pyobjc / build-support /

Module defining a topological sort function, see 
<> for more

Original topological sort code written by Ofer Faigon ( and used with permission

def topological_sort(items, partial_order):
    Perform topological sort.
    items is a list of items to be sorted.
    partial_order is a list of pairs. If pair (a,b) is in it, it means
    that item a should appear before item b.
    Returns a list of the items in one of the possible orders, or None
    if partial_order contains a loop.

    def add_node(graph, node):
        """Add a node to the graph if not already exists."""
        if node not in graph:
            graph[node] = [0] # 0 = number of arcs coming into this node.

    def add_arc(graph, fromnode, tonode):
        """Add an arc to a graph. Can create multiple arcs.
           The end nodes must already exist."""
        # Update the count of incoming arcs in tonode.
        graph[tonode][0] += 1

    # step 1 - create a directed graph with an arc a->b for each input
    # pair (a,b).
    # The graph is represented by a dictionary. The dictionary contains
    # a pair item:list for each node in the graph. /item/ is the value
    # of the node. /list/'s 1st item is the count of incoming arcs, and
    # the rest are the destinations of the outgoing arcs. For example:
    #           {'a':[0,'b','c'], 'b':[1], 'c':[1]}
    # represents the graph:   c <-- a --> b
    # The graph may contain loops and multiple arcs.
    # Note that our representation does not contain reference loops to
    # cause GC problems even when the represented graph contains loops,
    # because we keep the node names rather than references to the nodes.
    graph = {}
    for v in items:
        add_node(graph, v)
    for a,b in partial_order:
        add_arc(graph, a, b)

    # Step 2 - find all roots (nodes with zero incoming arcs).
    roots = [node for (node,nodeinfo) in graph.items() if nodeinfo[0] == 0]

    # step 3 - repeatedly emit a root and remove it from the graph. Removing
    # a node may convert some of the node's direct children into roots.
    # Whenever that happens, we append the new roots to the list of
    # current roots.
    sorted = []
    while len(roots) != 0:
        # If len(roots) is always 1 when we get here, it means that
        # the input describes a complete ordering and there is only
        # one possible output.
        # When len(roots) > 1, we can choose any root to send to the
        # output; this freedom represents the multiple complete orderings
        # that satisfy the input restrictions. We arbitrarily take one of
        # the roots using pop(). Note that for the algorithm to be efficient,
        # this operation must be done in O(1) time.
        root = roots.pop()
        for child in graph[root][1:]:
            graph[child][0] = graph[child][0] - 1
            if graph[child][0] == 0:
        del graph[root]
    if len(graph.items()) != 0:
        # There is a loop in the input.
        return None
    return sorted