题目：

Table: Prices

+---------------+---------+
| Column Name | Type |
+---------------+---------+
| product_id | int |
| start_date | date |
| end_date | date |
| price | int |
+---------------+---------+
(product_id，start_date，end_date) 是 Prices 表的主键。
Prices 表的每一行表示的是某个产品在一段时期内的价格。
每个产品的对应时间段是不会重叠的，这也意味着同一个产品的价格时段不会出现交叉。

Table: UnitsSold

+---------------+---------+
| Column Name | Type |
+---------------+---------+
| product_id | int |
| purchase_date | date |
| units | int |
+---------------+---------+
UnitsSold 表没有主键，它可能包含重复项。
UnitsSold 表的每一行表示的是每种产品的出售日期，单位和产品 id。

编写SQL查询以查找每种产品的平均售价。
average_price 应该四舍五入到小数点后两位。
查询结果格式如下例所示：

Prices table:
+------------+------------+------------+--------+
| product_id | start_date | end_date | price |
+------------+------------+------------+--------+
| 1 | 2019-02-17 | 2019-02-28 | 5 |
| 1 | 2019-03-01 | 2019-03-22 | 20 |
| 2 | 2019-02-01 | 2019-02-20 | 15 |
| 2 | 2019-02-21 | 2019-03-31 | 30 |
+------------+------------+------------+--------+

UnitsSold table:
+------------+---------------+-------+
| product_id | purchase_date | units |
+------------+---------------+-------+
| 1 | 2019-02-25 | 100 |
| 1 | 2019-03-01 | 15 |
| 2 | 2019-02-10 | 200 |
| 2 | 2019-03-22 | 30 |
+------------+---------------+-------+

Result table:
+------------+---------------+
| product_id | average_price |
+------------+---------------+
| 1 | 6.96 |
| 2 | 16.96 |
+------------+---------------+
平均售价 = 产品总价 / 销售的产品数量。
产品 1 的平均售价 = ((100 * 5)+(15 * 20) )/ 115 = 6.96
产品 2 的平均售价 = ((200 * 15)+(30 * 30) )/ 230 = 16.96

mysql:

SELECT
    product_id,
    Round(SUM(sales) / SUM(units), 2) AS average_price
FROM (
    SELECT
        Prices.product_id AS product_id,
        Prices.price * UnitsSold.units AS sales,
        UnitsSold.units AS units
    FROM Prices 
    JOIN UnitsSold ON Prices.product_id = UnitsSold.product_id
    WHERE UnitsSold.purchase_date BETWEEN Prices.start_date AND Prices.end_date
) T
GROUP BY product_id