# 查找根区间
def FindRootZone(fx,start,stop,step):
    x = start
    while x < stop:
        if fx(x) * fx(x+step) < 0:
            return x
        x += step
    return None

# 求n次方根迭代过程如下
def GetNthRoot(a,n):
    if a < 0 and n % 2 == 0:
        print("Cannot compute even root of negative number")
        return None
    fx = lambda x: x**n - a
    dfx = lambda x: n * x**(n-1)
    err = 1e-10
    N0 = 100
    x0 = 0
    if a > 0:
        x0 = FindRootZone(fx, 0, a, 0.01)
    else:
        x0 = FindRootZone(fx, a, 0, 0.01)

    count = 0
    x1 = x0 + 1 + err
    while abs(x1 - x0) > err or abs(fx(x1)) > err: # 添加条件修正根误差太大的问题
        x1 = x0 - fx(x0) / dfx(x0)
        count += 1
        if count > N0:
            return None
        x0 = x1
    return x1

if __name__ == "__main__":
    re = GetNthRoot(30, 5)   #30的5次方根###########################
    print(re)