伯克利 CS61A 课堂笔记 09 —— Data Abstraction
本系列为加州伯克利大学著名 Python 基础课程 CS61A 的课堂笔记整理，全英文内容，文末附词汇解释。
目录
01 Data Abstraction 数据抽象
Ⅰ Rational Numbers
Ⅱ Rational Number Arithmetic
02 Pairs 对
Ⅰ Representing Pairs Using Lists
Ⅱ Reducing to Lowest Terms
03 Abstraction Barriers 抽象障碍
04 Data Representations 数据表示
Ⅰ What is Data?
Ⅱ Demo
Ⅲ Rational Data Abstraction Implemented as Functions
01 Data Abstraction 数据抽象
Compound objects combine objects together:
A date: a year, a month, and a day.
A geographic position: latitude and longitude.
An abstract data type lets us manipulate compound objects as units.
Isolate two parts of any program that uses data:
How data are represented (as parts).
How data are manipulated (as units).
Data abstraction: A methodology by which functions enforce an abstraction barrier between representation and use.
Ⅰ Rational Numbers
Exact representation of fractions is a pair of integers. However, as soon as division occurs, the exact representation may be lost !
Assume we can compose and decompose rational numbers:
Ⅱ Rational Number Arithmetic
#最上层
def mul_rational(x, y):
"""Multiply rational numbers x and y."""
return rational(numer(x) * numer(y),
denom(x) * denom(y))
def add_rational(x, y):
"""Add rational numbers x and y."""
return rational(numer(x) * denom(y) + numer(y) * denom(x),
denom(x) * denom(y))
def equal_rational(x, y):
"""Return whether rational numbers x and y are equal."""
return numer(x) * denom(y) == numer(y) * denom(x)rational(n, d) returns a rational number x.
numer(x) returns the numerator of x.
denom(x) returns the denominator of x.
These functions implement an abstract data type for rational numbers.
02 Pairs 对
Ⅰ Representing Pairs Using Lists
#最底层
#A list literal: Comma-seperated expressions in brackets
>>> pair = [1, 2]
>>> pair
[1, 2]
#"Unpacking" a list
>>> a, b = pair
>>> a
1
>>> b
2
#Element selection using the selection operator
>>> pair[0]
1
>>> pair[1]
2
#Element selection function
>>> from operator import getitem
>>> getitem(pair, 0)
1
>>> getitem(pair, 1)
2#中间层
def rational(n, d):
"""Construct a rational number that represents N/D."""
return [n, d] #Construct a list
def numer(x):
"""Return the numerator of rational number X."""
return x[0] #Select item from a list
def denom(x):
"""Return the denominator of rational number X."""
return x[1]Ⅱ Reducing to Lowest Terms
from fractions import gcd #Greatest common divisor
def rational(n, d):
"""Construct a rational number that represents N/D."""
g = gcd(n, d)
return (n // g, d // g)03 Abstraction Barriers 抽象障碍
Violating abstraction barriers:
04 Data Representations 数据表示
Ⅰ What is Data?
We need to guarantee that constructor and selector functions work together to specify the right behavior.
Behavior condition: If we construct rational number x from numerator n and denominator d, then numer(x)/denom(x) must equal to n/d.
Data abstraction uses selectors and constructors to define behavior.
If behavior conditions are met, then the representation is valid.
Ⅱ Demo
#Rational arithmetic
def mul_rational(x, y):
return rational(numer(x) * numer(y),
denom(x) * denom(y))
def add_rational(x, y):
return rational(numer(x) * denom(y) + numer(y) * denom(x),
denom(x) * denom(y))
def equal_rational(x, y):
return numer(x) * denom(y) == numer(y) * denom(x)
def print_rational(x):
print(numer(x), "/", denom(x))
# Constructor and selectors
def rational(n, d):
return [n, d]
def numer(x):
return x[0]
def denom(x):
return x[1]>>> x, y = rational(1, 2), rational(3, 8)
>>> print_rational(mul_rational(x, y))
3 / 16# Constructor and selectors
def rational(n, d):
def select(name):
if name == 'n':
return n
elif name == 'd':
return d
return select
def numer(x):
return x('n')
def denom(x):
return x('d')>>> x, y = rational(1, 2), rational(3, 8)
>>> print_rational(mul_rational(x, y))
3 / 16
>>> x
<function rational.<locals>.select at 0x10293e6a8>Ⅲ Rational Data Abstraction Implemented as Functions
附：词汇解释
latitude / ˈlætɪtuːd / 纬度、longitude / ˈlɑːndʒɪtuːd / 经度、represent 表示、manipulate / məˈnɪpjuleɪt / 操作、numerator / ˈnuːməreɪtər / 分子、denominator / dɪˈnɑːmɪneɪtər / 分母、fraction / ˈfrækʃ(ə)n / 分数、exact representation 精确表示、rational numbers 有理数、compose / kəmˈpoʊz / 构成、decompose / ˌdiːkəmˈpoʊz / 分解、arithmetic / əˈrɪθmətɪk / 算术，演算、constructor 构造器、selector 选择器、selection operator 选择操作符、bracket / ˈbrækɪt / 中括号、parentheses / pəˈrenθəsiːz / 小括号、lowest terms 最简形式、violate / ˈvaɪəleɪt / 违背、list literals 文字列表、element selection 元素选择、rational operation 有理运算、guarantee / ˌɡærənˈtiː / 确保、specify / ˈspesɪfaɪ / 明确指出，具体说明、met 符合、valid 有效的