package q3453

import (
	"math"
	"slices"
)

func separateSquares(squares [][]int) float64 {
	slices.SortFunc(squares, func(a, b []int) int { return a[1] - b[1] })
	var totalArea float64
	var maxY int
	for i := range squares {
		totalArea += math.Pow(float64(squares[i][2]), 2)
		maxY = max(maxY, squares[i][1]+squares[i][2])
	}

	target := totalArea / 2

	// Binary search
	var l, r float64 = 0, float64(maxY)
	for range 64 {
		m := (l + r) / 2

		var area float64
		for i := range squares {
			y, l := float64(squares[i][1]), float64(squares[i][2])
			if y >= m {
				break
			}
			area += l * min(l, m-y)
		}
		if area < target {
			l = m
		} else {
			r = m
		}
	}
	return l
}

var _ = separateSquares