System Engineer

There are ‘N’ friends who have borrowed money from one another. Now, they wanted to settle their debts by giving or taking some money among themselves.

Your task is to design a series of transactions, such that the total cash flow among them is minimized.

For example:

Let there be three friends ‘A’, ‘B’, ‘C’  with debts-

• A has to pay $ 2000 to B.
• A has to pay $ 1000 to C.
• B has to pay $ 3000 to C.
• C has to pay $ 1000 to A.

Then their minimized cash flow system will be-

• A will finally pay $ 2000 to C.
• B will finally pay $ 1000 to C.

Thus, the total cash flow among them will be $ 3000. 

You have been given an integer array/list(ARR) of size 'N'. It only contains 0s, 1s and 2s. Write a solution to sort this array/list.

Note :

Try to solve the problem in 'Single Scan'. ' Single Scan' refers to iterating over the array/list just once or to put it in other words, you will be visiting each element in the array/list just once.