{ "data": { "question": { "questionId": "1928", "questionFrontendId": "1801", "categoryTitle": "Algorithms", "boundTopicId": 665732, "title": "Number of Orders in the Backlog", "titleSlug": "number-of-orders-in-the-backlog", "content": "

You are given a 2D integer array orders, where each orders[i] = [pricei, amounti, orderTypei] denotes that amounti orders have been placed of type orderTypei at the price pricei. The orderTypei is:

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Note that orders[i] represents a batch of amounti independent orders with the same price and order type. All orders represented by orders[i] will be placed before all orders represented by orders[i+1] for all valid i.

\r\n\r\n

There is a backlog that consists of orders that have not been executed. The backlog is initially empty. When an order is placed, the following happens:

\r\n\r\n\r\n\r\n

Return the total amount of orders in the backlog after placing all the orders from the input. Since this number can be large, return it modulo 109 + 7.

\r\n\r\n

 

\r\n

Example 1:

\r\n\"\"\r\n
\r\nInput: orders = [[10,5,0],[15,2,1],[25,1,1],[30,4,0]]\r\nOutput: 6\r\nExplanation: Here is what happens with the orders:\r\n- 5 orders of type buy with price 10 are placed. There are no sell orders, so the 5 orders are added to the backlog.\r\n- 2 orders of type sell with price 15 are placed. There are no buy orders with prices larger than or equal to 15, so the 2 orders are added to the backlog.\r\n- 1 order of type sell with price 25 is placed. There are no buy orders with prices larger than or equal to 25 in the backlog, so this order is added to the backlog.\r\n- 4 orders of type buy with price 30 are placed. The first 2 orders are matched with the 2 sell orders of the least price, which is 15 and these 2 sell orders are removed from the backlog. The 3rd order is matched with the sell order of the least price, which is 25 and this sell order is removed from the backlog. Then, there are no more sell orders in the backlog, so the 4th order is added to the backlog.\r\nFinally, the backlog has 5 buy orders with price 10, and 1 buy order with price 30. So the total number of orders in the backlog is 6.\r\n
\r\n\r\n

Example 2:

\r\n\"\"\r\n
\r\nInput: orders = [[7,1000000000,1],[15,3,0],[5,999999995,0],[5,1,1]]\r\nOutput: 999999984\r\nExplanation: Here is what happens with the orders:\r\n- 109 orders of type sell with price 7 are placed. There are no buy orders, so the 109 orders are added to the backlog.\r\n- 3 orders of type buy with price 15 are placed. They are matched with the 3 sell orders with the least price which is 7, and those 3 sell orders are removed from the backlog.\r\n- 999999995 orders of type buy with price 5 are placed. The least price of a sell order is 7, so the 999999995 orders are added to the backlog.\r\n- 1 order of type sell with price 5 is placed. It is matched with the buy order of the highest price, which is 5, and that buy order is removed from the backlog.\r\nFinally, the backlog has (1000000000-3) sell orders with price 7, and (999999995-1) buy orders with price 5. So the total number of orders = 1999999991, which is equal to 999999984 % (109 + 7).\r\n
\r\n\r\n

 

\r\n

Constraints:

\r\n\r\n", "translatedTitle": "积压订单中的订单总数", "translatedContent": "

给你一个二维整数数组 orders ，其中每个 orders[i] = [pricei, amounti, orderTypei] 表示有 amounti 笔类型为 orderTypei 、价格为 pricei 的订单。

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订单类型 orderTypei 可以分为两种：

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注意，orders[i] 表示一批共计 amounti 笔的独立订单，这些订单的价格和类型相同。对于所有有效的 i ，由 orders[i] 表示的所有订单提交时间均早于 orders[i+1] 表示的所有订单。

\n\n

存在由未执行订单组成的 积压订单 。积压订单最初是空的。提交订单时，会发生以下情况：

\n\n\n\n

输入所有订单后，返回积压订单中的 订单总数 。由于数字可能很大，所以需要返回对 109 + 7 取余的结果。

\n\n

 

\n\n

示例 1：

\n\"\"\n
\n输入：orders = [[10,5,0],[15,2,1],[25,1,1],[30,4,0]]\n输出：6\n解释：输入订单后会发生下述情况：\n- 提交 5 笔采购订单，价格为 10 。没有销售订单，所以这 5 笔订单添加到积压订单中。\n- 提交 2 笔销售订单，价格为 15 。没有采购订单的价格大于或等于 15 ，所以这 2 笔订单添加到积压订单中。\n- 提交 1 笔销售订单，价格为 25 。没有采购订单的价格大于或等于 25 ，所以这 1 笔订单添加到积压订单中。\n- 提交 4 笔采购订单，价格为 30 。前 2 笔采购订单与价格最低（价格为 15）的 2 笔销售订单匹配，从积压订单中删除这 2 笔销售订单。第 3 笔采购订单与价格最低的 1 笔销售订单匹配，销售订单价格为 25 ，从积压订单中删除这 1 笔销售订单。积压订单中不存在更多销售订单，所以第 4 笔采购订单需要添加到积压订单中。\n最终，积压订单中有 5 笔价格为 10 的采购订单，和 1 笔价格为 30 的采购订单。所以积压订单中的订单总数为 6 。\n
\n\n

示例 2：

\n\"\"\n
\n输入：orders = [[7,1000000000,1],[15,3,0],[5,999999995,0],[5,1,1]]\n输出：999999984\n解释：输入订单后会发生下述情况：\n- 提交 109 笔销售订单，价格为 7 。没有采购订单，所以这 109 笔订单添加到积压订单中。\n- 提交 3 笔采购订单，价格为 15 。这些采购订单与价格最低（价格为 7 ）的 3 笔销售订单匹配，从积压订单中删除这 3 笔销售订单。\n- 提交 999999995 笔采购订单，价格为 5 。销售订单的最低价为 7 ，所以这 999999995 笔订单添加到积压订单中。\n- 提交 1 笔销售订单，价格为 5 。这笔销售订单与价格最高（价格为 5 ）的 1 笔采购订单匹配，从积压订单中删除这 1 笔采购订单。\n最终，积压订单中有 (1000000000-3) 笔价格为 7 的销售订单，和 (999999995-1) 笔价格为 5 的采购订单。所以积压订单中的订单总数为 1999999991 ，等于 999999984 % (109 + 7) 。
\n\n

 

\n\n

提示：

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