from typing import Set

# Implement the ‘mark’ phase of a mark & sweep collector. That is,
# find all objects which are reachable from the root set.
#
# Like before, roots are marked using ‹add_root› and references are
# added/removed using ‹add_ref› and ‹del_ref›. You can assume that
# the number of ‹del_ref› calls on given arguments is always at most
# the same as the number of corresponding ‹add_ref› calls.

class Heap:
    def add_root( self, obj: int ) -> None: pass
    def add_ref( self, obj_from: int, obj_to: int ) -> None: pass
    def del_ref( self, obj_from: int, obj_to: int ) -> None: pass
    def reachable( self ) -> Set[ int ]: pass

def test_basic() -> None:
    h = Heap()
    assert h.reachable() == set()
    h.add_root( 1 )
    assert h.reachable() == { 1 }
    h.add_ref( 1, 2 )
    assert h.reachable() == { 1, 2 }
    h.add_ref( 1, 3 )
    assert h.reachable() == { 1, 2, 3 }
    h.add_ref( 2, 3 )
    assert h.reachable() == { 1, 2, 3 }
    h.add_ref( 3, 4 )
    h.add_ref( 4, 3 )
    assert h.reachable() == { 1, 2, 3, 4 }
    h.del_ref( 1, 3 )
    assert h.reachable() == { 1, 2, 3, 4 }
    h.del_ref( 1, 2 )
    assert h.reachable() == { 1 }

if __name__ == '__main__':
    test_basic()