# 追赶法求解
def ZGsolve(A,b):
    n = len(b)
    beta = [0]*n
    for i in range(n):
        if i == 0:
            beta[i] = A[i][2] / A[i][1]
        else:
            beta[i] = A[i][2] / (A[i][1] - A[i][0]*beta[i-1])
    print("beta:")
    print(beta[:-1])
    for i in range(n):
        if i == 0:
            b[i] = b[i] / A[i][1]
        else:
            b[i] = (b[i] - A[i][0]*b[i-1]) / (A[i][1] - A[i][0]*beta[i-1])
    print("y:")
    print(b)
    for i in range(n-2,-1,-1):
        b[i] = b[i] - beta[i]*b[i+1]

    return b

#把A,b换成题干的数值###########################################
if __name__ == "__main__":
    # 储存追赶法A矩阵
    A = [
        [0,4,-1],
        [-1,4,-1],
        [-1,4,-1],
        [-1,4,-1],
        [-1,4,0]
    ]


    b = [100,200,200,200,100]
    print("x:")
    print(ZGsolve(A,b))