01 algorithm data structure / algorithm Architectural Overview

01 algorithm data structure / algorithm Architectural Overview

1. Algorithm

• Algorithm Overview

  It is the essence of computer algorithms to process information, because a computer program is essentially an algorithm that tells the computer the exact steps to perform a specified task. Generally, when the information processing algorithm, reads data from the storage device or the address input data, writes the result to an output device or a memory address for later recall.

  Algorithm is independent of the presence of a problem-solving methods and ideas.

  For the algorithm, language is not important, important is the idea.

• Five characteristics of the algorithm

  1. Input : 0 or algorithm having a plurality of inputs
  2. Output : algorithm outputs at least one or more of
  3. Finite resistance : after a limited step algorithm automatically closed without an endless loop, and each step can be completed within an acceptable time
  4. Uncertainty : Algorithms Each step has a definite meaning, does not appear ambiguous
  5. Feasibility : Each step of the algorithm are feasible, which means that every step possible to complete a limited number of executions

2. The method of judging the merits of the program

• Consume computer resources and efficiency (not intuitive)

• Consuming calculation algorithm execution (not recommended, as it will be affected machines and execution environment)

• Time complexity (recommended)

3. Time Complexity

• Number / quantization step algorithm executed: Rule Evaluation

• Expressions: Big O notation

  • The most important item: time complexity of expression of the most significant items
  • O (most important item): O (n), O (n ** 2)

• Common time complexity:

  O(1) < O(logn) < O(n) < O(nlogn) < O(n^2) < O(n^3) < O(2^n)  < O(n!) < O(n^n)

  Code Example: calculating the time complexity of the following algorithm

  a=5
  b=6
  c=10
  for i in range(n):
     for j in range(n):
        x = i * i
        y = j * j
        z = i * j
  for k in range(n):
     w = a*k + 45
     v = b*b
  d = 33
  
  # 时间复杂度：4+3n**2+2n==>n**2

4. Data structure

• Concept: For data (basic data types (int, float, char)) of the organization was known as a data structure. How is a set of data structures solved to save, save what form.

Performance Analysis of the data structure 5. python

• timeit Module: This module may be used to test the speed of execution of code python section length / time.

• Timer class: class is length / time timeit python module designed to measure code execution speed. Prototype: class timeit.Timer (stmt = 'pass', setup = 'pass').

  • stmt argument: that the upcoming test code block statements.
  • setup: setting necessary for the operation's code block.
  • timeit function: timeit.Timer.timeit (number = 100000), the function returns the average time statement execution block number of times.

• Code Example:

  import timeit
  def test01():
      alist = []
      for i in range(1,1001):
          alist += [i]
      return alist
  def test02():
      alist = []
      for i in range(1,1001):
          alist.append(i)
      return alist
  def test03():
      alist = list(range(1,1001))
      return alist
  def test04():
      alist = [i for i in range(1,1001)]
      return alist
  if __name__ == '__main__':
      #stmt:待执行的代码块
      #setup:
      timer = timeit.Timer(stmt='test01()',setup='from __main__ import test01')
      print(timer.timeit(5000))
  
      timer1 = timeit.Timer(stmt='test02()',setup='from __main__ import test02')
      print(timer1.timeit(5000))
  
      timer2 = timeit.Timer(stmt='test03()',setup='from __main__ import test03')
      print(timer2.timeit(5000))
  
      timer3 = timeit.Timer(stmt='test04()',setup='from __main__ import test04')
      print(timer3.timeit(5000))
  
  """ 
  0.41899349999999913
  0.4362713999999954
  0.0754374999999925
  0.2028786999999994
  """  

6. Summary

• Use a different form of organization data, based on the complexity of the time when a query is not the same. Therefore considered algorithm is designed to solve practical problems, the data structure is a vector algorithm to deal with the problem.