python回溯算法

如何利用python回溯算法求三元不等式的所有正整数解呀，要有伪码和解

def solution():
    def back(x,y,z):
        res = 0;
        if x>12//3 or y>12//4 or z>12//2:
            return res;
        if 3*x+4*y+2*z<=12:
            solutions.add((x,y,z))
            return 1 + back(x+1,y,z) + back(x,y+1,z) + back(x,y,z+1)
        return res
    
    solutions = set()
    back(0,0,0)
    return len(solutions),sorted(solutions)

print(solution())

返回解的个数 和 解集列表 组成的元组：
(34, [(0, 0, 0), (0, 0, 1), (0, 0, 2), (0, 0, 3), (0, 0, 4), (0, 0, 5), (0, 0, 6), (0, 1, 0), (0, 1, 1), (0, 1, 2), (0, 1, 3), (0, 1, 4), (0, 2, 0), (0, 2, 1), (0, 2, 2), (0, 3, 0), (1, 0, 0), (1, 0, 1), (1, 0, 2), (1, 0, 3), (1, 0, 4), (1, 1, 0), (1, 1, 1), (1, 1, 2), (1, 2, 0), (2, 0, 0), (2, 0, 1), (2, 0, 2), (2, 0, 3), (2, 1, 0), (2, 1, 1), (3, 0, 0), (3, 0, 1), (4, 0, 0)])

如要求正整数解，第12行从 back(1,1,1)开始回溯
(3, [(1, 1, 1), (1, 1, 2), (2, 1, 1)])