#2412

Hard

auto_awesomeGreedy choice plus invariant validation

LeetCode Problem Workspace

Minimum Money Required Before Transactions

Find the minimum money required to complete all transactions in any order while considering cost and cashback.

Problem Statement

You are given an array of transactions where each transaction consists of a cost and a cashback. In order to complete a transaction, you need money greater than or equal to the cost. After completing a transaction, your money decreases by the cost but increases by the cashback. The task is to determine the minimum starting money needed to perform all transactions in any order.

The order of transactions doesn't matter, but you must ensure that you have enough money to complete each one. The goal is to minimize the initial amount of money, taking into account that some transactions might provide cashback greater than or equal to the cost, while others provide less.

Examples

Example 1

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

Output: 10

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

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

Solution Approach

Categorizing Transactions

Group the transactions into two categories: those with a cashback greater than or equal to the cost, and those with less. Transactions in the first group can be executed first, as they don't require additional upfront money, while those in the second group need to be handled later.

Greedy Approach for Minimizing Money

The greedy approach ensures that for transactions where cashback is less than the cost, you track the maximum deficit. The total starting money will need to account for both the maximum deficit and any leftover money after completing the first category of transactions.

Handling the Edge Case

In cases where all transactions provide cashback equal to or greater than the cost, the required starting money is simply the cost of the most expensive transaction. If cashback is always less than the cost, ensure you have enough starting money to cover the total deficit before completing any transaction.

Complexity Analysis

Metric	Value
Time	Depends on the final approach
Space	Depends on the final approach

Time complexity is O(n), where n is the number of transactions, as we iterate through the list once to categorize and calculate the required money. Space complexity is O(1) because we only store a few variables to track the maximum deficit and the total cost of transactions with cashback greater than or equal to the cost.

What Interviewers Usually Probe

Candidate demonstrates understanding of greedy algorithms and how to apply them to financial transaction problems.
Candidate is able to identify the need for categorizing transactions based on cashback and cost.
Candidate can efficiently handle the two categories of transactions and track the maximum deficit to calculate the required money.

Common Pitfalls or Variants

Common pitfalls

Not properly categorizing transactions based on cashback vs cost, leading to incorrect results.
Failing to track the maximum deficit across transactions where cashback is less than cost.
Overcomplicating the problem by trying to consider transaction order beyond the greedy approach.

Follow-up variants

Consider how the problem would change if there were different transaction types with additional constraints.
How would the solution change if you were allowed to reorder the transactions yourself before processing?
What if the problem involved adding more types of transaction attributes, such as interest rates or transaction fees?

FAQ

What is the main strategy to solve the Minimum Money Required Before Transactions problem?

The main strategy is using a greedy approach by categorizing transactions based on whether their cashback is greater than or equal to their cost, then tracking the maximum deficit.

How does the greedy approach help in this problem?

The greedy approach ensures that transactions with cashback equal to or greater than their cost are handled first, reducing the initial money required, while tracking deficits from transactions with lower cashback.

What are common mistakes when solving this problem?

Common mistakes include not properly categorizing transactions or failing to track the maximum deficit when cashback is less than the cost.

How do I optimize for the minimum starting money?

By categorizing transactions and calculating the total deficit from the group where cashback is less than the cost, you ensure the minimum required starting money is reached.

What is the time complexity of the solution?

The time complexity is O(n), where n is the number of transactions, since we iterate through the list only once.

terminal

Solution

Solution 1: Greedy

First, we accumulate all negative profits, denoted as $s$. Then, we enumerate each transaction $\text{transactions}[i] = [a, b]$ as the last transaction. If $a > b$, it means the current transaction is a loss, and this transaction has already been included when we accumulated the negative profits earlier. Therefore, we update the answer with $s + b$. Otherwise, we update the answer with $s + a$.

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class Solution:
    def minimumMoney(self, transactions: List[List[int]]) -> int:
        s = sum(max(0, a - b) for a, b in transactions)
        ans = 0
        for a, b in transactions:
            if a > b:
                ans = max(ans, s + b)
            else:
                ans = max(ans, s + a)
        return ans

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