Macroscopic assembly offers immense potential for constructing complex systems due to the high design flexibility of the building blocks. In such assembly systems, hydrogels are promising candidates for building blocks due to their versatile chemical compositions and ease of property tuning. However, two major challenges must be addressed to facilitate application in a broader context: the precision of assembly and the quantity of orthogonally matching pairs must both be increased. Although previous studies have attempted to address these challenges, none have successfully dealt with both simultaneously. Here, we propose topology-based design criteria for the selective assembly of hydrogel building blocks. By introducing the dual lock-and-key structures, we demonstrate highly precise assembly exclusively between the matching pairs. We establish principles for selecting multiple orthogonally matching pairs and achieve selective assembly involving simple one-to-one matching and complex assemblies with multiple orthogonal matching points. Moreover, by harnessing hydrogel tunability and the abundance of matching pairs, we synthesize complementary single-stranded structures for programmable assembly and successfully assemble them in the correct order. Finally, we demonstrate a hydrogel-based self-assembled logic gate system, including a YES gate, an OR gate, and an AND gate. The output is generated only when the corresponding inputs are provided according to each logic.