Computation time | Wikipedia audio article
Channel: wikipedia tts
Date: 15/01/2019

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Time_complexity


00:02:59 1 Table of common time complexities
00:03:18 2 Constant time
00:03:25 3 Logarithmic time
00:05:53 4 Polylogarithmic time
00:07:56 5 Sub-linear time
00:08:12 6 Linear time
00:08:26 7 Quasilinear time
00:08:36 8 Sub-quadratic time
00:10:55 9 Polynomial time
00:12:21 9.1 Strongly and weakly polynomial time
00:12:38 9.2 Complexity classes
00:14:42 10 Superpolynomial time
00:15:04 11 Quasi-polynomial time
00:15:43 11.1 Relation to NP-complete problems
00:17:20 12 Sub-exponential time
00:21:53 12.1 First definition
00:22:49 12.2 Second definition
00:24:21 12.2.1 Exponential time hypothesis
00:27:32 13 Exponential time
00:29:01 14 Double exponential time
00:29:44 15 See also
00:31:09 16 References
00:34:19 Exponential time hypothesis
00:35:16 Exponential time
00:37:02 Double exponential time
00:38:24 See also



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SUMMARY
=======
In computer science, the time complexity is the computational complexity that describes the amount of time it takes to run an algorithm. Time complexity is commonly estimated by counting the number of elementary operations performed by the algorithm, supposing that each elementary operation takes a fixed amount of time to perform. Thus, the amount of time taken and the number of elementary operations performed by the algorithm are taken to differ by at most a constant factor.
Since an algorithm's running time may vary among different inputs of the same size, one commonly considers the worst-case time complexity, which is the maximum amount of time required for inputs of a given size. Less common, and usually specified explicitly, is the average-case complexity, which is the average of the time taken on inputs of a given size (this makes sense because there are only a finite number of possible inputs of a given size). In both cases, the time complexity is generally expressed as a function of the size of the input. Since this function is generally difficult to compute exactly, and the running time for small inputs is usually not consequential, one commonly focuses on the behavior of the complexity when the input size increases—that is, the asymptotic behavior of the complexity. Therefore, the time complexity is commonly expressed using big O notation, typically 
  
    
      
        O
        (
        n
        )
        ,
      
    
    {\displaystyle O(n),}
  

  
    
      
        O
        (
        n
        log
        ⁡
        n
        )
        ,
      
    
    {\displaystyle O(n\log n),}
   
  
    
      
        O
        (
        
          n
          
            α
          
        
        )
        ,
      
    
    {\displaystyle O(n^{\alpha }),}
   
  
    
      
        O
        (
        
          2
          
            n
          
        
        )
        ,
      
    
    {\displaystyle O(2^{n}),}
   etc., where n is the input size in units of bits needed to represent the input.
Algorithmic complexities are classified according to the type of function appearing in the big O notation. For example, an algorithm with time complexity 
  
    
      
        O
        (
        n
        )
      
    
    {\displaystyle O(n)}
   is a linear time algorithm and an algorithm with time complexity 
  
    
      
        O
        (
        
          n
          
            α
          
        
        )
      
    
    {\displaystyle O(n^{\alpha })}
   for some constant 
  
    
      
        α
        
        1
      
    
    {\displaystyle \alpha 1}
   is a polynomial time algorithm.