Package g3001_3100.s3047_find_the_largest_area_of_square_inside_two_rectangles

Class Solution

java.lang.Object
g3001_3100.s3047_find_the_largest_area_of_square_inside_two_rectangles.Solution
public class Solution extends java.lang.Object
3047 - Find the Largest Area of Square Inside Two Rectangles.

Medium

There exist n rectangles in a 2D plane. You are given two 0-indexed 2D integer arrays bottomLeft and topRight, both of size n x 2, where bottomLeft[i] and topRight[i] represent the bottom-left and top-right coordinates of the ith rectangle respectively.

You can select a region formed from the intersection of two of the given rectangles. You need to find the largest area of a square that can fit inside this region if you select the region optimally.

Return the largest possible area of a square, or 0 if there do not exist any intersecting regions between the rectangles.

Example 1:

Input: bottomLeft = [[1,1],[2,2],[3,1]], topRight = [[3,3],[4,4],[6,6]]

Output: 1

Explanation: A square with side length 1 can fit inside either the intersecting region of rectangle 0 and rectangle 1, or the intersecting region of rectangle 1 and rectangle 2. Hence the largest area is side * side which is 1 * 1 == 1.

It can be shown that a square with a greater side length can not fit inside any intersecting region.

Example 2:

Input: bottomLeft = [[1,1],[2,2],[1,2]], topRight = [[3,3],[4,4],[3,4]]

Output: 1

Explanation: A square with side length 1 can fit inside either the intersecting region of rectangle 0 and rectangle 1, the intersecting region of rectangle 1 and rectangle 2, or the intersection region of all 3 rectangles. Hence the largest area is side * side which is 1 * 1 == 1.

It can be shown that a square with a greater side length can not fit inside any intersecting region. Note that the region can be formed by the intersection of more than 2 rectangles.

Example 3:

Input: bottomLeft = [[1,1],[3,3],[3,1]], topRight = [[2,2],[4,4],[4,2]]

Output: 0

Explanation: No pair of rectangles intersect, hence, we return 0.

Constraints:

  • n == bottomLeft.length == topRight.length
  • 2 <= n <= 103
  • bottomLeft[i].length == topRight[i].length == 2
  • 1 <= bottomLeft[i][0], bottomLeft[i][1] <= 107
  • 1 <= topRight[i][0], topRight[i][1] <= 107
  • bottomLeft[i][0] < topRight[i][0]
  • bottomLeft[i][1] < topRight[i][1]

  • Constructor Summary

    Constructors
    Constructor
    Description
    Solution()
     

  • Method Summary

    Modifier and Type
    Method
    Description
    long
    largestSquareArea(int[][] bottomLeft, int[][] topRight)
     

    Methods inherited from class java.lang.Object

    clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

  • Constructor Details

    • Solution

      public Solution()

  • Method Details

    • largestSquareArea

      public long largestSquareArea(int[][] bottomLeft, int[][] topRight)