2412. Minimum Money Required Before Transactions
Description
You are given a 0-indexed 2D integer array transactions
, where transactions[i] = [costi, cashbacki]
.
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 >= costi
must hold true. After performing a transaction, money
becomes money - costi + cashbacki
.
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:
1 <= transactions.length <= 105
transactions[i].length == 2
0 <= costi, cashbacki <= 109
Solutions
Solution 1: Greedy
First, we accumulate all the negative profits, denoted as $s$. Then we enumerate each transaction as the last transaction. If transactions[i].x > transactions[i].y
, it means the current transaction is losing money, and this transaction has been calculated when we previously accumulated negative profits, so we update the answer with s + transactions[i].y
; otherwise, we update the answer with s + transactions[i].x
.
The time complexity is $O(n)$, where $n$ is the number of transactions. The space complexity is $O(1)$.
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