def bintree(ids, parent=None):
    """construct {child:parent} dict representation of a binary tree
    
    keys are the nodes in the tree, and values are the parent of each node.
    
    The root node has parent `parent`, default: None.
    
    >>> tree = bintree(range(7))
    >>> tree
    {0: None, 1: 0, 2: 1, 3: 1, 4: 0, 5: 4, 6: 4}
    >>> print_bintree(tree)
    0
      1
        2
        3
      4
        5
        6
    """
    parents = {}
    n = len(ids)
    if n == 0:
        return parents
    root = ids[0]
    parents[root] = parent
    if len(ids) == 1:
        return parents
    else:
        ids = ids[1:]
        n = len(ids)
        left = bintree(ids[:n//2], parent=root)
        right = bintree(ids[n//2:], parent=root)
        parents.update(left)
        parents.update(right)
    return parents