package q1292

func pfSum(mat [][]int) [][]int {
	w, h := len(mat[0])+1, len(mat)+1
	pfs := make([][]int, h)
	for i := range pfs {
		pfs[i] = make([]int, w)
	}

	for y := 1; y < h; y++ {
		for x := 1; x < w; x++ {
			pfs[y][x] = mat[y-1][x-1] + pfs[y][x-1] + pfs[y-1][x] - pfs[y-1][x-1]
		}
	}
	return pfs
}

func sumOfSquare(pfs [][]int, x, y, w int) int {
	return pfs[y+w][x+w] - pfs[y][x+w] - pfs[y+w][x] + pfs[y][x]
}

func hasSquare(pfs [][]int, edgeLen, threshold int) bool {
	w, h := len(pfs[0])-1, len(pfs)-1
	for y := range h - edgeLen + 1 {
		for x := range w - edgeLen + 1 {
			if sumOfSquare(pfs, x, y, edgeLen) <= threshold {
				return true
			}
		}
	}
	return false
}

func maxSideLength(mat [][]int, threshold int) int {
	pfs := pfSum(mat)
	w, h := len(pfs[0]), len(pfs)
	maxAllowed := min(w, h)

	l, r := 0, maxAllowed+1
	for l+1 < r {
		m := (l + r) / 2
		if hasSquare(pfs, m, threshold) {
			l = m
		} else {
			r = m
		}
	}
	return l
}

var _ = maxSideLength