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3278. Find the Number of Ways to Place People I

Medium
Array
Math
Geometry
Sorting
Enumeration
Solve on LeetCode View Solutions

Description

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].

Count the number of pairs of points (A, B), where

  • A is on the upper left side of B, and
  • there are no other points in the rectangle (or line) they make (including the border), except for the points A and B.

Return the count.

 

Example 1:

Input: points = [[1,1],[2,2],[3,3]]

Output: 0

Explanation:

There is no way to choose A and B such that A is on the upper left side of B.

Example 2:

Input: points = [[6,2],[4,4],[2,6]]

Output: 2

Explanation:

  • The left one is the pair (points[1], points[0]), where points[1] is on the upper left side of points[0] and the rectangle is empty.
  • The middle one is the pair (points[2], points[1]), same as the left one it is a valid pair.
  • The right one is the pair (points[2], points[0]), where points[2] is on the upper left side of points[0], but points[1] is inside the rectangle so it's not a valid pair.

Example 3:

Input: points = [[3,1],[1,3],[1,1]]

Output: 2

Explanation:

  • The left one is the pair (points[2], points[0]), where points[2] is on the upper left side of points[0] and there are no other points on the line they form. Note that it is a valid state when the two points form a line.
  • The middle one is the pair (points[1], points[2]), it is a valid pair same as the left one.
  • The right one is the pair (points[1], points[0]), it is not a valid pair as points[2] is on the border of the rectangle.

 

Constraints:

  • 2 <= n <= 50
  • points[i].length == 2
  • 0 <= points[i][0], points[i][1] <= 50
  • All points[i] are distinct.

Hints

Hint 1
We can enumerate all the upper-left and lower-right corners.
Hint 2
If the upper-left corner is <code>(x1, y1)</code> and lower-right corner is <code>(x2, y2)</code>, check that there is no point <code>(x, y)</code> such that <code>x1 <= x <= x2</code> and <code>y2 <= y <= y1</code>.

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