package q216

// k numbers sum up to n

func calc(k int, buf []int, offset int, remSum int, ret [][]int) [][]int {
	if offset == k-1 && remSum > 0 && remSum < 10 {
		buf[offset] = remSum
		cp := make([]int, len(buf))
		copy(cp, buf)
		return append(ret, cp)
	}

	remK := k - offset
	minI := 1
	if offset > 0 {
		minI = buf[offset-1] + 1
	}
	maxI := 9 - remK + 1

	for i := minI; i <= maxI; i++ {
		minSum := (i + i + remK - 1) * remK / 2
		maxSum := (19 - remK) * remK / 2
		if remSum < minSum || remSum > maxSum {
			continue
		}

		buf[offset] = i
		ret = calc(k, buf, offset+1, remSum-i, ret)
	}
	return ret
}

func combinationSum3(k int, n int) [][]int {
	return calc(k, make([]int, k), 0, n, [][]int{})
}

var _ = combinationSum3