前序遍历树

摘要：前序输出从这一路下来，有两个是正确的，如果先判断要遍历的节点是否已经遍历过的话，那么就走不通了，所以应该允许，点到就记一次输出，再来判断是否能继续往下走。

代码来自：pickle and cPickle – Python object serialization
首先树的结构，如图

import pickle

class Node(object):
    """A simple digraph where each node knows about the other nodes
    it leads to.
    """
    def __init__(self, name):
        self.name = name
        self.connections = []
        return

    def add_edge(self, node):
        "Create an edge between this node and the other."
        self.connections.append(node)
        return

    def __iter__(self):
        return iter(self.connections)

def preorder_traversal(root, seen=None, parent=None):
    """Generator function to yield the edges via a preorder traversal."""
    if seen is None:
        seen = set()
    yield (parent, root)
    if root in seen:
        return
    seen.add(root)
    for node in root:
        for (parent, subnode) in preorder_traversal(node, seen, root):
            yield (parent, subnode)
    return

def show_edges(root):
    "Print all of the edges in the graph."
    for parent, child in preorder_traversal(root):
        if not parent:
            continue
        print "%5s -> %2s (%s)" % (parent.name, child.name, id(child))

# Set up the nodes.
root = Node("root")
a = Node("a")
b = Node("b")
c = Node("c")

# Add edges between them.
root.add_edge(a)
root.add_edge(b)
a.add_edge(b)
b.add_edge(a)
b.add_edge(c)
a.add_edge(a)

print "ORIGINAL GRAPH:"
show_edges(root)

# Pickle and unpickle the graph to create
# a new set of nodes.
dumped = pickle.dumps(root)
reloaded = pickle.loads(dumped)

print
print "RELOADED GRAPH:"
show_edges(reloaded)

输出结果：

$ python pickle_cycle.py

ORIGINAL GRAPH:
 root ->  a (4299721744)
    a ->  b (4299721808)
    b ->  a (4299721744)
    b ->  c (4299721872)
    a ->  a (4299721744)
 root ->  b (4299721808)

RELOADED GRAPH:
 root ->  a (4299722000)
    a ->  b (4299722064)
    b ->  a (4299722000)
    b ->  c (4299722128)
    a ->  a (4299722000)
 root ->  b (4299722064)

其中preorder_traversal是生成器。这里记录下生成器方法的每一步的意思。

# root 要遍历的根节点
# seen 保存遍历过的节点（集合）
# parent 每次yield的父节点，有可能不存在
def preorder_traversal(root, seen=None, parent=None):
    """Generator function to yield the edges via a preorder traversal."""
    if seen is None: # 如果没有开始遍历，seen是空，初始化集合
        seen = set()
    yield (parent, root) # 记一次输出，这个要在下面判断之前
    if root in seen: # 要遍历的根节点是否已经遍历过，防止循环遍历
        return
    seen.add(root) # 保存已遍历的“根”节点
    for node in root: # 遍历子节点
        for (parent, subnode) in preorder_traversal(node, seen, root):
            yield (parent, subnode)
    return

一开始不明白的地方是这样

    yield (parent, root) # 记一次输出，这个要在下面判断之前
    if root in seen: # 要遍历的根节点是否已经遍历过，防止循环遍历
        return

为什么不是先判断呢。
看循环引用的情况。
前序输出从root -> a -> b -> a这一路下来，有两个a是正确的，
如果先判断要遍历的节点是否已经遍历过的话，那么
b -> a就走不通了，所以应该允许，点到就记一次输出，再来判断是否能继续往下走。
b -> a记一次输出，接下来发现a已经遍历过它的子节点了(a in seen)，才停止不往下遍历。