将有向图按拓扑排序到不相交的子图的存储桶中 [英] Topologically sort directed graph into buckets for disjoint sub graphs

问题描述

我正在寻找一种算法，该算法可以对图形进行拓扑排序，从而生成一组列表，每个列表包含不相交子图的拓扑排序顶点.

I am looking for an algorithm which can take a graph and topologically sort it such that it produces a set of lists, each which contains the topologically sorted vertices of a disjoint subgraph.

当节点依赖两个不同列表中的节点时，困难的部分是合并列表.

The difficult part is merging the lists when a node depends on a node in two different lists.

这是我不完整的代码/伪代码，其中graph是字典 {node:[node，node，...]}}

Here is my incomplete code/pseudocode where graph is a dict {node: [node, node, ...]}

sorted_subgraphs = []

while graph:
    cyclic = True
    for node, edges in list(graph.items()):
        for edge in edges:
            if edge in graph:
                break
        else:
            del graph[node]
            cyclic = False

            sub_sorted = []
            for edge in edges:
                bucket.extend(...) # Get the list with edge in it, and remove it from sorted_subgraphs
            bucket.append(node)

            sorted_subgraphs.append(bucket)

    if cyclic:
        raise Exception('Cyclic graph')

推荐答案

首先使用泛洪填充算法将其划分为不相交的子图，然后对每个图进行拓扑排序.

First divide it into disjoint subgraphs using a flood fill algorithm, and then topologically sort each one.

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