[英]Print all possible paths in binary tree
我正在嘗試在二叉樹中打印所有可能的路徑。 我能夠打印所有根到葉的路徑,但無法弄清楚如何添加葉到葉的路徑。(我正在使用根到葉的預序遍歷)。 所以,基本上:
如果我的樹是
6
/ \
4 0
/ \ \
1 3 1
如果要打印所有路徑的代碼:
6,4,1
6,4,3
6,0,1
1,4,6,0,1
3,4,6,0,1
1,4,3
4,6,0
4,6,0,1
etc.
誰能幫我這個二叉樹? 我非常感謝您的幫助,因為我是這個社會和 Python/Java 的新手。
謝謝
樹的一個顯着特性是對於節點(x, y)
每個組合,都存在從x
到y
的唯一非重復路徑。 特別是,可以通過找到x
和y
的第一個共同祖先z
並采用路徑x -> z + z -> y
到此路徑。
因此,查找所有路徑的算法可能如下所示
for each pair of distinct nodes x, y in the tree:
find all common ancestors of x and y
let z be the lowest common acestor in the tree
let p be the path from x to z
append the path from z to y to p, excluding the duplicate z
print p
這是一種面向對象的方法,它實現了完成上述任務所需的方法。
class Tree:
def __init__(self, value, left=None, right=None):
self.value = value
self.left = left
self.right = right
self.parent = None
if left is not None:
left.parent = self
if right is not None:
right.parent = self
def __iter__(self):
"""Return a left-to-right iterator on the tree"""
if self.left:
yield from iter(self.left)
yield self
if self.right:
yield from iter(self.right)
def __repr__(self):
return str(self.value)
def get_ancestors(self):
"""Return a list of all ancestors including itself"""
ancestors = {self}
parent = self.parent
while parent:
ancestors.add(parent)
parent = parent.parent
return ancestors
def get_path_to_ancestor(self, ancestor):
"""
Return the path from self to ancestor as a list
output format: [self, ..., ancestor]
"""
path = []
parent = self
try:
while True:
path.append(parent)
if parent is ancestor:
break
else:
parent = parent.parent
except AttributeError:
return None
return path
def get_path_to(self, other):
"""
Return the path from self to other as a list
output format: [self, ..., first common acestor, ..., other]
"""
common_ancestors = self.get_ancestors() & other.get_ancestors()
first_common_ancestor = {
a for a in common_ancestors
if a.left not in common_ancestors and a.right not in common_ancestors
}.pop()
return self.get_path_to_ancestor(first_common_ancestor)\
+ list(reversed(other.get_path_to_ancestor(first_common_ancestor)))[1:]
以下是它如何應用於您作為示例提供的樹。
tree = Tree(
6,
Tree(4,
Tree(1),
Tree(3)),
Tree(0,
Tree(1)))
nodes = list(tree)
for i in range(len(nodes)):
for j in range(i + 1, len(nodes)):
print([t for t in nodes[i].get_path_to(nodes[j])])
這是打印的所有路徑。
[1, 4]
[1, 4, 3]
[1, 4, 6]
[1, 4, 6, 0, 1]
[1, 4, 6, 0]
[4, 3]
[4, 6]
[4, 6, 0, 1]
[4, 6, 0]
[3, 4, 6]
[3, 4, 6, 0, 1]
[3, 4, 6, 0]
[6, 0, 1]
[6, 0]
[1, 0]
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