newton

function NewtonPoly(x, dataX, dataY)
    n = length(dataY)
    numOfDiff = Int(((1+n)*n)/2)
    Result = zeros(numOfDiff)
    Elems = zeros(n+1)

    for i = 2 : n+1
        Elems[i] = Elems[i-1] + (n-(i-2))
    end

    for i = 1 : n
        Result[i] = dataY[i]
    end

    for i = n+1 : numOfDiff
        level = n+1
        while Elems[level] >= i
            level-=1
        end
        iterator = Int(i-Elems[level] + Elems[level-1])
        Result[i] = (Result[iterator+1] - Result[iterator]) / (dataX[Int(i-Elems[level] + level - 1)] - dataX[Int(i-Elems[level])])
    end

    Coef = zeros(n)
    for i = 1 : n
        Coef[i] = Result[Int(Elems[i] + 1)]
    end

    return Coef
end