This is a notebook of lectures of CS61A

A course of abstraction

Lecture 2

1.Q: analyse what is the output of the block

f = min
f = max 
g,h =min, max
max=g
max(f(2,g(h(1,5),3)),4)

2. 从终端调用python mul/add函数/pi值：

from operator import mul,add
from math import pi

3. 执行顺序：

a = 1
b = 2
b,a = a + b, b

Output: a=2,b=3 ~~真的有人这样子写代码吗~~

Rules:

Evaluate all expressions to the right of= from left to right.
Bind all names to the left of = to the resulting values in the current frame

4. How to define a function:

def <name>(<formal parameters>):
    return <return expression>

Plus: 如果在括号内直接给变量赋值，则为”默认值“，即若无特殊声明，默认为默认值。

Lecture 3

1.None Indicateds that Nothing is Returned

The special value None represents nothing in Python
A function that does not explicitly return a value will return None Careful: None is not displayed by the interpreter as the value of an expression.

Q: analyse what is the output of the following code

print(print(1),print(2))

A

1
2
None None

2.python交互界面： 例如以下代码：

from operator import floordiv,mod
def divide_exact(n,d):
    return floordiv(n,d),mod(n,d)

如果要查看q,r的值，我们通常会采取print函数，但是！~~不仅麻烦还不够帅~~！所以这里就采用交互模式

python3 -i pytest.py
>>> q
201
>>> r
3

That's what we see from Terminal

交互模式！

Lecture 4

1.assert语句

assert condition, "Error message"

E.g.

def square_area(x):
    assert x>0, 'A length must be positive'
    return x*x

square_area(-2)
报错！
2.用自定义函数传递函数名 ~~瞎起的名字~~
大概需求：五项求和（自然数/自然数的立方）

def cube(k):
    return pow(k,3)
def identity(k):
    return k
def sum_naturals(n,term):
    sum,k = 0 , 1
    while k <= n:
        sum , k = sum + k , k + 1
    return sum

通过了“term”传递了函数，使得我们不需要分别写两个自定义函数分别进行自然数/立方的求和
函数也可以作为return 后的值被返回

Lecture 5

1. Environment!

def make_adder(n):
    def adder(k):
        return n+k
    return adder

adder_three=make_adder(3)
result=adder_three(4)
result2=adder_three(5)
adder_four=make_adde(4)
result3=adder_four(4)

And you will get the answers:

result=6
result2=7
result3=8

Explain:
每个函数都有运行的环境框架，正常情况下，我们定义的函数是全局框架（global），而嵌套定义的函数，如代码中的make_adder和adder ,make_adder是在全局框架中运行的，而adder是在make_adder的框架中运行的，因此，我们赋予adder_three函数类型，之后再多次给其值，并不会改变其parent frame

2.Lambda定义函数
一张图浅浅带过

Lecture 7

一些调用函数的规则
if else语句太低级，怎么办？
想写高级的！

def if_(c,t,f):
    if c:
        return t
    else:
        return f
from math import sqrt

def real_sqrt(x):
    return if_(x>=0,sqrt(x),0);

大概翻译一下，代码意思是写了一个~~ctf~~新的if+else语句,然后想在后面的real_sqrt里面调用，但是！
调用表达式不允许跳过计算部分！！！
因此其实它会直接计算x>=0 和sqrt这俩，不会作为条件语句和函数跑到if_里面去 ~~正常人会这样子写吗~~
不过可以在里面丢进去and 和 or这俩的语句

Lecture 8

Function Decorators

def trace1(fn):
    def traced(x):
        print("Calling",fn,'on argument',x)
        return fn(x)
    return traced

@trace1
def square(x):
    return x*x

@trace1
def sum_squares_up_to(n):
    k=1
    total=0
    while k<=n:
        total,k=total+square(k),k+1
    return total

and get

>>> sum_squares_up_to(5)
Calling <function sum_squares_up_to at 0x101712480> on argument 5
Calling <function square at 0x101712340> on argument 1
Calling <function square at 0x101712340> on argument 2
Calling <function square at 0x101712340> on argument 3
Calling <function square at 0x101712340> on argument 4
Calling <function square at 0x101712340> on argument 5
55

Actually

This

@trace1 
def triple(x):
    return x*3

is identical to

def triple(x):
    return 3*x 
triple = trace1(triple)

But 前一个比较好，The Magic of Decorator!

Lecture 10

递归！
终于会用lambda了，但是要注意调用

def inverse_cascade(n):
    grow(n)
    print(n)
    shrink(n)
def f_then_g(f,g,n):
    if n:
        f(n)
        g(n)

grow = lambda n: f_then_g(grow,print,n//10)
shrink = lambda n: f_then_g(print,shrink,n//10)

Output

以及递归要注意什么时候离开递归，建议把离开条件先写。

Lecture 11

list !!
~~int a[100]~~
python的数组（一些基本的定义的事情）：

>>>digits= [1,2,3,4]
#we can get the number of elements:
>>>len(digits)
4
>>>[2,7]+digits*2
[2,7,1,2,3,4,1,2,3,4]#write twice
#Nested lists
>>>pairs[[30,40],[50,60]]
>>>pairs[1]
[50,60]
>>>pairs[1][0]
50 #amazing to C

还有一些C没有的内置功能

#whether an element in a compound value
>>>digits = [1,8,2,8]
>>>1 in digits
True
>>>5 not in digits
True
>>>5 in digits
False
>>>not (5 in digits)
True
#in doesn't find subsequece ,but a single element
#like:
>>>[1,8] in digits
False
>>>[1,8] in [1,[1,8],8]
True
#but
>>>[1,8] in [1,[[1,8]],8]
False  
#don't hide so deep

奇妙的for语句

#a piece with "while"
def count(s,value):
    total,index=0,0
    while index<len(s):
        element = s[index]
        if element == value:
            total =total + 1
        index += 1
    return total
#and we can use for statement !
def count(s,value):
    total=0
    for element in s:
        if element == value:
            total += 1
    return total
#two lines less than the former one !
for <name> in <expressions>:
    <suite>

>>>pairs=[[1,2],[2,2],[2,3],[4,4]]
>>>same_count=0
>>>for x,y in pairs:##give each element a name —— sequence unpacking!
    if x == y:
        same_count += 1


>>>same_count
2
##two figures in one element

至于普通的多次循环怎么写：

def cheer(n):
    for _ in range(5):
        '''
        range(5)=[0,1,2,3,4]
        use _ or    (a blank) when we don't want to use that name
        '''
        print('Go bears!')

Go bears!
Go bears!
Go bears!
Go bears!
Go bears!

List comprehension!

>>>odds = [1,3,5,7,9]
>>> [x+1 for x in odds]
[2,4,6,8,10]
>>> [x for x in odds if 25%x == 0]
[1,5]
>>> [x+1 for x in odds if 25%x == 0]
[2,6] 
# amazing to C

Lecture 12

好复杂一数组，这在C我都不敢想

slice
就是获取一个数组里面一些东西
比如

oods=[1,3,5,7,9]
# want elements with index of 1,2
>>> list(range(1,3))
[1,2]
>>> [odd[i] for i in range(1,3)]
[3,5]
>>> odd[1:3] #slicing operator
[3,5] #so many methods to reach the destination
#if blank a begin/end ,it would be set as the first/last

some other functions
1. sum

>>>sum([2,3,4])
9
>>>sum([2,3,4],5)
14
# try to understand why the output is [2,3,4]:
sum([[2,3],[4]],[])

max

>>>max(range(5))
4
>>>max(range(10),key=lambda x:7-(x-4)*(x-2))
3 #use key=func

all

>>>[x<5 for x in range(5)]
[True,True,True,True,True]
>>>all([x<5 for x in range(5)])
True
>>>all(range(5))
False # bool(0) is False

string

use " " or ' '

>>>"here" in "where"
True

Dictionary
a kind of special sequence

>>>numerals={'I':1, 'V':5, 'X':10}
""" 
the value of dictionary can be list ,string or others 
the key could be numbers as well,but not list
"""
>>>numerals
{'I': 1, 'V': 5, 'X': 10}
>>>numerals[V]
5
>>>list(numerals)
['I','V','X']
>>> numerals.values()
dict_values([1, 5, 10])
>>>sum(numerals.values())
16
list(numerals.values())
[1,5,10]

dictionary comprehensions

# {<key exp>:<value exp> for <name> in <iter exp> if <fliter exp>}
#short version:{<key exp>:<value exp> for <name> in <iter exp>}
# like
{x*x : x for x in [1,2,3,4,5] if x>2 }
{9:3, 16:4, 25:5}

Lecture 13

import math
math.gcd(25,10)
5 # C say : impossible

顺便附上math库吧 : 菜鸟教程
Data abstraction
一个有些抽象的思想，我不太清楚我是否完全理解

例子：处理分数的加减乘除：

# rational(n,d) :returns a rational number x
# numer(x) : returns the numerators of x
# denom(x) : returns the denominator of x
def mul_rational(x,y):
    return rational(numer(x)*numer(y),demon(x)*demon(y))
# add/equal ·····

def rational(n,d):
    return [n,d]
def numer(x):
    return x[0]
def demom(x):
    retur x[1]

An example of violating data abstraction:

def mul_rational(a,b):
    return [a[0]*b[0],a[1]*b[1]]
mul_rational([1,2],[3,4])

~~第一次看这教授红温😋~~

维护一些复杂的东西应该很重要吧

# we can even write rational / demon / numer like this
def rational(n,d):
    def select(name):
        if name == 'n':
            return n 
        elif name == 'd':
            return d
    return select
def demon(x):
    return x('d')
def numer(x):
    return x('n')

这时候的x不再是一个数据结构，而是一个函数！