Python编程之数据结构与算法练习_009
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练习内容:
判断一棵树是否是搜索二叉树。
正文内容提要:
1.创建类实现双向链表及基本栈结构。
2.创建类表示二叉树。
3.判断一棵树是否是搜索二叉树的递归与非递归实现。
4.简单测试,验证正确性。
1.创建类实现双向链表及基本栈结构。
代码如下:
class DoubleLinkedList: class Node: def __init__(self, data): self._data = data self._next = None self._pre = None def __init__(self): self.__head = DoubleLinkedList.Node("__head") self.__tail = DoubleLinkedList.Node("__tail") self.__head._next = self.__tail self.__tail._pre = self.__head def append(self, data): node = DoubleLinkedList.Node(data) self.__tail._pre._next = node node._pre = self.__tail._pre self.__tail._pre = node node._next = self.__tail def remove(self, data): node = self.__head while node != self.__tail: if node._data == data: node._pre._next = node._next node._next._pre = node._pre break node = node._next def pop(self): node = self.__tail._pre if node != self.__head: node._pre._next = node._next node._next._pre = node._pre node._next = None node._pre = None return node._data return None def is_empty(self) -> bool: return self.__head._next == self.__tail def iternodes(self) -> None: node = self.__head._next while node != self.__tail: yield node._data node = node._next def add_last(self, data: object) -> None: self.append(data) def poll_first(self): node = self.__head._next if node != self.__tail: self.__head._next = node._next node._next._pre = self.__head node._next = None node._pre = None return node._data return None def poll_last(self): return self.pop() def peek_first(self): node = self.__head._next if node != self.__tail: return node._data return None def peek_last(self): node = self.__tail._pre if node != self.__head: return node._data return None class Stack: def __init__(self): self.__dlnklst = DoubleLinkedList() def pop(self): return self.__dlnklst.pop() def add(self, data): self.__dlnklst.append(data) def push(self, data): return self.__dlnklst.append(data) def peek(self): return self.__dlnklst.peek_last() def poll(self): return self.__dlnklst.poll_last() def is_empty(self): return self.__dlnklst.is_empty()
2.创建类表示二叉树。
代码如下:
class Node: def __init__(self, data): self.__data = data self.__left = None self.__right = None @property def data(self): return self.__data @property def left(self): return self.__left @left.setter def left(self, node): self.__left = node @property def right(self): return self.__right @right.setter def right(self, node): self.__right = node
3.判断一棵树是否是搜索二叉树的递归与非递归实现。
代码如下:
def is_bst_recur(head, pre=None): if not head: return True cur = head if not is_bst_recur(cur.left, pre): return False if pre and pre.data > cur.data: return False pre = cur return is_bst_recur(cur.right, pre) def is_bst_unrecur(head): if not head: return stack = Stack() pre = None while not stack.is_empty() or head: if head: stack.add(head) head = head.left else: head = stack.pop() if pre and pre.data > head.data: return False pre = head head = head.right else: return True
4.简单测试,验证正确性。
代码如下:
if __name__ == "__main__": # BST head1 = Node(9) head1.left = Node(8) head1.right = Node(10) head1.left.left = Node(7) head1.left.right = Node(9) head1.right.left = Node(9) head1.right.right = Node(11) print(is_bst_recur(head1)) # True print(is_bst_unrecur(head1)) # True # Not BST head2 = Node(9) head2.left = Node(8) head2.right = Node(1) head2.left.left = Node(7) head2.left.right = Node(9) head2.right.left = Node(9) head2.right.right = Node(11) print(is_bst_recur(head2)) # False print(is_bst_unrecur(head2)) # False
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