//FindSecretLinearMultiEquation finds the secrets
func FindSecretLinearMultiEquation(x []int, y []int64, degree int) int {
	if len(x) < degree+1 || len(y) < degree+1 {
		return -1
	}
	var matrix [][]int64
	var foundSeed int
	for i := 0; i < degree+1; i++ {
		var vector []int64
		for j := 0; j < degree; j++ {
			vector = append(vector, int64(math.Pow(float64(x[i]), float64(j+1))))
		}
		vector = append(vector, 1)
		vector = append(vector, y[i])
		matrix = append(matrix, vector)
	}
	//printMatrix(matrix)
	transformMatrix(matrix)
	lastRow := matrix[len(matrix)-1]
	length := len(lastRow)
	printMatrix(matrix)
	foundSeed = int(lastRow[length-1] / lastRow[length-2])
	return foundSeed
}

func transformMatrix(matrix [][]int64) {
	for i := 0; i < len(matrix)-1; i++ {
		for k := i + 1; k < len(matrix); k++ {
			transformRow(matrix[i], matrix[k], i)
		}
	}
}

func transformRow(v1 []int64, v2 []int64, round int) {
	if v1[round] == 0 {
		SwapVector(v1, v2)
	} else if v2[round] != 0 {
		lcm := calculateLCM(
			int64(math.Abs(float64(v1[round]))),
			int64(math.Abs(float64(v2[round]))))
		timesV1 := lcm / v1[round]
		timesV2 := lcm / v2[round]
		AlgebraVector(v1, v2, "-", timesV1, timesV2)
	}
}

func multiply(v []int64, a int64) {
	for i := 0; i < len(v); i++ {
		v[i] = a * v[i]
	}
}