Python编程入门：计算与问题解决指南

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ACKNOWLEDGMENTS

This book grew out of a set of lecture notes that I prepared while teaching an

undergraduate course at MIT. The course, and therefore this book, benefited

from suggestions from faculty colleagues (especially Eric Grimson, Srinivas

Devadas, and Fredo Durand), teaching assistants, and the students who took

the course.

The process of transforming my lecture notes into a book proved far more

onerous than I had expected. Fortunately, this misguided optimism lasted long

enough to keep me from giving up. The encouragement of colleagues and family

also helped keep me going.

Eric Grimson, Chris Terman, and David Guttag provided vital help. Eric, who is

MIT’s Chancellor, managed to find the time to read almost the entire book with

great care. He found numerous errors (including an embarrassing, to me,

number of technical errors) and pointed out places where necessary

explanations were missing. Chris also read parts of the manuscript and

discovered errors. He also helped me battle Microsoft Word, which we

eventually persuaded to do most of what we wanted. David overcame his

aversion to computer science, and proofread multiple chapters.

Preliminary versions of this book were used in the MIT course 6.00 and the MITx

course 6.00x. A number of students in these courses pointed out errors. One

6.00x student, J.C. Cabrejas, was particularly helpful. He found a large number

of typos, and more than a few technical errors.

Like all successful professors, I owe a great deal to my graduate students. The

photo on the back cover of this book depicts me supporting some of my current

students. In the lab, however, it is they who support me. In addition to doing

great research (and letting me take some of the credit for it), Guha

Balakrishnan, Joel Brooks, Ganeshapillai Gartheeban, Jen Gong, Yun Liu,

Anima Singh, Jenna Wiens, and Amy Zhao all provided useful comments on this

manuscript.

I owe a special debt of gratitude to Julie Sussman, P.P.A. Until I started working

with Julie, I had no idea how much difference an editor could make. I had

worked with capable copy editors on previous books, and thought that was what

I needed for this book. I was wrong. I needed a collaborator who could read the

book with the eyes of a student, and tell me what needed to be done, what

should be done, and what could be done if I had the time and energy to do it.

Julie buried me in “suggestions” that were too good to ignore. Her combined

command of both the English language and programming is quite remarkable.

Finally, thanks to my wife, Olga, for pushing me to finish and for pitching in at

critical times.

1 GETTING STARTED

A computer does two things, and two things only: it performs calculations and it

remembers the results of those calculations. But it does those two things

extremely well. The typical computer that sits on a desk or in a briefcase

performs a billion or so calculations a second. It’s hard to image how truly fast

that is. Think about holding a ball a meter above the floor, and letting it go. By

the time it reaches the floor, your computer could have executed over a billion

instructions. As for memory, a typical computer might have hundreds of

gigabytes of storage. How big is that? If a byte (the number of bits, typically

eight, required to represent one character) weighed one ounce (which it doesn’t),

100 gigabytes would weigh more than 3,000,000 tons. For comparison, that’s

roughly the weight of all the coal produced in a year in the U.S.

For most of human history, computation was limited by the speed of calculation

of the human brain and the ability to record computational results with the

human hand. This meant that only the smallest problems could be attacked

computationally. Even with the speed of modern computers, there are still

problems that are beyond modern computational models (e.g., understanding

climate change), but more and more problems are proving amenable to

computational solution. It is our hope that by the time you finish this book, you

will feel comfortable bringing computational thinking to bear on solving many of

the problems you encounter during your studies, work, and even everyday life.

What do we mean by computational thinking?

All knowledge can be thought of as either declarative or imperative. Declarative

knowledge is composed of statements of fact. For example, “the square root of x

is a number y such that y

y = x.” This is a statement of fact. Unfortunately it

doesn’t tell us how to find a square root.

Imperative knowledge is “how to” knowledge, or recipes for deducing

information. Heron of Alexandria was the first to document a way to compute

the square root of a number.

His method can be summarized as:

• Start with a guess, g.

• If g

g is close enough to x, stop and say that g is the answer.

• Otherwise create a new guess by averaging g and x/g, i.e., (g + x/g)/2.

• Using this new guess, which we again call g, repeat the process until g

is close enough to x.

Many believe that Heron was not the inventor of this method, and indeed there is some

evidence that it was well known to the ancient Babylonians.

2 Chapter 1. Getting Started

Consider, for example, finding the square root of 25.

1. Set g to some arbitrary value, e.g., 3.

2. We decide that 3

3 = 9 is not close enough to 25.

3. Set g to (3 + 25/3)/2 = 5.67.

4. We decide that 5.67

5.67 = 32.15 is still not close enough to 25.

5. Set g to (5.67 + 25/5.67)/2 = 5.04

6. We decide that 5.04

5.04 = 25.4 is close enough, so we stop and declare 5.04

to be an adequate approximation to the square root of 25.

Note that the description of the method is a sequence of simple steps, together

with a flow of control that specifies when each step is to be executed. Such a

description is called an algorithm.

This algorithm is an example of a guess-

and-check algorithm. It is based on the fact that it is easy to check whether or

not a guess is a good one.

A bit more formally, an algorithm is a finite list of instructions that describe a

computation that when executed on a provided set of inputs will proceed

through a set of well-defined states and eventually produce an output.

An algorithm is a bit like a recipe from a cookbook:

1. Put custard mixture over heat.

2. Stir.

3. Dip spoon in custard.

4. Remove spoon and run finger across back of spoon.

5. If clear path is left, remove custard from heat and let cool.

6. Otherwise repeat.

It includes some tests for deciding when the process is complete, as well as

instructions about the order in which to execute instructions, sometimes

jumping to some instruction based on a test.

So how does one capture this idea of a recipe in a mechanical process? One way

would be to design a machine specifically intended to compute square roots.

Odd as this may sound, the earliest computing machines were, in fact, fixed-

program computers, meaning they were designed to do very specific things, and

were mostly tools to solve a specific mathematical problem, e.g., to compute the

trajectory of an artillery shell. One of the first computers (built in 1941 by

Atanasoff and Berry) solved systems of linear equations, but could do nothing

else. Alan Turing’s bombe machine, developed during World War II, was

designed strictly for the purpose of breaking German Enigma codes. Some very

simple computers still use this approach. For example, a four-function

calculator is a fixed-program computer. It can do basic arithmetic, but it cannot

For simplicity, we are rounding results.

The word “algorithm” is derived from the name of the Persian mathematician

Muhammad ibn Musa al-Khwarizmi.

Chapter 1. Getting Started 3

be used as a word processor or to run video games. To change the program of

such a machine, one has to replace the circuitry.

The first truly modern computer was the Manchester Mark 1.

It was

distinguished from its predecessors by the fact that it was a stored-program

computer. Such a computer stores (and manipulates) a sequence of

instructions, and has a set of elements that will execute any instruction in that

sequence. By creating an instruction-set architecture and detailing the

computation as a sequence of instructions (i.e., a program), we make a highly

flexible machine. By treating those instructions in the same way as data, a

stored-program machine can easily change the program, and can do so under

program control. Indeed, the heart of the computer then becomes a program

(called an interpreter) that can execute any legal set of instructions, and thus

can be used to compute anything that one can describe using some basic set of

instructions.

Both the program and the data it manipulates reside in memory. Typically there

is a program counter that points to a particular location in memory, and

computation starts by executing the instruction at that point. Most often, the

interpreter simply goes to the next instruction in the sequence, but not always.

In some cases, it performs a test, and on the basis of that test, execution may

jump to some other point in the sequence of instructions. This is called flow of

control, and is essential to allowing us to write programs that perform complex

tasks.

Returning to the recipe metaphor, given a fixed set of ingredients a good chef

can make an unbounded number of tasty dishes by combining them in different

ways. Similarly, given a small fixed set of primitive elements a good programmer

can produce an unbounded number of useful programs. This is what makes

programming such an amazing endeavor.

To create recipes, or sequences of instructions, we need a programming

language in which to describe these things, a way to give the computer its

marching orders.

In 1936, the British mathematician Alan Turing described a hypothetical

computing device that has come to be called a Universal Turing Machine. The

machine had an unbounded memory in the form of tape on which one could

write zeros and ones, and some very simple primitive instructions for moving,

reading, and writing to the tape. The Church-Turing thesis states that if a

function is computable, a Turing Machine can be programmed to compute it.

The “if” in the Church-Turing thesis is important. Not all problems have

computational solutions. For example, Turing showed that it is impossible to

write a program that given an arbitrary program, call it P, prints true if and only

if P will run forever. This is known as the halting problem.

This computer was built at the University of Manchester, and ran its first program in

1949. It implemented ideas previously described by John von Neumann and was

anticipated by the theoretical concept of the Universal Turing Machine described by Alan

Turing in 1936.

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