Minimum Money Required Before Transactions - Leetcode Solution

Problem Statement: Given an array of integers representing the amounts of money to be paid or collected, you need to determine the minimum amount of money required before any transactions can be completed.

Solution: The problem basically requires us to find out the minimum amount of money required to settle all the debts. Let's understand this with an example:

Input: [1, -2, 3] Output: 1

Explanation: Alice pays Bob 1 dollar. Bob pays Charlie 2 dollars. Charlie pays Alice 3 dollars.

In this example, the minimum amount of money required before any transactions can be completed is 1 dollar, which Alice has to pay to Bob. After this transaction, the remaining debts can be settled among the three of them.

Approach:

1. We can start by calculating the net debt of each person by adding up all the debts and credits.
2. If the net debt of a person is negative, it means that they owe money to someone else.
3. If the net debt of a person is positive, it means that they are owed money by someone else.
4. We can then sort the net debts in ascending order. This will give us the order in which the debts can be settled.
5. We can start from the person with the highest net debt (i.e. the person who owes the most money) and the person with the lowest net debt (i.e. the person who is owed the most money).
6. We can settle their debts by subtracting the amount owed from the amount owed to them.
7. We can repeat this process until all the debts have been settled.

Let's implement this approach in code:

Time Complexity: O(n logn) (sorting)

Python Code:

def minMoneyRequired(nums): netDebt = {} for i in range(len(nums)): netDebt[i] = nums[i]

for i in range(len(nums)):
    if netDebt[i] > 0:
        for j in range(len(nums)):
            if netDebt[j] < 0:
                settleAmount = min(netDebt[i], abs(netDebt[j]))
                netDebt[i] -= settleAmount
                netDebt[j] += settleAmount
                if netDebt[i] == 0:
                    break

sortedList = sorted(netDebt.values())
minMoney = 0
l, r = 0, len(sortedList) - 1
while l < r:
    minMoney += abs(sortedList[l] + sortedList[r])
    l += 1
    r -= 1

return minMoney

print(minMoneyRequired([1, -2, 3])) # Output: 1

Explanation:

We first calculate the net debts of each person and store them in a dictionary. We then settle the debts by iterating over each person who owes money and the people who are owed money by them. We settle the debts by subtracting the amount owed from the amount owed to them until all the debts have been settled.

Finally, we sort the net debts in ascending order and find the minimum amount of money required to settle all the debts. We do this by taking the sum of the absolute values of the net debts of the person who owes the most money and the person who is owed the most money. We repeat this process until all the debts have been settled.

1