Package g3001_3100.s3047_find_the_largest_area_of_square_inside_two_rectangles

Class Solution

  • All Implemented Interfaces:
    
public final class Solution

    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 <code>i<sup>th</sup></code> 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

    • <code>2 <= n <= 10<sup>3</sup></code>

    • bottomLeft[i].length == topRight[i].length == 2

    • <code>1 <= bottomLeft0, bottomLeft1<= 10<sup>7</sup></code>

    • <code>1 <= topRight0, topRight1<= 10<sup>7</sup></code>

    • bottomLeft[i][0] &lt; topRight[i][0]

    • bottomLeft[i][1] &lt; topRight[i][1]

    • Nested Class Summary

      Nested Classes 
      Modifier and Type Class Description

    • Field Summary

      Fields 
      Modifier and Type Field Description

    • Constructor Summary

      Constructors 
      Constructor Description
      Solution()

    • Enum Constant Summary

      Enum Constants 
      Enum Constant Description

    • Method Summary

      Modifier and Type Method Description
      final Long largestSquareArea(Array<IntArray> bottomLeft, Array<IntArray> topRight)

      • Methods inherited from class java.lang.Object

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