  One of the main quests in quantum metrology is to attain the ultimate
precision limit with given resources, where the resources are not only of the
number of queries, but more importantly of the allowed strategies. With the
same number of queries, the restrictions on the strategies constrain the
achievable precision. In this work, we establish a systematic framework to
identify the ultimate precision limit of different families of strategies,
including the parallel, the sequential, and the indefinite-causal-order
strategies, and provide an efficient algorithm that determines an optimal
strategy within the family of strategies under consideration. With our
framework, we show there exists a strict hierarchy of the precision limits for
different families of strategies.
