[英]How to list the longest path in binary tree?
在这里,我们尝试列出二叉树中最长的路径。 例如,
list_longest_path(None)
[]
list_longest_path(BinaryTree(5))
[5]
b1 = BinaryTree(7)
b2 = BinaryTree(3, BinaryTree(2), None)
b3 = BinaryTree(5, b2, b1)
list_longest_path(b3)
[5, 3, 2]
我的代码在底部。 显然,代码返回树中的每个节点。 在这里,我很难同时使用max()
时如何生成所有列表?
class BinaryTree:
"""
A Binary Tree, i.e. arity 2.
=== Attributes ===
@param object data: data for this binary tree node
@param BinaryTree|None left: left child of this binary tree node
@param BinaryTree|None right: right child of this binary tree node
"""
def __init__(self, data, left=None, right=None):
"""
Create BinaryTree self with data and children left and right.
@param BinaryTree self: this binary tree
@param object data: data of this node
@param BinaryTree|None left: left child
@param BinaryTree|None right: right child
@rtype: None
"""
self.data, self.left, self.right = data, left, right
def __eq__(self, other):
"""
Return whether BinaryTree self is equivalent to other.
@param BinaryTree self: this binary tree
@param Any other: object to check equivalence to self
@rtype: bool
>>> BinaryTree(7).__eq__("seven")
False
>>> b1 = BinaryTree(7, BinaryTree(5))
>>> b1.__eq__(BinaryTree(7, BinaryTree(5), None))
True
"""
return (type(self) == type(other) and
self.data == other.data and
(self.left, self.right) == (other.left, other.right))
def __repr__(self):
"""
Represent BinaryTree (self) as a string that can be evaluated to
produce an equivalent BinaryTree.
@param BinaryTree self: this binary tree
@rtype: str
>>> BinaryTree(1, BinaryTree(2), BinaryTree(3))
BinaryTree(1, BinaryTree(2, None, None), BinaryTree(3, None, None))
"""
return "BinaryTree({}, {}, {})".format(repr(self.data),
repr(self.left),
repr(self.right))
def __str__(self, indent=""):
"""
Return a user-friendly string representing BinaryTree (self)
inorder. Indent by indent.
>>> b = BinaryTree(1, BinaryTree(2, BinaryTree(3)), BinaryTree(4))
>>> print(b)
4
1
2
3
<BLANKLINE>
"""
right_tree = (self.right.__str__(
indent + " ") if self.right else "")
left_tree = self.left.__str__(indent + " ") if self.left else ""
return (right_tree + "{}{}\n".format(indent, str(self.data)) +
left_tree)
def __contains__(self, value):
"""
Return whether tree rooted at node contains value.
@param BinaryTree self: binary tree to search for value
@param object value: value to search for
@rtype: bool
>>> BinaryTree(5, BinaryTree(7), BinaryTree(9)).__contains__(7)
True
"""
return (self.data == value or
(self.left and value in self.left) or
(self.right and value in self.right))
def list_longest_path(node):
"""
List the data in a longest path of node.
@param BinaryTree|None node: tree to list longest path of
@rtype: list[object]
>>> list_longest_path(None)
[]
>>> list_longest_path(BinaryTree(5))
[5]
>>> b1 = BinaryTree(7)
>>> b2 = BinaryTree(3, BinaryTree(2), None)
>>> b3 = BinaryTree(5, b2, b1)
>>> list_longest_path(b3)
[5, 3, 2]
"""
if node is None:
return []
elif not node.left and not node.right:
return [node]
else:
return [node]+list_longest_path(node.left)+list_longest_path(node.right)
树中最长的路径称为“ 直径 ”。 因此,您正在寻找类似“ python树直径计算器”的东西 。
您可以在此处查看算法的实现:
http://www.geeksforgeeks.org/diameter-of-a-binary-tree/
和这里:
http://tech-queries.blogspot.com.br/2010/09/diameter-of-tree-in-on.html
由于此网站仅包含C和JAVA的代码,因此您可以在此处查看一些pythonic编码思想:
这是一个Python函数,它将返回路径:
def list_longest_path(root):
if not root:
return []
l = list_longest_path(root.left)
r = list_longest_path(root.right)
if len(l) > len(r):
return [root] + l
else:
return [root] + r
在您的代码中,无需检查左孩子或右孩子是否存在,因为您的函数无论如何都会返回列表。 但是,您需要做的是检查从子级返回的列表的长度,然后选择更长的列表。
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