{
  my @untested_blocks;
  my @needed_paths;

  sub test_all_paths {
    @needed_paths = @untested_blocks = ();
    _test_all_paths(@_);
    return @needed_paths;
  }

  sub _test_all_paths {
    my @to_test = @_;

    return unless @to_test;

    # Mark the first half as not to test.
    push @untested_blocks, [splice @to_test, 0, int(@to_test/2)];

    # Find needed blocks in second half recursively
    if (not path_works( (map @$_, @untested_blocks), @needed_paths ) {
      if (1 == @to_test) {
        push @needed_paths, @to_test;
      }
      else {
        _test_all_paths(@to_test);
      }
    }

    # Find needed paths in the untested block we just added
    _test_all_paths( @{ pop @untested_blocks } );
  }
}