
min_transaction(l) = [(2, 3, 8), (0, 4, 7), (1, 3, 5)]

l = [(3, 0, 7), (3, 1, 5), (3, 2, 1), (4, 2, 7)]
minTransaction l = [(2, 3, 8), (0, 4, 7), (1, 3, 5)]

l = [[3, 0, 7], [3, 1, 5], [3, 2, 1], [4, 2, 7]]
minTtransaction(l) = [[2, 3, 8], [0, 4, 7], [1, 3, 5]]

Input/Output means

• Person 0 took 7, so should give 7 in total
• Person 1 took 5, so should give 5 in total
• Person 2 took 8, so should give 8 in total
• Person 3 gave 13, so should get 13 in total
• Person 4 gave 7, so should get 7 in total

We can balance these transactions with the following 3 transactions:

• Person 2 pays 8 to person 3
• Person 1 pays 5 to person 3
• Person 0 pays 7 to person 4

Example #2

l = [(4, 1, 7), (4, 8, 7), (1, 8, 22), (8, 2, 24), (1, 8, 21), (8, 1, 8)]
Possible solution    -> [(2, 1, 24), (8, 1, 4), (8, 4, 14)]
Alternative solution -> [(2, 4, 14), (2, 1, 10), (8, 1, 18)]

l = [(4, 1, 7), (4, 8, 7), (1, 8, 22), (8, 2, 24), (1, 8, 21), (8, 1, 8)]
Possible solution    -> [(2, 1, 24), (8, 1, 4), (8, 4, 14)]
Alternative solution -> [(2, 4, 14), (2, 1, 10), (8, 1, 18)]

l = [[4, 1, 7], [4, 8, 7], [1, 8, 22], [8, 2, 24], [1, 8, 21], [8, 1, 8]]
Possible solution    -> [[2, 1, 24], [8, 1, 4], [8, 4, 14]]
Alternative solution -> [[2, 4, 14], [2, 1, 10], [8, 1, 18]]

Constraints

• Number of people will not exceed 8
• Transaction list can contain up to 100 transactions
• Transaction amount cannot be negative
• In the resulting list, some people can owe money to someone that s/he didnt take money directly from. That is fine; we are trying to minimize the number oftransactions and ( then ) the minimum amount of money that should be transferred

If there is no one that should pay anything just return empty list.

There can be multiple solutions. It is enough to return one of them.
Your solution will be tested in terms of correct minimum transaction count, correct minimum transaction amount, and people paying or receiving exactly what they owe or are owed.
Transaction order is not important.