Topological sorting

最新推荐文章于 2025-08-19 14:43:05 发布

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#算法 #dfs

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本文介绍了图论中两种重要的排序算法：Kahn算法和深度优先搜索（DFS）算法。Kahn算法通过找到所有没有入边的节点开始，逐步移除这些节点及它们的出边，最终实现拓扑排序。而DFS算法则通过递归地访问每个节点的所有邻接节点，为每个节点标记状态，以确保不会出现环状结构。

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algorithm

Kahn algorithm

L ← Empty list that will contain the sorted elements
S ← Set of all nodes with no incoming edges
while S is non-empty do
    remove a node n from S
    add n to tail of L
    for each node m with an edge e from n to m do
        remove edge e from the graph
        if m has no other incoming edges then
            insert m into S
if graph has edges then
    return error (graph has at least one cycle)
else 
    return L (a topologically sorted order)

dfs algorithm

L ← Empty list that will contain the sorted nodes
while there are unmarked nodes do
    select an unmarked node n
    visit(n)

function visit(node n)
    if n has a temporary mark then stop (not a DAG)
    if n is not marked (i.e. has not been visited yet) then
        mark n temporarily
        for each node m with an edge from n to m do
            visit(m)
        mark n permanently
        unmark n temporarily
        add n to head of L