def reverse_bintree(parents):
    """construct {parent:[children]} dict from {child:parent}
    
    keys are the nodes in the tree, and values are the lists of children
    of that node in the tree.
    
    reverse_tree[None] is the root node
    
    >>> tree = bintree(range(7))
    >>> reverse_bintree(tree)
    {None: 0, 0: [1, 4], 4: [5, 6], 1: [2, 3]}
    """
    children = {}
    for child, parent in parents.iteritems():
        if parent is None:
            children[None] = child
            continue
        elif parent not in children:
            children[parent] = []
        children[parent].append(child)
    return children
