输入输出为>>> t1 = Tree(6, [Tree(2, [Tree(1), Tree(4)]), Tree(7, [Tree(7), Tree(8)])]) >>> is_bst(t1) True >>> t2 = Tree(8, [Tree(2, [Tree(9), Tree(1)]), Tree(3, [Tree(6)]), Tree(5)]) >>> is_bst(t2) False >>> t3 = Tree(6, [Tree(2, [Tree(4), Tree(1)]), Tree(7, [Tree(7), Tree(8)])]) >>> is_bst(t3) False >>> t4 = Tree(1, [Tree(2, [Tree(3, [Tree(4)])])]) >>> is_bst(t4) True >>> t5 = Tree(1, [Tree(0, [Tree(-1, [Tree(-2)])])]) >>> is_bst(t5) True >>> t6 = Tree(1, [Tree(4, [Tree(2, [Tree(3)])])]) >>> is_bst(t6) True >>> t7 = Tree(2, [Tree(1, [Tree(5)]), Tree(4)]) >>> is_bst(t7) False请写代码

这里需要定义 `is_bst` 函数，判断输入的树是否为二叉搜索树。以下是代码实现：

class Tree:
    def __init__(self, label, branches=[]):
        self.label = label
        self.branches = list(branches)

def is_bst(tree):
    def helper(tree, low=float('-inf'), high=float('inf')):
        if tree is None:
            return True
        if not low <= tree.label <= high:
            return False
        left_bst = helper(tree.branches[0], low, tree.label)
        right_bst = helper(tree.branches[-1], tree.label, high)
        return left_bst and right_bst
    return helper(tree)

其中 `helper` 函数递归判断每个子树是否满足二叉搜索树的定义。在递归过程中需要传入当前节点应该满足的最大值 `high` 和最小值 `low`，判断当前节点是否满足条件。如果左右子树都是二叉搜索树，则当前树也是二叉搜索树。

相关问题

上述问题输入输出应为>>> t1 = Tree(6, [Tree(2, [Tree(1), Tree(4)]), Tree(7, [Tree(7), Tree(8)])]) >>> is_bst(t1) True >>> t2 = Tree(8, [Tree(2, [Tree(9), Tree(1)]), Tree(3, [Tree(6)]), Tree(5)]) >>> is_bst(t2) False >>> t3 = Tree(6, [Tree(2, [Tree(4), Tree(1)]), Tree(7, [Tree(7), Tree(8)])]) >>> is_bst(t3) False >>> t4 = Tree(1, [Tree(2, [Tree(3, [Tree(4)])])]) >>> is_bst(t4) True >>> t5 = Tree(1, [Tree(0, [Tree(-1, [Tree(-2)])])]) >>> is_bst(t5) True >>> t6 = Tree(1, [Tree(4, [Tree(2, [Tree(3)])])]) >>> is_bst(t6) True >>> t7 = Tree(2, [Tree(1, [Tree(5)]), Tree(4)]) >>> is_bst(t7) False

Here's how the `is_bst` function could be tested using the input/output pairs you provided:

t1 = Tree(6, [Tree(2, [Tree(1), Tree(4)]), Tree(7, [Tree(7), Tree(8)])])
assert is_bst(t1) == True

t2 = Tree(8, [Tree(2, [Tree(9), Tree(1)]), Tree(3, [Tree(6)]), Tree(5)])
assert is_bst(t2) == False

t3 = Tree(6, [Tree(2, [Tree(4), Tree(1)]), Tree(7, [Tree(7), Tree(8)])])
assert is_bst(t3) == False

t4 = Tree(1, [Tree(2, [Tree(3, [Tree(4)])])])
assert is_bst(t4) == True

t5 = Tree(1, [Tree(0, [Tree(-1, [Tree(-2)])])])
assert is_bst(t5) == True

t6 = Tree(1, [Tree(4, [Tree(2, [Tree(3)])])])
assert is_bst(t6) == True

t7 = Tree(2, [Tree(1, [Tree(5)]), Tree(4)])
assert is_bst(t7) == False

These assertions test the `is_bst` function against the expected output for each of the provided input trees. If all of the assertions pass, then the function should be correct for these test cases.

## Problem 7: Is BST Write a function `is_bst`, which takes a Tree `t` and returns `True` if, and only if, `t` is a valid binary search tree, which means that: - Each node has at most two children (a leaf is automatically a valid binary search tree). - The children are valid binary search trees. - For every node, the entries in that node's left child are less than or equal to the label of the node. - For every node, the entries in that node's right child are greater than the label of the node. An example of a BST is:  Note that, if a node has only one child, that child could be considered either the left or right child. You should take this into consideration. Hint: It may be helpful to write helper functions `bst_min` and `bst_max` that return the minimum and maximum, respectively, of a Tree if it is a valid binary search tree. ```python def is_bst(t): """Returns True if the Tree t has the structure of a valid BST. >>> t1 = Tree(6, [Tree(2, [Tree(1), Tree(4)]), Tree(7, [Tree(7), Tree(8)])]) >>> is_bst(t1) True >>> t2 = Tree(8, [Tree(2, [Tree(9), Tree(1)]), Tree(3, [Tree(6)]), Tree(5)]) >>> is_bst(t2) False >>> t3 = Tree(6, [Tree(2, [Tree(4), Tree(1)]), Tree(7, [Tree(7), Tree(8)])]) >>> is_bst(t3) False >>> t4 = Tree(1, [Tree(2, [Tree(3, [Tree(4)])])]) >>> is_bst(t4) True >>> t5 = Tree(1, [Tree(0, [Tree(-1, [Tree(-2)])])]) >>> is_bst(t5) True >>> t6 = Tree(1, [Tree(4, [Tree(2, [Tree(3)])])]) >>> is_bst(t6) True >>> t7 = Tree(2, [Tree(1, [Tree(5)]), Tree(4)]) >>> is_bst(t7) False """ "*** YOUR CODE HERE ***" ``` 。

根据你的问题，`is_bst` 函数存在问题，因为它只有一个参数。为了实现该函数，需要编写两个辅助函数 `bst_min` 和 `bst_max`，它们返回一个树的最小值和最大值。然后，可以使用这些帮助器函数来实现主函数 `is_bst`。以下是代码的修改版本：

def bst_min(t):
    """Returns the minimum value in a binary search tree."""
    if t.is_leaf():
        return t.label
    return min(t.label, bst_min(t.branches[0]), bst_min(t.branches[-1]))

def bst_max(t):
    """Returns the maximum value in a binary search tree."""
    if t.is_leaf():
        return t.label
    return max(t.label, bst_max(t.branches[-1]), bst_max(t.branches[0]))

def is_bst(t):
    """Returns True if the Tree t has the structure of a valid BST.
    >>> t1 = Tree(6, [Tree(2, [Tree(1), Tree(4)]), Tree(7, [Tree(7), Tree(8)])])
    >>> is_bst(t1)
    True
    >>> t2 = Tree(8, [Tree(2, [Tree(9), Tree(1)]), Tree(3, [Tree(6)]), Tree(5)])
    >>> is_bst(t2)
    False
    >>> t3 = Tree(6, [Tree(2, [Tree(4), Tree(1)]), Tree(7, [Tree(7), Tree(8)])])
    >>> is_bst(t3)
    False
    >>> t4 = Tree(1, [Tree(2, [Tree(3, [Tree(4)])])])
    >>> is_bst(t4)
    True
    >>> t5 = Tree(1, [Tree(0, [Tree(-1, [Tree(-2)])])])
    >>> is_bst(t5)
    True
    >>> t6 = Tree(1, [Tree(4, [Tree(2, [Tree(3)])])])
    >>> is_bst(t6)
    True
    >>> t7 = Tree(2, [Tree(1, [Tree(5)]), Tree(4)])
    >>> is_bst(t7)
    False
    """
    if t.is_leaf():
        return True
    elif len(t.branches) == 1:
        return is_bst(t.branches[0])
    else:
        left = t.branches[0]
        right = t.branches[-1]
        if bst_max(left) <= t.label < bst_min(right):
            return is_bst(left) and is_bst(right)
        else:
            return False