1. Introduction

An algorithm is any well-defined computational procedure that takes some value or a set of values as input, and produces some value or a set of values as output.（一个程序有输入也有输出，并且输出是固定的。）

Analysis of an algorithm is to predict the resources that the algorithm requires. Resources are measured in relation to a model of computation, which is a mathematical abstraction of a computer on which the algorithm is implemented.

常见的resource：
RAM: time and space (traditional computers)
PRAM: parallel running time, number of processors, and read-and-write restrictions
Message Passing Model: communication cost (number of messages), and computational cost
Turing Machine: time and space

重要的概念：
Input size

Running time: The running time of an algorithm on a particular input is the number of primitive operations or steps executed.
Unless otherwise specified, we shall concentrate on finding only the worst case running time.

Order of growth: To simplify the analysis of algorithms, we are interested in the growth rate of the running time, i.e., we only consider the leading term of a time formula.
n^2 in the expression n^2 + 100n + 5000.

分治策略###

Divide-and-Conquer (D&C) Paradigm
Steps：

1. Divide A into a number of subproblems with equal size roughly.
2. Conquer the subproblems by solving them recursively. For small enough subproblems, solve them directly without dividing them further.
3. Combine the solutions of the subproblems into the solution of the original problem.