Hi, I'm Carrie Anne, and welcome to Crash Course Computer Science!
(｡･∀･)ﾉﾞ嗨，我是 Carrie Anne，欢迎收看计算机科学速成课！

Last episode, we discussed a few example classic algorithms,
上集讲了一些经典算法

like sorting a list of numbers and finding the shortest path in a graph.
比如给数组排序，找图的最短路径

What we didn't talk much about,
而上集没讲的是

is how the data the algorithms ran on was stored in computer memory.
算法处理的数据  存在内存里的格式是什么

You don't want your data to be like John Green's college dorm room,
你肯定不想数据像 John Green 的大学宿舍一样乱 \N 到处都是食物，衣服和纸

with food, clothing and papers strewn everywhere.
你肯定不想数据像 John Green 的大学宿舍一样乱 \N 到处都是食物，衣服和纸

Instead, we want our data to be structured,
我们希望数据是结构化的，方便读取

so that it's organized, allowing things to be easily retrieved and read.
我们希望数据是结构化的，方便读取

For this, computer scientists use Data Structures!
因此计算机科学家发明了 "数据结构"！

We already introduced one basic data structure last episode,
上集已经介绍了一种基本数据结构：

Arrays, also called lists or Vectors in some languages.
数组（Array）\N 也叫列表（list）或向量（Vector）（在其它编程语言里）

These are a series of values stored in memory.
数组的值一个个连续存在内存里

So instead of just a single value being saved into a variable, like 'j equals 5',
所以不像之前，一个变量里只存一个值（比如 j = 5）

we can define a whole series of numbers, and save that into an array variable.
我们可以把多个值存在数组变量里

To be able to find a particular value in this array, we have to specify an index.
为了拿出数组中某个值，我们要指定一个下标（index）

Almost all programing languages start arrays at index 0,
大多数编程语言里，数组下标都从 0 开始

and use a square bracket syntax to denote array access.
用方括号 [ ] 代表访问数组

So, for example, if we want to add the values in the first and third spots of our array 'j',
如果想相加数组 J 的第一个和第三个元素

and save that into a variable 'a', we would write a line of code like this.
把结果存在变量 a，可以写上图这样一行代码

How an array is stored in memory is pretty straightforward.
数组存在内存里的方式  十分易懂

For simplicity, let's say that the compiler chose to store ours at memory location 1,000.
为了简单，假设编译器从内存地址 1000 开始存数组

The array contains 7 numbers, and these are stored one after another in memory, as seen here.
数组有7个数字，像上图一样按顺序存.

So when we write "j index of 0", the computer goes to memory location 1,000,
写 j[0]，会去内存地址 1000

with an offset of 0, and we get the value 5.
加 0 个偏移，得到地址 1000，拿值：5

If we wanted to retrieve "j index of 5", our program goes to memory location 1000,
如果写 j[5]，会去内存地址 1000

plus an offset of 5, which in this case, holds a value of 4.
加 5 个偏移，得到地址 1005，拿值： 4

It's easy to confuse the fifth number in the array with the number at index 5.
很容易混淆 "数组中第 5 个数" 和 "数组下标为 5 的数"

They are not the same.
它们不是一回事

Remember, the number at index 5 is the 6th number in the array
记住，下标 5 其实是数组中第 6 个数

because the first number is at index 0.
因为下标是从 0 开始算的

Arrays are extremely versatile data structures, used all the time,
数组的用途广泛

and so there are many functions that can handle them to do useful things.
所以几乎所有编程语言  都自带了很多函数来处理数组

For example, pretty much every programming language comes with a built-in sort function,
举例，数组排序函数很常见

where you just pass in your array, and it comes back sorted.
只需要传入数组，就会返回排序后的数组

So there's no need to write that algorithm from scratch.
不需要写排序算法

Very closely related are Strings, which are just arrays of characters,
数组的亲戚是 字符串 (string)

like letters, numbers, punctuation and other written symbols.
其实就是字母,数字,标点符号等  组成的数组

We talked about how computers store characters way back in Episode 4.
第 4 集讨论过计算机怎么存储字符

Most often, to save a string into memory, you just put it in quotes, like so.
写代码时 用引号括起来就行了  \N j = "STAN ROCKS"

Although it doesn't look like an array, it is.
虽然长的不像数组，但的确是数组

Behind the scenes, the memory looks like this.
幕后看起来像这样

Note that the string ends with a zero in memory.
注意，字符串在内存里以 0 结尾

It's not the character zero, but the binary value 0.
不是"字符0"，是"二进制值0" \N 这叫字符"null"，表示字符串结尾

This is called the null character, and denotes the end of the string in memory.
不是"字符0"，是"二进制值0" \N 这叫字符"null"，表示字符串结尾

This is important because if I call a function like "print quote",
这个字符非常重要，如果调用 print 函数

which writes the string to the screen,
print 在屏幕上输出字符串

it prints out each character in turn starting at the first memory location,
会从开始位置，逐个显示到屏幕

but it needs to know when to stop!
但得知道什么时候停下来！

Otherwise, it would print out every single thing in memory as text.
否则会把内存里所有东西 都显示出来

The zero tells string functions when to stop.
0 告诉函数何时停下

Because computers work with text so often,
因为计算机经常处理字符串，所以有很多函数专门处理字符串

there are many functions that specifically handle strings.
因为计算机经常处理字符串，所以有很多函数专门处理字符串

For example, many programming languages have a string concatenation function, or "strcat",
比如连接字符串的 strcat

which takes in two strings, and copies the second one to the end of the first.
strcat 接收两个字符串，把第二个放到第一个结尾.

We can use arrays for making one dimensional lists,
我们可以用数组做一维列表

but sometimes you want to manipulate data that is two dimensional,
但有时想操作二维数据

like a grid of numbers in a spreadsheet, or the pixels on your computer screen.
比如电子表格，或屏幕上的像素

For this, we need a Matrix.
那么需要 矩阵（Matrix）

You can think of a Matrix as an array of arrays!
可以把矩阵看成  数组的数组！

So a 3 by 3 matrix is really  an array of size 3, with each index storing an array of size 3.
一个 3x3 矩阵就是一个长度为3的数组 \N 数组里每个元素都是一个长度为3的数组

We can initialize a matrix like so.
可以这样初始化.

In memory, this is packed together in order like this.
内存里是这样排列的

To access a value, you need to specify two indexes, like "J index of 2, then index of 1" -
为了拿一个值，需要两个下标，比如 j[2][1]

this tells the computer you're looking for the item in subarray 2 at position 1.
告诉计算机在找数组 2 里，位置是 1 的元素

And this would give us the value 12.
得到数字 12

The cool thing about matrices is we're not limited to 3 by 3
矩阵酷的地方是，不止能做 3x3 的矩阵

-- we can make them any size we want
任何维度都行

-- and we can also make them any number of dimensions we want.
任何维度都行

For example, we can create a five dimensional matrix and access it like this.
可以做一个5维矩阵，然后这样访问 \N a = j[2][0][18][18][3]

That's right, you now know how to access a five dimensional matrix
现在你知道了  怎么读一个 5 维矩阵

-- tell your friends!
快去告诉你的朋友！

So far, we've been storing individual numbers or letters into our arrays or matrices.
目前我们只存过单个数字/字符，存进数组或矩阵

But often it's useful to store a block of related variables together.
但有时, 把几个有关系的变量存在一起, 会很有用

Like, you might want to store a bank account number along with its balance.
比如银行账户号和余额

Groups of variables like these can be bundled together into a Struct.
多个变量打包在一起叫  结构体 (Struct)

Now we can create variables that aren't just single numbers,
现在多个不同类型数据，可以放在一起

but are compound data structures, able to store several pieces of data at once.
现在多个不同类型数据，可以放在一起

We can even make arrays of structs that we define,
甚至可以做一个数组，里面放很多结构体

which are automatically bundled together in memory.
这些数据在内存里  会自动打包在一起

If we access, for example, J index of 0, we get back the whole struct stored there,
如果写 j[0]，能拿到  j[0] 里的结构体

and we can pull the specific account number and balance data we want.
然后拿银行账户和余额

This array of structs, like any other array,
存结构体的数组，和其它数组一样

gets created at a fixed size that can't be enlarged to add more items.
创建时就有固定大小，不能动态增加大小

Also, arrays must be stored in order in memory,
还有，数组在内存中 按顺序存储

making it hard to add a new item to the middle.
在中间插入一个值很困难

But, the struct data structure can be used for
但结构体可以创造更复杂的数据结构，消除这些限制

building more complicated data structures that avoid these restrictions.
但结构体可以创造更复杂的数据结构，消除这些限制

Let's take a look at this struct that's called a "node".
我们来看一个结构体，叫 节点(node)

It stores a variable, like a number, and also a pointer.
它存一个变量 \N 一个指针（pointer）

A pointer is a special variable that points, hence the name, to a location in memory.
"指针" 是一种特殊变量，指向一个内存地址，因此得名.

Using this struct, we can create a linked list,
用 节点 可以做 链表（linked list）

which is a flexible data structure that can store many nodes.
链表是一种灵活数据结构，能存很多个 节点 (node)

It does this by having each node point to the next node in the list.
灵活性是通过每个节点 指向 下一个节点实现的

Let's imagine we have three node structs saved in memory, at locations 1000, 1002 and 1008.
假设有三个节点，在内存地址 1000，1002, 1008

They might be spaced apart because they were created at different times,
隔开的原因 可能是创建时间不同

and other data can sit between them.
它们之间有其他数据

So, you see that the first node contains the value 7, and the location 1008 in its "next" pointer.
可以看到第一个节点，值是 7，指向地址 1008

This means that the next node in the linked list is located at memory location 1008.
代表下一个节点，位于内存地址 1008

Looking down the linked list, to the next node,
现在来到下一个节点

we see it stores the value 112 and points to another node at location 1002.
值是 112，指向地址 1002

If we follow that, we find a node that contains the value 14
如果跟着它，会看到一个值为 14 的节点

and points back to the first node at location 1000.
这个节点  指回地址 1000，也就是第一个节点

So this linked list happened to be circular,
这叫 循环链表

but it could also have been terminated by using a next pointer value of 0
但链表也可以是非循环的，最后一个指针是 0

-- the null value -- which would indicate we've reached the end of the list.
"null"，代表链表尽头

When programmers use linked lists,
当程序员用链表时

they rarely look at the memory values stored in the next pointers.
很少看指针具体指向哪里

Instead, they can use an abstraction of a linked list, that looks like this,
而是用链表的抽象模型，就像上图

which is much easier to conceptualize.
更容易看懂

Unlike an array, whose size has to be pre-defined,
数组大小需要预先定好

linked lists can be dynamically extended or shortened.
链表大小可以动态增减

For example, we can allocate a new node in memory,
可以创建一个新节点，通过改变指针值，把新节点插入链表

and insert it into this list, just by changing the next pointers.
可以创建一个新节点，通过改变指针值，把新节点插入链表

Linked Lists can also easily be re-ordered, trimmed, split, reversed, and so on.
链表也很容易重新排序，两端缩减，分割，倒序等

Which is pretty nifty!
超方便！

And pretty useful for algorithms like sorting, which we talked about last week.
链表也适合上集的排序算法

Owing to this flexibility, many more-complex data structures are built on top of linked lists
因为灵活，很多复杂数据结构 都用链表

The most famous and universal are queues and stacks.
最出名的是 队列（queue）和 栈（stack）

A queue - like the line at your post office - goes in order of arrival.
"队列" 就像邮局排队，谁先来就排前面

The person who has been waiting the longest, gets served first.
"队列" 就像邮局排队，谁先来就排前面

No matter how frustrating it is that all you want to do is buy stamps
虽然你可能只想买邮票，而前面的人要寄 23 个包裹

and the person in front of you seems to be mailing 23 packages.
虽然你可能只想买邮票，而前面的人要寄 23 个包裹

But, regardless, this behavior is called First-In First-Out, or FIFO.
这叫 先进先出（FIFO）

That's the first part.
我指队列，不是指那 23 个包裹

Not the 23 packages thing.
我指队列，不是指那 23 个包裹

Imagine we have a pointer, named "post office queue", that points to the first node in our linked list.
想象有个指针叫"邮局队列"，指向链表第一个节点

Once we're done serving Hank, we can read Hank's next pointer,
第一个节点是 Hank，服务完 Hank 之后 \N 读取 Hank 的指针

and update our "post office queue" pointer to the next person in the line.
把"邮局队列"指向下一个人

We've successfully dequeued Hank -- he's gone, done, finished.
这样就把 Hank "出队"（dequeue）了

If we want to enqueue someone, that is, add them to the line,
如果我们想把某人"入队"（enqueue） \N 意思是加到队列里

we have to traverse down the linked list until we hit the end,
要遍历整个链表到结尾

and then change that next pointer to point to the new person.
然后把结尾的指针，指向新人（Nick）

With just a small change, we can use linked lists as stacks, which are LIFO…
只要稍作修改，就能用链表做 栈，\N 栈是后进先出(LIFO)

Last-In First-Out.
只要稍作修改，就能用链表做 栈，\N 栈是后进先出(LIFO)

You can think of this like a stack of pancakes...
可以把"栈"想成一堆松饼

as you make them, you add them to the top of stack.
做好一个新松饼，就堆在之前上面

And when you want to eat one, you take them from the top of the stack.
吃的时候，是从最上面开始

Delicious!
美味！

Instead of enqueueing and dequeuing,
栈就不叫"入队""出队"了

data is pushed onto the stack and popped from the stacks.
叫"入栈"（push） "出栈"（pop）

Yep, those are the official terms!
对，这些是正确术语！

If we update our node struct to contain not just one, but two pointers,
如果节点改一下，改成 2 个指针

we can build trees,
就能做 树（tree）

another data structure that's used in many algorithms.
很多算法用了 "树" 这种数据结构

Again, programmers rarely look at the values of these pointers,
同样，程序员很少看指针的具体值

and instead conceptualize trees like this: The top most node is called the root.
而是把"树"抽象成这样：最高的节点叫"根节点"（root）

And any nodes that hang from other nodes are called children nodes.
"根节点"下的所有节点   都叫"子节点"（children）

As you might expect, nodes above children are called parent nodes.
任何子节点的直属上层节点，叫"母节点"（parent node）

Does this example imply that Thomas Jefferson is the parent of Aaron Burr?
这个例子能说明 托马斯·杰斐逊 是 阿龙·伯尔 的父亲吗？

I'll leave that to your fanfiction to decide.
我让你们的同人文来决定

And finally, any nodes that have no children
没有任何"子节点"的节点

-- where the tree ends -- are called Leaf Nodes.
也就是"树"结束的地方，叫"叶节点"（leaf）

In our example, nodes can have up to two children,
在这里的例子中，节点最多只可以有 2 个子节点

and for that reason, this particular data structure is called a binary tree.
因此叫 二叉树（binary tree）

But you could just as easily have trees with three, four or any number of children
但你可以随便改，弄成 3个，4个，或更多

by modifying the data structure accordingly.
但你可以随便改，弄成 3个，4个，或更多

You can even have tree nodes that use linked lists to store all the nodes they point to.
甚至节点 可以用链表存所有子节点

An important property of trees - both in real life and in data structures - is that
"树"的一个重要性质是（不管现实中还是数据结构中）

there's a one-way path from roots to leaves.
"根"到"叶"是 单向 的

It'd be weird if roots connected to leaves, that connected to roots.
如果根连到叶，叶连到根  就很奇怪

For data that links arbitrarily, that include things like loops,
如果数据随意连接，包括循环

we can use a graph data structure instead.
可以用"图"表示

Remember our graph from last episode of cities connected by roads?
还记得上集用路连接城市的"图"吗？

This can be stored as nodes with many pointers, very much like a tree,
这种结构  可以用有多个指针的节点表示

but there is no notion of roots and leaves, and children and parents…
因此没有 根 叶 子节点 父节点 这些概念

Anything can point to anything!
可以随意指向！

So that's a whirlwind overview
以上概述了计算机科学中，最主要的一些数据结构

of pretty much all of the fundamental data structures used in computer science.
以上概述了计算机科学中，最主要的一些数据结构

On top of these basic building blocks,
这些基本结构之上，程序员做了各种新变体，有不同性质.

programmers have built all sorts of clever variants, with slightly different properties
这些基本结构之上，程序员做了各种新变体，有不同性质.

-- data structures like red-black trees and heaps, which we don't have time to cover.
比如"红黑树"和"堆"，我们没时间讲

These different data structures have properties that are useful for particular computations.
不同数据结构适用于不同场景

The right choice of data structure can make your job a lot easier,
选择正确数据结构会让工作更简单

so it pays off to think about how you want to structure your data before you jump in.
所以花时间考虑用什么数据结构是值得的

Fortunately, most programming languages come with
幸运的是，大多数编程语言自带了预先做好的数据结构

libraries packed full of ready-made data structures.
幸运的是，大多数编程语言自带了预先做好的数据结构

For example, C++ has its Standard Template Library, and Java has the Java Class Library.
比如，C++有"标准模板库"，Java有"Java 类库"

These mean programmers don't have to waste time implementing things from scratch,
程序员不用浪费时间从零写

and can instead wield the power of data structures to do more interesting things,
时间可以花在更有趣的事情

once again allowing us to operate at a new level of abstraction!
又提升了一层抽象！

I'll see you next week.
下周见！