table of Contents
Higher order function
Variables can point to functions, and the function itself can also be assigned to variables , that is: variables can point to functions
>>> f = abs
>>> f(-10)
10The function name is also a variable , the function name is actually the variable that points to the function
A function can receive another function as a parameter, this function is called a higher-order function
#一个最简单的高阶函数：
def add(x, y, f):
return f(x) + f(y)
The derivation process when calling the above function is as follows
x = -5
y = 6
f = abs
f(x) + f(y) ==> abs(-5) + abs(6) ==> 11
return 11map/reduce
map()The function receives two parameters, one is a function, and the other is Iterableto mapapply the passed function to each element of the sequence in turn, and return the result as a new one Iterator.
>>> def f(x):
... return x * x
...
>>> r = map(f, [1, 2, 3, 4, 5, 6, 7, 8, 9])
>>> list(r)
[1, 4, 9, 16, 25, 36, 49, 64, 81]map()The first parameter passed in fis the function object itself. Since the result ris one Iterator, it Iteratoris a lazy sequence, so list()let it calculate the entire sequence through a function and return a list
reduce(function, sequence, initializer=None) applies a function to a sequence[x1, x2, x3, ...], this function must receive two parameters, andreducethe result continues to be accumulated with the next element of the sequence.
- If the optional parameter initializer is provided, it is equivalent to inserting it as an element of the sequence into the first part of the sequence
The effect is:
For example, to sum a sequence:
>>> from functools import reduce
>>> def add(x, y):
... return x + y
>>> reduce(add, [1, 3, 5, 7, 9])
25If we consider that a string stris also a sequence, with a slight modification to the above example map(), we can write a function to strconvert toint :
>>> from functools import reduce
>>> def fn(x, y):
... return x * 10 + y
>>> def char2num(s):
... digits = {'0': 0, '1': 1, '2': 2, '3': 3, '4': 4, '5': 5, '6': 6, '7': 7, '8': 8, '9': 9}
... return digits[s]
>>> reduce(fn, map(char2num, '13579'))
13579str2intThe function organized into one is:
from functools import reduce
DIGITS = {'0': 0, '1': 1, '2': 2, '3': 3, '4': 4, '5': 5, '6': 6, '7': 7, '8': 8, '9': 9}
def str2int(s):
def fn(x, y):
return x * 10 + y
def char2num(s):
return DIGITS[s]
return reduce(fn, map(char2num, s))
You can also use lambda functions to further simplify:
from functools import reduce
DIGITS = {'0': 0, '1': 1, '2': 2, '3': 3, '4': 4, '5': 5, '6': 6, '7': 7, '8': 8, '9': 9}
def char2num(s):
return DIGITS[s]
def str2int(s):
return reduce(lambda x, y: x * 10 + y, map(char2num, s))filter(function, iterable)
Used to filter the sequence
filter()It also receives a function and a sequence. The map()difference is that filter()the passed function acts on each element in turn, and then decides Truewhether Falseto keep or discard the element according to the return value . To delete the empty string in a sequence, you can write:
def not_empty(s):
return s and s.strip()
list(filter(not_empty, ['A', '', 'B', None, 'C', ' ']))
# 结果: ['A', 'B', 'C']Use filter to find prime numbers
One method of calculating prime numbers is the Ehrlich Sieve method , and its algorithm is very simple to understand:
First, list 2all natural numbers from the beginning to construct a sequence: 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, ...
Take the first number of the sequence 2, it must be a prime number, and then filter out the multiples of 2the sequence 2: 3, 4 , 5, 6, 7, 8 , 9, 10 , 11, 12 , 13, 14, 15, 16 , 17, 18 , 19, 20 , take the first number of the new sequence 3, it must be a prime number, and then filter out the multiples of 3the sequence 3: 5, 6 , 7, 8, 9 , 10, 11, 12 , 13 , 14, 15 , 16, 17, 18 , 19, 20, ... take the first number of the new sequence 5, and then filter out the multiples of 5the sequence 5: 7, 8, 9, 10 , 11, 12, 13 , 14, 15, 16, 17, 18, 19, 20 , ... Keep sifting down, and you can get all the prime numbers.
def _odd_iter(): #构造一个从3开始的奇数序列
n = 1
while True:
n = n + 2
yield n
def _not_divisible(n): #定义一个筛选函数
return lambda x: x % n > 0
def primes(): #定义一个生成器，不断返回下一个素数
yield 2
it = _odd_iter() # 初始序列
while True:
n = next(it) # 返回序列的第一个数
yield n
it = filter(_not_divisible(n), it) # 构造新序列
# 打印1000以内的素数:
for n in primes():
if n < 1000:
print(n)
else:
breakSorted
sorted()Function is also a higher-order function, it can also receive a keyfunction to achieve custom sorting, such as sorting by absolute value:
>>> sorted([36, 5, -12, 9, -21], key=abs)
[5, 9, -12, -21, 36]To sort strings , in accordance with the size of the ASCII comparison
Suppose we use a set of tuples to represent student names and grades:
L = [('Bob', 75), ('Adam', 92), ('Bart', 66), ('Lisa', 88)]
Use sorted()to sort the above list by name:
L = [('Bob',75), ('Admin', 92), ('Bart', 66), ('List', 88)]
def by_name(t):
return t[0].lower()
L2 = sorted(L, key=by_name)
print(L2)Sorting a list of tuples
Suppose we use a set of tuples to represent names and ages, and then use the sorted() function to sort the names in ascending order and age in descending order:
def sort_by_name(t):
return t[0]
def sort_by_age(t):
return t[1]
L = [('Tom', 18), ('Jerry', 15), ('Peter', 16), ('John', 20)]
list1 = sorted(L, key=sort_by_name)
list2 = sorted(L, key=sort_by_age, reverse=True)
print('sort by name asc: ', list1)
print('sort by age desc: ', list2)
Output result:
sort by name asc: [('Jerry', 15), ('John', 20), ('Peter', 16), ('Tom', 18)]
sort by age desc: [('John', 20), ('Tom', 18), ('Peter', 16), ('Jerry', 15)]
Example 4: Sorting the contents of a dictionary
There are many ways to sort a dictionary, but the core idea is the same: separate the key or value or item in the dict into a list, and then sort the list, thereby indirectly sorting the dict.
D = {'Tom': 18, 'Jerry': 15, 'Peter': 16, 'John': 20}
list1 = sorted(D.items(), key=lambda d: d[0])
list2 = sorted(D.items(), key=lambda d: d[1], reverse=True)
print('sort by key asc:', list1)
print('sort by value desc:', list2)
Output result:
sort by key asc: [('Jerry', 15), ('John', 20), ('Peter', 16), ('Tom', 18)]
sort by value desc: [('John', 20), ('Tom', 18), ('Peter', 16), ('Jerry', 15)]