How do Python non unidirectional recursive functions return all results? This classic knapsack question gives the answer

Tianyuan prodigal son 2020-11-13 09:06:14
python non unidirectional recursive functions


recursive ( recursion) It's a magic programming technique , Can greatly simplify the code , Make it look simpler . But recursive design is very abstract , It's not easy to master . Usually , We are all thinking from the top down , Recursion is a bottom-up solution —— That's why recursion doesn't seem intuitive enough .

In the concept of recursion , Linear recursion / Nonlinear recursion 、 One way recursion / Non unidirectional recursion , It's very important , To master recursion , We have to understand . About the basic concept of recursion , Interested readers , Please refer to my blog 《Python Recursive algorithm refers to 》. today , In this paper, we discuss how non unidirectional recursive functions return all results .

Behind the knapsack problem , It's one of the seven mathematical problems in the world , The uncertainty of polynomial complexity . As a programmer , This problem can be roughly understood as a combinatorial optimization problem . The knapsack problem is usually described as : Given a set of items , Each item has its own weight and price , Within the total weight limit , How to choose , To maximize the total price of the item . If you add different restrictions and conditions , Knapsack problem can be derived from many varieties . such as , The following question seems far from the knapsack problem , It's still a typical knapsack problem in essence .

In a hero to war game , Players have m Pieces of equipment and n hero , He can assign to every hero 0 Pieces or pieces of equipment , Different heroes will gain different attack power when they have different numbers of equipment . How players allocate this m Pieces of equipment , You can make n A hero gains the most attack power ? With players owning 5 Pieces of equipment and 3 Take heroes for example , The following table is common 3 That's ok 6 Column , Corresponding 3 Each of the heroes has his own from 0 To 5 The attack power of equipment .

0 Pieces of 1 Pieces of 2 Pieces of 3 Pieces of 4 Pieces of 5 Pieces of
hero 1 0 1 3 5 7 9
hero 2 0 1 1 3 3 7
hero 3 0 3 4 5 6 7

Even if you're not familiar with knapsack problems , It's not hard to find a solution :

  1. Find out all possible equipment allocation plans
  2. Calculate the attack value of each scheme
  3. Select the allocation scheme with the largest attack value

1. Find out all possible equipment allocation plans

Find out m Pieces of equipment are assigned to n All the solutions of heroes are at the heart of the solution . here , Loop nesting doesn't work , Because nesting levels are input variables . Recursion is the way I think it works .

>>> def bag(m, n, series=list()):
if n == 1:
for i in range(m+1):
print(series+[i])
else:
for i in range(m+1):
bag(m-i, n-1, series+[i])
>>> bag(3,2) # take 3 Pieces of equipment are assigned to 2 The whole plan of Heroes 
[0, 0]
[0, 1]
[0, 2]
[0, 3]
[1, 0]
[1, 1]
[1, 2]
[2, 0]
[2, 1]
[3, 0]

Recursive function bag, Printed out will be 3 Pieces of equipment are assigned to 2 The whole plan of Heroes . obviously , It's not a one-way recursion , Because there are multiple recursive calls at the same level , This means that the recursive process goes out of the recursive exit many times . For non unidirectional recursion , Can't use return Return the result of . that , How to get recursive functions to return all solutions ? Please see the following example .

>>> def bag(m, n, result, series=list()):
if n == 1:
for i in range(m+1):
result.append(series+[i])
#print(result[-1])
else:
for i in range(m+1):
bag(m-i, n-1, result, series+[i])
>>> result = list()
>>> bag(5, 3, result) # take 5 Pieces of equipment are assigned to 3 hero , share 56 There are three kinds of distribution schemes 
>>> len(result)
56
>>> result
[[0, 0, 0], [0, 0, 1], [0, 0, 2], [0, 0, 3], [0, 0, 4], [0, 0, 5],
[0, 1, 0], [0, 1, 1], [0, 1, 2], [0, 1, 3], [0, 1, 4], [0, 2, 0],
[0, 2, 1], [0, 2, 2], [0, 2, 3], [0, 3, 0], [0, 3, 1], [0, 3, 2],
[0, 4, 0], [0, 4, 1], [0, 5, 0], [1, 0, 0], [1, 0, 1], [1, 0, 2],
[1, 0, 3], [1, 0, 4], [1, 1, 0], [1, 1, 1], [1, 1, 2], [1, 1, 3],
[1, 2, 0], [1, 2, 1], [1, 2, 2], [1, 3, 0], [1, 3, 1], [1, 4, 0],
[2, 0, 0], [2, 0, 1], [2, 0, 2], [2, 0, 3], [2, 1, 0], [2, 1, 1],
[2, 1, 2], [2, 2, 0], [2, 2, 1], [2, 3, 0], [3, 0, 0], [3, 0, 1],
[3, 0, 2], [3, 1, 0], [3, 1, 1], [3, 2, 0], [4, 0, 0], [4, 0, 1],
[4, 1, 0], [5, 0, 0]]

In the above code , Before calling recursive functions , First create a global list object result, And pass it as an argument to the recursive function . After the recursive call ends , All equipment allocation schemes are saved in the list object result in .

2. Calculate the attack value of each scheme

Traverse 56 There are three kinds of distribution schemes , Calculate the sum of the attack power of each scheme , Save to a new list v in .p by 3 Each of the heroes has his own from 0 To 5 The attack power of equipment .

>>> p = [
[0,1,3,5,7,9],
[0,1,1,3,3,7],
[0,3,4,5,6,7]
]
>>> v = list()
>>> for item in result:
v.append(p[0][item[0]] + p[1][item[1]] + p[2][item[2]])
>>> v
[0, 3, 4, 5, 6, 7, 1, 4, 5, 6, 7, 1, 4, 5, 6, 3, 6, 7, 3,
6, 7, 1, 4, 5, 6, 7, 2, 5, 6, 7, 2, 5, 6, 4, 7, 4, 3, 6,
7, 8, 4, 7, 8, 4, 7, 6, 5, 8, 9, 6, 9, 6, 7, 10, 8, 9]

3. Select the allocation scheme with the largest attack value

find v The ordinal number of the maximum value of the list , Then get the equipment distribution scheme with the largest attack power .

>>> max(v)
10
>>> result[v.index(max(v))]
[4, 0, 1]

The best allocation scheme is 1 Heroes hold 4 Pieces of equipment , The first 2 One hero is not equipped , The first 3 Heroes hold 1 Pieces of equipment , here 3 The sum of attack power of heroes is the biggest , Its value is 10.

版权声明
本文为[Tianyuan prodigal son]所创,转载请带上原文链接,感谢

  1. 利用Python爬虫获取招聘网站职位信息
  2. Using Python crawler to obtain job information of recruitment website
  3. Several highly rated Python libraries arrow, jsonpath, psutil and tenacity are recommended
  4. Python装饰器
  5. Python实现LDAP认证
  6. Python decorator
  7. Implementing LDAP authentication with Python
  8. Vscode configures Python development environment!
  9. In Python, how dare you say you can't log module? ️
  10. 我收藏的有关Python的电子书和资料
  11. python 中 lambda的一些tips
  12. python中字典的一些tips
  13. python 用生成器生成斐波那契数列
  14. python脚本转pyc踩了个坑。。。
  15. My collection of e-books and materials about Python
  16. Some tips of lambda in Python
  17. Some tips of dictionary in Python
  18. Using Python generator to generate Fibonacci sequence
  19. The conversion of Python script to PyC stepped on a pit...
  20. Python游戏开发,pygame模块,Python实现扫雷小游戏
  21. Python game development, pyGame module, python implementation of minesweeping games
  22. Python实用工具,email模块,Python实现邮件远程控制自己电脑
  23. Python utility, email module, python realizes mail remote control of its own computer
  24. 毫无头绪的自学Python,你可能连门槛都摸不到!【最佳学习路线】
  25. Python读取二进制文件代码方法解析
  26. Python字典的实现原理
  27. Without a clue, you may not even touch the threshold【 Best learning route]
  28. Parsing method of Python reading binary file code
  29. Implementation principle of Python dictionary
  30. You must know the function of pandas to parse JSON data - JSON_ normalize()
  31. Python实用案例,私人定制,Python自动化生成爱豆专属2021日历
  32. Python practical case, private customization, python automatic generation of Adu exclusive 2021 calendar
  33. 《Python实例》震惊了,用Python这么简单实现了聊天系统的脏话,广告检测
  34. "Python instance" was shocked and realized the dirty words and advertisement detection of the chat system in Python
  35. Convolutional neural network processing sequence for Python deep learning
  36. Python data structure and algorithm (1) -- enum type enum
  37. 超全大厂算法岗百问百答(推荐系统/机器学习/深度学习/C++/Spark/python)
  38. 【Python进阶】你真的明白NumPy中的ndarray吗?
  39. All questions and answers for algorithm posts of super large factories (recommended system / machine learning / deep learning / C + + / spark / Python)
  40. [advanced Python] do you really understand ndarray in numpy?
  41. 【Python进阶】Python进阶专栏栏主自述:不忘初心,砥砺前行
  42. [advanced Python] Python advanced column main readme: never forget the original intention and forge ahead
  43. python垃圾回收和缓存管理
  44. java调用Python程序
  45. java调用Python程序
  46. Python常用函数有哪些?Python基础入门课程
  47. Python garbage collection and cache management
  48. Java calling Python program
  49. Java calling Python program
  50. What functions are commonly used in Python? Introduction to Python Basics
  51. Python basic knowledge
  52. Anaconda5.2 安装 Python 库(MySQLdb)的方法
  53. Python实现对脑电数据情绪分析
  54. Anaconda 5.2 method of installing Python Library (mysqldb)
  55. Python implements emotion analysis of EEG data
  56. Master some advanced usage of Python in 30 seconds, which makes others envy it
  57. python爬取百度图片并对图片做一系列处理
  58. Python crawls Baidu pictures and does a series of processing on them
  59. python链接mysql数据库
  60. Python link MySQL database