import math

def NewtonDownHillSolve(fx, dfx, x0, err1,err2, N0,min_t):
    count = 0
    print(f"k={count}, x0={x0}\n")
    x1 = x0 + 1 + err1
    while abs(x1 - x0) > err1 or abs(fx(x1)) > err2:
        t = 1
        if abs(dfx(x1)) < 1e-10:
            print("导数为0，无法下山")
            return None, 0
        print(f"当前点: x0={x0}")
        while t >= min_t:
            x1 = x0 - t * fx(x0) / dfx(x0)
            print(f"下山: t={t}, x1={x1}, fx(x{count+1})={fx(x1)}, fx(x{count})={fx(x0)}")
            if abs(fx(x1)) < abs(fx(x0)):
                break
            t *= 0.5
        if t < min_t:
            print("达到最小t，下山失败")
            return None, -2
        # x1 = x0 - fx(x0) / dfx(x0)
        count += 1
        print(f"k={count}, x{count}={x1},x1-x0={abs(x1-x0)}\n")
        if count > N0:
            return None, -1
        x0 = x1
    print(f"收敛: x1={x1}, fx(x1)={fx(x1)}")
    return x1, 1


if __name__ == "__main__":
    ##############################################################################################################
    err1 = 1e-5      # 根的误差限   见P147
    err2 = 1e-5      # 残量精度     见P147
    N0 = 100         # 最大迭代次数
    min_t = 1e-10    # 最小t值
    x0 = 0.6         # 初始值
    fx = lambda x: x**3 - x - 1       # 原函数
    dfx = lambda x: 3*x**2 - 1        # 导函数

    result, status = NewtonDownHillSolve(fx, dfx, x0, err1, err2, N0, min_t)
    if status == 1:
        print(f"收敛 解为: {result}")
    elif status == -1:
        print("不收敛")
    elif status == -2:
        print("下山失败")
    else:
        print("导数为0，无法收敛")