# Time:  O(n)
# Space: O(h)

class TreeNode(object):
    def __init__(self, val=0, left=None, right=None):
        pass


# dfs with stack
class Solution(object):
    def evaluateTree(self, root):
        """
        :type root: Optional[TreeNode]
        :rtype: bool
        """
        INF = float("inf")
        OP = {
            2: lambda x, y: x or y,
            3: lambda x, y: x and y
        }
        
        def iter_dfs(root):
            ret = [0]
            stk = [(1, (root, ret))]
            while stk:
                step, args = stk.pop()
                if step == 1:
                    node, ret = args
                    if node.left == node.right:
                        ret[0] = node.val
                        continue
                    ret1, ret2 = [0], [0]
                    stk.append((2, (node, ret1, ret2, ret)))
                    stk.append((1, (node.right, ret2)))
                    stk.append((1, (node.left, ret1)))
                elif step == 2:
                    node, ret1, ret2, ret = args
                    ret[0] = OP[node.val](ret1[0], ret2[0])
            return ret[0]

        return iter_dfs(root)


# Time:  O(n)
# Space: O(h)
# dfs with recursion
class Solution2(object):
    def evaluateTree(self, root):
        """
        :type root: Optional[TreeNode]
        :rtype: bool
        """
        INF = float("inf")
        OP = {
            2: lambda x, y: x or y,
            3: lambda x, y: x and y,
        }
        
        def dfs(node):
            if node.left == node.right:
                return node.val
            return OP[node.val](dfs(node.left), dfs(node.right))

        return dfs(root)