3454 - Separate Squares II.

Hard

You are given a 2D integer array squares. Each <code>squaresi = x_i, y_i, l_i</code> represents the coordinates of the bottom-left point and the side length of a square parallel to the x-axis.

Find the minimum y-coordinate value of a horizontal line such that the total area covered by squares above the line equals the total area covered by squares below the line.

Answers within <code>10^-5</code> of the actual answer will be accepted.

Note: Squares may overlap. Overlapping areas should be counted only once in this version.

Example 1:

Input: squares = [0,0,1,2,2,1]

Output: 1.00000

Explanation:

Any horizontal line between y = 1 and y = 2 results in an equal split, with 1 square unit above and 1 square unit below. The minimum y-value is 1.

Example 2:

Input: squares = [0,0,2,1,1,1]

Output: 1.00000

Explanation:

Since the blue square overlaps with the red square, it will not be counted again. Thus, the line y = 1 splits the squares into two equal parts.

Constraints:

• <code>1 <= squares.length <= 5 * 10⁴</code>

• <code>squaresi = x_i, y_i, l_i</code>

• squares[i].length == 3

• <code>0 <= x_i, y_i<= 10⁹</code>

• <code>1 <= l_i<= 10⁹</code>