import numpy as np

# 给定数据
t_values = np.array([0, 10, 15, 20, 22.5, 30])
v_values = np.array([0, 227.04, 362.78, 517.35, 602.97, 901.67])


# 计算Newton插值法所需的差商
def divided_diff(t_values, v_values):
    # 用给定的数值初始化差商数组
    differences = v_values.copy()

    # 遍历每个数据点，计算差商
    for i in range(1, len(t_values)):
        for j in range(len(t_values) - 1, i - 1, -1):
            differences[j] = (differences[j] - differences[j - 1]) / (t_values[j] - t_values[j - i])

    return differences


# 使用Newton插值法寻找 t=16 时的速度
def newton_interpolation(t_values, v_values, target_t):
    differences = divided_diff(t_values, v_values)
    p = differences[0]

    for i in range(1, len(t_values)):
        term = differences[i]
        for j in range(i):
            term *= (target_t - t_values[j])

        p += term

    return p


t_target = 16
velocity_at_16 = newton_interpolation(t_values, v_values, t_target)

print(f"使用Newton插值法，t=16 秒时的速度为: {velocity_at_16:.2f} m/s")