{ "data": { "question": { "questionId": "3886", "questionFrontendId": "3623", "categoryTitle": "Algorithms", "boundTopicId": 3727790, "title": "Count Number of Trapezoids I", "titleSlug": "count-number-of-trapezoids-i", "content": "
You are given a 2D integer array points
, where points[i] = [xi, yi]
represents the coordinates of the ith
point on the Cartesian plane.
A horizontal trapezoid is a convex quadrilateral with at least one pair of horizontal sides (i.e. parallel to the x-axis). Two lines are parallel if and only if they have the same slope.
\n\nReturn the number of unique horizontal trapezoids that can be formed by choosing any four distinct points from points
.
Since the answer may be very large, return it modulo 109 + 7
.
\n
Example 1:
\n\nInput: points = [[1,0],[2,0],[3,0],[2,2],[3,2]]
\n\nOutput: 3
\n\nExplanation:
\n\n
There are three distinct ways to pick four points that form a horizontal trapezoid:
\n\n[1,0]
, [2,0]
, [3,2]
, and [2,2]
.[2,0]
, [3,0]
, [3,2]
, and [2,2]
.[1,0]
, [3,0]
, [3,2]
, and [2,2]
.Example 2:
\n\nInput: points = [[0,0],[1,0],[0,1],[2,1]]
\n\nOutput: 1
\n\nExplanation:
\n\nThere is only one horizontal trapezoid that can be formed.
\n\n
Constraints:
\n\n4 <= points.length <= 105
–108 <= xi, yi <= 108
给你一个二维整数数组 points
,其中 points[i] = [xi, yi]
表示第 i
个点在笛卡尔平面上的坐标。
水平梯形 是一种凸四边形,具有 至少一对 水平边(即平行于 x 轴的边)。两条直线平行当且仅当它们的斜率相同。
\n\n返回可以从 points
中任意选择四个不同点组成的 水平梯形 数量。
由于答案可能非常大,请返回结果对 109 + 7
取余数后的值。
\n\n
示例 1:
\n\n输入: points = [[1,0],[2,0],[3,0],[2,2],[3,2]]
\n\n输出: 3
\n\n解释:
\n\n
有三种不同方式选择四个点组成一个水平梯形:
\n\n[1,0]
、[2,0]
、[3,2]
和 [2,2]
。[2,0]
、[3,0]
、[3,2]
和 [2,2]
。[1,0]
、[3,0]
、[3,2]
和 [2,2]
。示例 2:
\n\n输入: points = [[0,0],[1,0],[0,1],[2,1]]
\n\n输出: 1
\n\n解释:
\n\n只有一种方式可以组成一个水平梯形。
\n\n\n
提示:
\n\n4 <= points.length <= 105
–108 <= xi, yi <= 108
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