不要求，讲数据结构时，参考一下。

In computer science, a linked list is a linear collection of data elements, in which linear order is not given by their physical placement in memory. Instead, each element points to the next. It is a data structure consisting of a group of nodes which together represent a sequence. 

In computability theory, the halting problem is the problem of determining, from a description of an arbitrary computer program and an input, whether the program will finish running (i.e., halt) or continue to run forever.

Alan Turing proved in 1936 that a general algorithm to solve the halting problem for all possible program-input pairs cannot exist. A key part of the proof was a mathematical definition of a computer and program, which became known as a Turing machine; the halting problem is undecidable over Turing machines. It is one of the first examples of a decision problem.

A Turing machine is a mathematical model of computation that defines an abstract machine, which manipulates symbols on a strip of tape according to a table of rules. Despite the model's simplicity, given any computer algorithm, a Turing machine capable of simulating that algorithm's logic can be constructed.

The Turing machine was invented in 1936 by Alan Turing, who called it an a-machine (automatic machine).

With this model, Turing was able to answer two questions in the negative: (1) Does a machine exist that can determine whether any arbitrary machine on its tape is "circular" (e.g., freezes, or fails to continue its computational task); similarly, (2) does a machine exist that can determine whether any arbitrary machine on its tape ever prints a given symbol. Thus by providing a mathematical description of a very simple device capable of arbitrary computations, he was able to prove properties of computation in general—and in particular, the uncomputability of the Entscheidungsproblem ("decision problem").

Thus, Turing machines prove fundamental limitations on the power of mechanical computation.

Stack (abstract data type)

In computer science, a stack is an abstract data type that serves as a collection of elements, with two principal operations:

• push, which adds an element to the collection, and
• pop, which removes the most recently added element that was not yet removed.

1，Easy and Hard for Persons

• 会者不难，难者不会。
• 人不会，计算机必然不会。

2，Easy and Hard for Computers

• 算得快还是慢，算上十年跟不会算一样。

3，Problems

• 3.1，乘法，计算，easy
• 3.2，因子分解，把n分解成因子的乘积，n=a×b， hard

Big-O notation

计算时间和问题大小的关系。

• \(O(n)\)，线性的,
• \(O(\log n)\)，对数级的，
• \(O(n^2)\)，平方级的，
• \(O(2^n)\)，指数级的，

Execution in computer and software engineering is the process by which a computer or virtual machine reads and acts on the instructions of a computer program. Each instruction of a program is a description of a particular action which must be carried out, in order for a specific problem to be solved. Execution involves repeatedly following a 'fetch–decode–execute' cycle for each instruction. As the executing machine follows the instructions, specific effects are produced in accordance with the semantics of those instructions.

In computer science, divide and conquer is an algorithm design paradigm based on multi-branched recursion. A divide-and-conquer algorithm works by recursively breaking down a problem into two or more sub-problems of the same or related type, until these become simple enough to be solved directly. The solutions to the sub-problems are then combined to give a solution to the original problem.

Table Lookup, Googling, .....

Mathematical tables are lists of numbers showing the results of a calculation with varying arguments. 

• Tables of trigonometric functions were used in ancient Greece and India for applications to astronomy and celestial navigation. They continued to be widely used until electronic calculators became cheap and plentiful, in order to simplify and drastically speed up computation.
• Tables of logarithms and trigonometric functions were common in math and science textbooks, and specialized tables were published for numerous applications.

In computing and telecommunications, a unit of information is the capacity of some standard data storage system or communication channel, used to measure the capacities of other systems and channels. In information theory, units of information are also used to measure the entropy of random variables and information contained in messages.

In mathematics and computing, the method of complements is a technique used to subtract one number from another using only addition of positive numbers. This method was commonly used in mechanical calculators and is still used in modern computers.