Problem Description
You are given a 0-indexed 2D integer array transactions, where transactions[i] = [cost_i, cashback_i]. 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, money >= cost_i must hold true. After performing a transaction, money becomes money - cost_i + cashback_i. 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.
Key Insights
- Each transaction requires a certain cost and yields a cashback.
- The challenge is to determine the minimum starting money required such that all transactions can be completed in any order.
- The effective cost of each transaction can be defined as the difference between cost and cashback: effective_cost_i = cost_i - cashback_i.
- The maximum effective cost across all transactions indicates the minimum starting money needed.
Space and Time Complexity
Time Complexity: O(n)
Space Complexity: O(1)
Solution
To solve the problem, we iterate through the list of transactions to calculate the effective cost for each transaction. The effective cost is defined as the cost required to complete the transaction minus the cashback received. We need to track the maximum effective cost encountered during this iteration. The minimum money required before any transaction is the sum of all costs and the maximum effective cost. This ensures that no matter the order of transactions, we will always have enough money to complete them.