Solution3.py

class Solution:
    def minimumOperations(self, nums: List[int], start: int, goal: int) -> int:
        def next(x):
            res = []
            for num in nums:
                res.append(x + num)
                res.append(x - num)
                res.append(x ^ num)
            return res

        def extend(m1, m2, q):
            for _ in range(len(q)):
                x = q.popleft()
                step = m1[x]
                for y in next(x):
                    if y in m1:
                        continue
                    if y in m2:
                        return step + 1 + m2[y]
                    if 0 <= y <= 1000:
                        m1[y] = step + 1
                        q.append(y)
            return -1

        m1, m2 = {start: 0}, {goal: 0}
        q1, q2 = deque([start]), deque([goal])
        while q1 and q2:
            t = extend(m1, m2, q1) if len(q1) <= len(q2) else extend(m2, m1, q2)
            if t != -1:
                return t
        return -1