如何用改进的DFS算法遍历循环有向图

Question

概述

我试图找出如何使用某种DFS迭代算法遍历有向循环图.这是我目前实现的一个小版本(它不涉及周期):

class Node(object):

    def __init__(self, name):
        self.name = name

    def start(self):
        print '{}_start'.format(self)

    def middle(self):
        print '{}_middle'.format(self)

    def end(self):
        print '{}_end'.format(self)

    def __str__(self):
        return "{0}".format(self.name)


class NodeRepeat(Node):

    def __init__(self, name, num_repeats=1):
        super(NodeRepeat, self).__init__(name)
        self.num_repeats = num_repeats


def dfs(graph, start):
    """Traverse graph from start node using DFS with reversed childs"""

    visited = {}
    stack = [(start, "")]
    while stack:
        # To convert dfs -> bfs
        # a) rename stack to queue
        # b) pop becomes pop(0)
        node, parent = stack.pop()
        if parent is None:
            if visited[node] < 3:
                node.end()
            visited[node] = 3
        elif node not in visited:
            if visited.get(parent) == 2:
                parent.middle()
            elif visited.get(parent) == 1:
                visited[parent] = 2

            node.start()
            visited[node] = 1

            stack.append((node, None))

            # Maybe you want a different order, if it's so, don't use reversed
            childs = reversed(graph.get(node, []))
            for child in childs:
                if child not in visited:
                    stack.append((child, node))


if __name__ == "__main__":
    Sequence1 = Node('Sequence1')
    MtxPushPop1 = Node('MtxPushPop1')
    Rotate1 = Node('Rotate1')
    Repeat1 = NodeRepeat('Repeat1', num_repeats=2)

    Sequence2 = Node('Sequence2')
    MtxPushPop2 = Node('MtxPushPop2')
    Translate = Node('Translate')
    Rotate2 = Node('Rotate2')
    Rotate3 = Node('Rotate3')
    Scale = Node('Scale')
    Repeat2 = NodeRepeat('Repeat2', num_repeats=3)
    Mesh = Node('Mesh')

    cyclic_graph = {
        Sequence1: [MtxPushPop1, Rotate1],
        MtxPushPop1: [Sequence2],
        Rotate1: [Repeat1],
        Sequence2: [MtxPushPop2, Translate],
        Repeat1: [Sequence1],
        MtxPushPop2: [Rotate2],
        Translate: [Rotate3],
        Rotate2: [Scale],
        Rotate3: [Repeat2],
        Scale: [Mesh],
        Repeat2: [Sequence2]
    }

    dfs(cyclic_graph, Sequence1)

    print '-'*80

    a = Node('a')
    b = Node('b')
    dfs({
        a : [b],
        b : [a]
    }, a)

上面的代码测试了几个案例,第一个是下图的某种表示:

第二个是一个包含一个"无限"循环的图的最简单的情况 {a->b, b->a}

要求

• 不存在诸如"无限循环"之类的东西,假设当找到一个"无限循环"时,将会有一个最大阈值(全局变量)来指示何时停止在那些"伪无限循环"周围循环
• 所有图形节点都能够创建循环,但是会存在一个特殊的节点Repeat,您可以在其中指示循环循环的迭代次数
• 我发布的上述mcve是遍历算法的迭代版本,它不知道如何处理循环图.理想情况下,解决方案也是迭代的,但如果存在更好的递归解决方案,那就太好了
• 我们在这里讨论的数据结构不应该被称为"有向非循环图",因为在这种情况下,每个节点都有其子节点,而在图中节点连接没有顺序.
• 一切都可以连接到编辑器中的任何内容.您将能够执行任何块组合,唯一的限制是执行计数器,如果您进行了无限循环或过多的迭代,它将会溢出.
• 算法将保留开始/中间/后节点的方法执行,类似于上面的代码片段

题

任何人都可以提供某种知道如何遍历无限/有限循环的解决方案吗？

参考

如果问题还不清楚在这一点上,你可以阅读更多有关这对这个问题的文章,整个构思将使用遍历算法来实现这样的文章中所示的类似的工具.

这是一个屏幕截图,显示了这种数据结构的全部功能我想弄清楚如何遍历和运行:

Answer 1

在开始之前,在CodeSkulptor上运行代码!我也希望这些评论能够详细阐述我的成就.如果您需要更多解释,请查看我对代码下面的递归方法的解释.

# If you don't want global variables, remove the indentation procedures
indent = -1

MAX_THRESHOLD = 10
INF = 1 << 63

def whitespace():
    global indent
    return '|  ' * (indent)

class Node:
    def __init__(self, name, num_repeats=INF):
        self.name = name
        self.num_repeats = num_repeats

    def start(self):
        global indent
        if self.name.find('Sequence') != -1:
            print whitespace()
            indent += 1
        print whitespace() + '%s_start' % self.name

    def middle(self):
        print whitespace() + '%s_middle' % self.name

    def end(self):
        global indent
        print whitespace() + '%s_end' % self.name
        if self.name.find('Sequence') != -1:
            indent -= 1
            print whitespace()

def dfs(graph, start):
    visits = {}
    frontier = [] # The stack that keeps track of nodes to visit

    # Whenever we "visit" a node, increase its visit count
    frontier.append((start, start.num_repeats))
    visits[start] = visits.get(start, 0) + 1

    while frontier:
        # parent_repeat_count usually contains vertex.repeat_count
        # But, it may contain a higher value if a repeat node is its ancestor
        vertex, parent_repeat_count = frontier.pop()

        # Special case which signifies the end
        if parent_repeat_count == -1:
            vertex.end()
            # We're done with this vertex, clear visits so that 
            # if any other node calls us, we're still able to be called
            visits[vertex] = 0
            continue

        # Special case which signifies the middle
        if parent_repeat_count == -2:
            vertex.middle()
            continue  

        # Send the start message
        vertex.start()

        # Add the node's end state to the stack first
        # So that it is executed last
        frontier.append((vertex, -1))

        # No more children, continue
        # Because of the above line, the end method will
        # still be executed
        if vertex not in graph:
            continue

        ## Uncomment the following line if you want to go left to right neighbor
        #### graph[vertex].reverse()

        for i, neighbor in enumerate(graph[vertex]):
            # The repeat count should propagate amongst neighbors
            # That is if the parent had a higher repeat count, use that instead
            repeat_count = max(1, parent_repeat_count)
            if neighbor.num_repeats != INF:
                repeat_count = neighbor.num_repeats

            # We've gone through at least one neighbor node
            # Append this vertex's middle state to the stack
            if i >= 1:
                frontier.append((vertex, -2))

            # If we've not visited the neighbor more times than we have to, visit it
            if visits.get(neighbor, 0) < MAX_THRESHOLD and visits.get(neighbor, 0) < repeat_count:
                frontier.append((neighbor, repeat_count))
                visits[neighbor] = visits.get(neighbor, 0) + 1

def dfs_rec(graph, node, parent_repeat_count=INF, visits={}):
    visits[node] = visits.get(node, 0) + 1

    node.start()

    if node not in graph:
        node.end()
        return

    for i, neighbor in enumerate(graph[node][::-1]):
        repeat_count = max(1, parent_repeat_count)
        if neighbor.num_repeats != INF:
            repeat_count = neighbor.num_repeats

        if i >= 1:
            node.middle()

        if visits.get(neighbor, 0) < MAX_THRESHOLD and visits.get(neighbor, 0) < repeat_count:
            dfs_rec(graph, neighbor, repeat_count, visits)

    node.end()  
    visits[node] = 0

Sequence1 = Node('Sequence1')
MtxPushPop1 = Node('MtxPushPop1')
Rotate1 = Node('Rotate1')
Repeat1 = Node('Repeat1', 2)

Sequence2 = Node('Sequence2')
MtxPushPop2 = Node('MtxPushPop2')
Translate = Node('Translate')
Rotate2 = Node('Rotate2')
Rotate3 = Node('Rotate3')
Scale = Node('Scale')
Repeat2 = Node('Repeat2', 3)
Mesh = Node('Mesh')

cyclic_graph = {
        Sequence1: [MtxPushPop1, Rotate1],
        MtxPushPop1: [Sequence2],
        Rotate1: [Repeat1],
        Sequence2: [MtxPushPop2, Translate],
        Repeat1: [Sequence1],
        MtxPushPop2: [Rotate2],
        Translate: [Rotate3],
        Rotate2: [Scale],
        Rotate3: [Repeat2],
        Scale: [Mesh],
        Repeat2: [Sequence2]
    }

dfs(cyclic_graph, Sequence1)

print '-'*40

dfs_rec(cyclic_graph, Sequence1)

print '-'*40

dfs({Sequence1: [Translate], Translate: [Sequence1]}, Sequence1)

print '-'*40

dfs_rec({Sequence1: [Translate], Translate: [Sequence1]}, Sequence1)

输入和(格式良好和缩进)输出可以在这里找到.如果您想查看我如何格式化输出,请参阅代码,该代码也可以在CodeSkulptor上找到.

对,解释.更容易理解但更低效的递归解决方案,我将用它来帮助解释,如下:

def dfs_rec(graph, node, parent_repeat_count=INF, visits={}):
    visits[node] = visits.get(node, 0) + 1

    node.start()

    if node not in graph:
        node.end()
        return

    for i, neighbor in enumerate(graph[node][::-1]):
        repeat_count = max(1, parent_repeat_count)
        if neighbor.num_repeats != INF:
            repeat_count = neighbor.num_repeats

        if i >= 1:
            node.middle()

        if visits.get(neighbor, 0) < MAX_THRESHOLD and visits.get(neighbor, 0) < repeat_count:
            dfs_rec(graph, neighbor, repeat_count, visits)

    node.end()  
    visits[node] = 0

1. 我们要做的第一件事是访问节点.我们通过增加字典中节点的访问次数来完成此操作.
2. 然后我们引发start节点的事件.
3. 我们做一个简单的检查,看看节点是否是无子(叶)节点.如果是,我们举起end活动并返回.
4. 现在我们已经确定节点有邻居,我们遍历每个邻居.注意:我graph[node][::-1]在递归版本中反转邻居列表(通过使用)以维持邻居遍历的相同顺序(从右到左),如在迭代版本中那样.
   1. 对于每个邻居,我们首先计算重复计数.重复计数从祖先节点传播(继承),因此除非邻居包含重复计数值,否则将使用继承的重复计数.
   2. 如果正在处理第二个(或更高)邻居,则引发middle当前节点(不是邻居)的事件.
   3. 如果可以访问邻居,则访问邻居.通过检查邻居是否被访问少于a MAX_THRESHOLD次(对于伪无限循环)和b)上述计算的重复计数次数来完成可访问性检查.
5. 我们现在已经完成了这个节点; 提升end事件并在哈希表中清除其访问.这样做是为了如果某个其他节点再次调用它,则它不会使可访问性检查失败和/或执行少于所需的次数.