2412 - Minimum Money Required Before Transactions.

Hard

You are given a 0-indexed 2D integer array transactions, where <code>transactionsi = cost_i, cashback_i</code>.

The array describes transactions, where each transaction must be completed exactly once in some order. At any given moment, you have a certain amount of money. In order to complete transaction i, <code>money >= cost_i</code> must hold true. After performing a transaction, money becomes <code>money - cost_i + cashback_i</code>.

Return the minimum amount of money required before any transaction so that all of the transactions can be completed regardless of the order of the transactions.

Example 1:

Input: transactions = [2,1,5,0,4,2]

Output: 10

Explanation:

Starting with money = 10, the transactions can be performed in any order.

It can be shown that starting with money < 10 will fail to complete all transactions in some order.

Example 2:

Input: transactions = [3,0,0,3]

Output: 3

Explanation:

• If transactions are in the order [3,0,0,3], the minimum money required to complete the transactions is 3.

• If transactions are in the order [0,3,3,0], the minimum money required to complete the transactions is 0.

Thus, starting with money = 3, the transactions can be performed in any order.

Constraints:

• <code>1 <= transactions.length <= 10⁵</code>

• transactions[i].length == 2

• <code>0 <= cost_i, cashback_i<= 10⁹</code>