这个怎么样？

select c.id_cust
from (select o.id_cust, year(buy_date) as yyyy, month(buy_date) as mm,
             row_number() over (partition by o.id_cust) as month_counter
      from orders o
      where buy_date >= date_format(current_date - interval 3 month, '%Y-%m-%d') and
            buy_date < date_format(current_date, '%Y-%m-%d')
      group by id_cust, yyyy, mm
     ) c
where month_counter = 3;

这只会过滤到你关心的三个月。然后它按年份和月份进行聚合，只返回第三行。
实际上，这更容易表达为：

select o.id_cust
from orders o
where buy_date >= date_format(current_date - interval 3 month, '%Y-%m-%d') and
      buy_date < date_format(current_date, '%Y-%m-%d')
group by o.id_cust
having count(distinct year(buy_date), month(buy_date)) = 3;

我会用戈登的第二个问题。但是如果您的代码正常工作（作为练习），您可以通过在上创建索引来优化执行时间 (buy_date, id_cust) 继续 (id_cust, buy_date) . 第一个用于where子句，第二个用于on子句。
使用此架构

CREATE TABLE orders (
  `ID` INTEGER primary key,
  `id_cust` INTEGER,
  `buy_date` VARCHAR(10)
);

查询的结果是

| id  | select_type | table | partitions | type | possible_keys | key | key_len | ref | rows | filtered | Extra                                              |
| --- | ----------- | ----- | ---------- | ---- | ------------- | --- | ------- | --- | ---- | -------- | -------------------------------------------------- |
| 1   | SIMPLE      | g1    |            | ALL  |               |     |         |     | 7    | 14.29    | Using where; Using temporary; Using filesort       |
| 1   | SIMPLE      | g2    |            | ALL  |               |     |         |     | 7    | 14.29    | Using where; Using join buffer (Block Nested Loop) |
| 1   | SIMPLE      | g3    |            | ALL  |               |     |         |     | 7    | 14.29    | Using where; Using join buffer (Block Nested Loop) |

没有使用键，“块嵌套循环”听起来很糟糕。
添加索引后

ALTER TABLE orders ADD INDEX (buy_date, id_cust);
ALTER TABLE orders ADD INDEX (id_cust, buy_date);

| id  | select_type | table | partitions | type  | possible_keys    | key     | key_len | ref             | rows | filtered | Extra                    |
| --- | ----------- | ----- | ---------- | ----- | ---------------- | ------- | ------- | --------------- | ---- | -------- | ------------------------ |
| 1   | SIMPLE      | g1    |            | index | buy_date,id_cust | id_cust | 48      |                 | 7    | 14.29    | Using where; Using index |
| 1   | SIMPLE      | g2    |            | ref   | buy_date,id_cust | id_cust | 5       | test.g1.id_cust | 2    | 14.29    | Using where; Using index |
| 1   | SIMPLE      | g3    |            | ref   | buy_date,id_cust | id_cust | 5       | test.g1.id_cust | 2    | 14.29    | Using where; Using index |

小提琴
现在看起来好多了，尽管它不再使用我的第一个索引（可能是由于groupby）。
然后我将查询简化为：

SELECT DISTINCT g1.id_cust
FROM orders g1 
    JOIN orders g2 ON g2.id_cust = g1.id_cust
    JOIN orders g3 ON g3.id_cust = g1.id_cust
    -- AND g3.id_cust  = g2.id_cust -- redundant condition
WHERE g1.buy_date >= DATE_FORMAT(NOW() - INTERVAL 3 MONTH, '%Y-%m-01')
  AND g1.buy_date <  DATE_FORMAT(NOW() - INTERVAL 2 MONTH, '%Y-%m-01')
  AND g2.buy_date >= DATE_FORMAT(NOW() - INTERVAL 2 MONTH, '%Y-%m-01')
  AND g2.buy_date <  DATE_FORMAT(NOW() - INTERVAL 1 MONTH, '%Y-%m-01')
  AND g3.buy_date >= DATE_FORMAT(NOW() - INTERVAL 1 MONTH, '%Y-%m-01')
  AND g3.buy_date <  DATE_FORMAT(NOW() - INTERVAL 0 MONTH, '%Y-%m-01')
-- GROUP BY g1.id_cust -- You can use DISTINCT instead

小提琴