1.3 Summary¶
1. Key Review¶
- Algorithms are ubiquitous in daily life and are not some distant, esoteric body of knowledge. In fact, we have already learned many algorithms unconsciously and use them to solve problems big and small in life.
- The principle of looking up a dictionary is consistent with the binary search algorithm. Binary search embodies the important algorithmic idea of divide and conquer.
- The process of organizing playing cards is very similar to the insertion sort algorithm. Insertion sort is suitable for sorting small datasets.
- The steps of making change are essentially a greedy algorithm, where the best choice is made at each step based on the current situation.
- An algorithm is a set of instructions or operational steps that solves a specific problem within a finite amount of time, while a data structure is a way of organizing and storing data in a computer.
- Data structures and algorithms are closely connected. Data structures are the foundation of algorithms, and algorithms breathe life into data structures.
- We can compare data structures and algorithms to assembling building blocks. The blocks represent data, the way they are shaped and connected represents the data structure, and the steps used to assemble them correspond to the algorithm.
2. Q & A¶
Q: As a programmer, I have never used algorithms to solve problems in my daily work. Common algorithms are already encapsulated by programming languages and can be used directly. Does this mean that the problems in our work have not yet reached the level where algorithms are needed?
If we compare specific work skills to "techniques" in martial arts, then fundamental subjects should be more like "internal skills".
I believe the significance of learning algorithms (and other fundamental subjects) is not that you will need to implement them from scratch at work, but that the knowledge you gain enables you to make sound professional judgments when solving problems, thereby improving the overall quality of your work. Here is a simple example. Every programming language has a built-in sorting function:
- If we have not studied data structures and algorithms, we might simply feed any given data to this sorting function. It runs smoothly with good performance, and there doesn't seem to be any problem.
- But if we have studied algorithms, we would know that the time complexity of the built-in sorting function is \(O(n \log n)\). However, if the given data consists of integers with a fixed number of digits (such as student IDs), we can use the more efficient "radix sort", reducing the time complexity to \(O(nk)\), where \(k\) is the number of digits. When the data volume is very large, the saved running time can create significant value (reduced costs, improved experience, etc.).
In engineering, many problems are difficult to solve optimally, and many others are only solved "well enough." The difficulty of a problem depends, on the one hand, on the nature of the problem itself and, on the other hand, on the knowledge of the person examining it. The more complete a person's knowledge and the more experience they have, the deeper their analysis will be, and the more elegantly the problem can be solved.
Q: Now that we let AI agents write almost all our code, do we still need to learn algorithms?
To quote Mu Li: “An agent is an amplifier of ability—it multiplies your ability by 10, rather than adding 10 to it.”
Since AI amplifies our abilities, the abilities being multiplied matter too. I think two abilities are especially worth developing. The first is communication, particularly the ability to work with AI: making goals clear, providing the necessary context, and correcting course in time. Explaining a problem to AI also helps us think it through ourselves. The second is foundational knowledge. AI can fill in the details, but we need to understand the basic concepts ourselves to ask the right questions, judge whether answers are correct, and turn its output into useful results.
One distinctive thing about AI is that, unlike earlier tools, it does not have clearly defined functional boundaries. It is a little like water, taking different shapes in different people's hands. The greater a person's abilities and the better their taste, the more pronounced AI's amplifying effect becomes.