# 1831. Maximum Transaction Each Day

<https://leetcode.com/problems/maximum-transaction-each-day>

## Description

Table: `Transactions`

```

+----------------+----------+
| Column Name    | Type     |
+----------------+----------+
| transaction\_id | int      |
| day            | datetime |
| amount         | int      |
+----------------+----------+
transaction\_id is the primary key for this table.
Each row contains information about one transaction.
```

Write an SQL query to report the IDs of the transactions with the **maximum** `amount` on their respective day. If in one day there are multiple such transactions, return all of them.

Return the result table **in ascending order by** `transaction_id`.

The query result format is in the following example:

```

Transactions table:
+----------------+--------------------+--------+
| transaction\_id | day                | amount |
+----------------+--------------------+--------+
| 8              | 2021-4-3 15:57:28  | 57     |
| 9              | 2021-4-28 08:47:25 | 21     |
| 1              | 2021-4-29 13:28:30 | 58     |
| 5              | 2021-4-28 16:39:59 | 40     |
| 6              | 2021-4-29 23:39:28 | 58     |
+----------------+--------------------+--------+

Result table:
+----------------+
| transaction\_id |
+----------------+
| 1              |
| 5              |
| 6              |
| 8              |
+----------------+
"2021-4-3"  --> We have one transaction with ID 8, so we add 8 to the result table.
"2021-4-28" --> We have two transactions with IDs 5 and 9. The transaction with ID 5 has an amount of 40, while the transaction with ID 9 has an amount of 21. We only include the transaction with ID 5 as it has the maximum amount this day.
"2021-4-29" --> We have two transactions with IDs 1 and 6. Both transactions have the same amount of 58, so we include both in the result table.
We order the result table by transaction\_id after collecting these IDs.
```

**Follow up:** Could you solve it without using the `MAX()` function?

## ac

```java
```