{ "data": { "question": { "questionId": "3277", "questionFrontendId": "3027", "categoryTitle": "Algorithms", "boundTopicId": 2629415, "title": "Find the Number of Ways to Place People II", "titleSlug": "find-the-number-of-ways-to-place-people-ii", "content": "

You are given a 2D array points of size n x 2 representing integer coordinates of some points on a 2D-plane, where points[i] = [xi, yi].

\n\n

We define the right direction as positive x-axis (increasing x-coordinate) and the left direction as negative x-axis (decreasing x-coordinate). Similarly, we define the up direction as positive y-axis (increasing y-coordinate) and the down direction as negative y-axis (decreasing y-coordinate)

\n\n

You have to place n people, including Alice and Bob, at these points such that there is exactly one person at every point. Alice wants to be alone with Bob, so Alice will build a rectangular fence with Alice's position as the upper left corner and Bob's position as the lower right corner of the fence (Note that the fence might not enclose any area, i.e. it can be a line). If any person other than Alice and Bob is either inside the fence or on the fence, Alice will be sad.

\n\n

Return the number of pairs of points where you can place Alice and Bob, such that Alice does not become sad on building the fence.

\n\n

Note that Alice can only build a fence with Alice's position as the upper left corner, and Bob's position as the lower right corner. For example, Alice cannot build either of the fences in the picture below with four corners (1, 1), (1, 3), (3, 1), and (3, 3), because:

\n\n\n\"\"\n

 

\n

Example 1:

\n\"\"\n
\nInput: points = [[1,1],[2,2],[3,3]]\nOutput: 0\nExplanation: There is no way to place Alice and Bob such that Alice can build a fence with Alice's position as the upper left corner and Bob's position as the lower right corner. Hence we return 0. \n
\n\n

Example 2:

\n\"\"\n
\nInput: points = [[6,2],[4,4],[2,6]]\nOutput: 2\nExplanation: There are two ways to place Alice and Bob such that Alice will not be sad:\n- Place Alice at (4, 4) and Bob at (6, 2).\n- Place Alice at (2, 6) and Bob at (4, 4).\nYou cannot place Alice at (2, 6) and Bob at (6, 2) because the person at (4, 4) will be inside the fence.\n
\n\n

Example 3:

\n\"\"\n
\nInput: points = [[3,1],[1,3],[1,1]]\nOutput: 2\nExplanation: There are two ways to place Alice and Bob such that Alice will not be sad:\n- Place Alice at (1, 1) and Bob at (3, 1).\n- Place Alice at (1, 3) and Bob at (1, 1).\nYou cannot place Alice at (1, 3) and Bob at (3, 1) because the person at (1, 1) will be on the fence.\nNote that it does not matter if the fence encloses any area, the first and second fences in the image are valid.\n
\n\n

 

\n

Constraints:

\n\n\n", "translatedTitle": "人员站位的方案数 II", "translatedContent": "

给你一个  n x 2 的二维数组 points ，它表示二维平面上的一些点坐标，其中 points[i] = [xi, yi] 。

\n\n

我们定义 x 轴的正方向为 右 （x 轴递增的方向），x 轴的负方向为 左 （x 轴递减的方向）。类似的，我们定义 y 轴的正方向为 上 （y 轴递增的方向），y 轴的负方向为 下 （y 轴递减的方向）。

\n\n

你需要安排这 n 个人的站位，这 n 个人中包括 Alice 和 Bob 。你需要确保每个点处 恰好 有 一个 人。同时，Alice 想跟 Bob 单独玩耍，所以 Alice 会以 Alice 的坐标为 左上角 ，Bob 的坐标为 右下角 建立一个矩形的围栏（注意，围栏可能 不 包含任何区域，也就是说围栏可能是一条线段）。如果围栏的 内部 或者 边缘 上有任何其他人，Alice 都会难过。

\n\n

请你在确保 Alice 不会 难过的前提下，返回 Alice 和 Bob 可以选择的 点对 数目。

\n\n

注意，Alice 建立的围栏必须确保 Alice 的位置是矩形的左上角，Bob 的位置是矩形的右下角。比方说，以 (1, 1) ，(1, 3) ，(3, 1) 和 (3, 3) 为矩形的四个角，给定下图的两个输入，Alice 都不能建立围栏，原因如下：

\n\n\n\"\"\n

 

\n\n

示例 1：

\n\n

\"\"

\n\n
\n输入：points = [[1,1],[2,2],[3,3]]\n输出：0\n解释：没有办法可以让 Alice 的围栏以 Alice 的位置为左上角且 Bob 的位置为右下角。所以我们返回 0 。\n
\n\n

示例 2：

\n\n

\"\"

\n\n
\n输入：points = [[6,2],[4,4],[2,6]]\n输出：2\n解释：总共有 2 种方案安排 Alice 和 Bob 的位置，使得 Alice 不会难过：\n- Alice 站在 (4, 4) ，Bob 站在 (6, 2) 。\n- Alice 站在 (2, 6) ，Bob 站在 (4, 4) 。\n不能安排 Alice 站在 (2, 6) 且 Bob 站在 (6, 2) ，因为站在 (4, 4) 的人处于围栏内。\n
\n\n

示例 3：

\n\n

\"\"

\n\n
\n输入：points = [[3,1],[1,3],[1,1]]\n输出：2\n解释：总共有 2 种方案安排 Alice 和 Bob 的位置，使得 Alice 不会难过：\n- Alice 站在 (1, 1) ，Bob 站在 (3, 1) 。\n- Alice 站在 (1, 3) ，Bob 站在 (1, 1) 。\n不能安排 Alice 站在 (1, 3) 且 Bob 站在 (3, 1) ，因为站在 (1, 1) 的人处于围栏内。\n注意围栏是可以不包含任何面积的，上图中第一和第二个围栏都是合法的。\n
\n\n

 

\n\n

提示：

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