I am from China, and I grew up in an environment where you need to solve sometimes tedious problems repeatedly to proficiency. This ensures that one will excel in the important exam that determines many aspects of a Chinese’s life: the Gaokao. Two important philosophies helped me survive those days: “举一反三” (jǔ yī fǎn sān) and “融会贯通” (róng huì guàn tōng).

“举一反三” (jǔ yī fǎn sān) means “from one example, deduce solutions for many other problems.” This emphasizes the concept of applying a solution or understanding from one specific problem to a variety of other, related problems, which is a fundamental skill in algorithmic thinking and problem-solving.

“融会贯通” (róng huì guàn tōng) means “integrate knowledge and achieve a thorough understanding.” This suggests not only learning various algorithms and concepts but also synthesizing them into a comprehensive, interconnected understanding, crucial in algorithm design and application.

You can see these ideas reflected in my lab and homework assignments:

• Understanding an algorithm means you can generalize it.
• Understanding an algorithm means you can adapt it to different, perhaps non-classical, scenarios.
• Understanding an algorithm means you can integrate it with other methods to solve bigger problems.
• Understanding an algorithm means you can reinvent it.