Javascript Time Complexity

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Like software engineers, sometimes our job is to find a solution to a problem that requires some sort of algorithm. A high-level algorithm is just a set of hints - the recipe for solving a problem. When do we get to a point where we know that the "recipe" that we have written to solve our problem is "good" enough?

is where the Big O notation comes into play . The Big O notation it is used to describe two things: the spatial complexity and the temporal complexity of an algorithm. In this article, we cover the complexity of time: what it is, how to understand it, and why knowing the time complexity - the big O notation - of an algorithm can improve your approach

Time complexity

The Big O notation for time complexity gives a rough idea of ‚Äã‚Äãhow long an algorithm takes to run depending on two things: the size of the input it has and the number of steps it takes. ’it takes to finish. Let’s compare the two to get our execution. Time complexity measures the efficiency of an algorithm when it has an extremely large data set. We look at the absolute worst case scenario and call our notation Big O.

O (1)

The first Big O as we speak is constant time, or O (1 ) (oh of one). When we talk about things in constant time, we are talking about declarations or operations of some sort:

Pretty much anything that is evaluated only once in our algorithm is counted as constant time.

When we evaluate overall runtime, we usually ignore these statements because they don’t take complexity into account . Note that there are O (1) expressions and why an expression could be O (1) relative to any other possible value.

O (n)

Take a look at this example:

Take a look at the first dataset in the example. What is the length of the table? Another look, but this time at the second dataset you created by going to mockaroo.com - how long is that array?

Now we are going to take a look at the actual function since the length of our input is known. To understand the Big O of an algorithm, take a look at blocking things by block and removing nonessential blocks from the code. Once you’ve gone through what you don’t need to figure out about run time, you can calculate the calculation to get the correct answer.

In this example we have a loop. This loop iterates over each element of the array that we pass to it. Because the code must touch every a single element in the array to complete its execution, it is linear time or O (n).

Final thoughts on O (n):

Since we are describing Big O in terms of a worst case scenario, it does not matter if we have a loop that works 10 times or 100 times before the loop breaks . The growth rate for the amount of time that entries increase is always linear.

One last example:

Take the same function as above, but add another block of code:

What would be the execution engine of this function?

technically it is O (2n), because we are running two for loops, one after the other .

However, when we express the complexity of time in terms of large O notation, we only look at the most essential parts that means the coefficient 2n -. 2 -. doesn’t make sense no matter how many loops we have stacked on top of each other - the Big O will always be O (n) because we are iterating the same array.

one thing to note:

If you create an algorithm that works with two networks and you have loops stacked on top of each other using either together, technically the time to execution are not O (n), unless the lengths of two separate arrays are not the same

When handling different datasets in a function -. in this case, two long networks of different sizes - we count separately. We use another variable to indicate the other network which has a different length.

The temporal complexity of this problem is O (n + m). The n is an array here and its elements; m is the other network and its elements. Since we are dealing with two different lengths and we do not know which one has more elements, it cannot be reduced to O (n).

Basics of Logarithms and Exponents

Before talking about other possible time complexity values, make sure you have a basic understanding of the work of exponents and logarithms .

Many see the words "exponent", "log" or "logarithm" and be nervous because they will have to do algebra or math that they do not remember in school. This is not the case! In this section, we’ll take a very high-level look at what a log is, what exponent is, and how each relates to the execution of a O (n).

examine logarithms and how they work, remember how exponents work. The syntax for lifting something to an exponent is:

x y = z

This is often read as "x to y the power is equal to z". The variable xz is multiplied by itself y times

The logarithmic syntax is as follows:.

log x z = y

Read this as "base log x of z equals y". See how the variables compare to the previous equation. If we take the base, we raise to the result, we get the number we are trying to take the log from. It is essentially the reverse of what the exponent is.

An important aspect is that when we are dealing with exponents, we are dealing with an outcome which is a large number. When you deal with logarithms, we are dealing with a smaller number as a result.

So how does this relate to the Big O rating? You will see in the following sections!

O (n x )

So far we have been talking about constant time and linear time. O (n 2), a version of O (nx) where x is equal to 2, is called quadratic time. This means that as the size of the input increases, the number of steps to solve the worst case problem is increased to the square or to the x power.

This can happen when it is necessary to nest loops together to compare an i-th value with another value in an array. Check for the presence of duplicates in an array:

The first loop marks our i-th placement in the array. The second loop examines all the indexes in the array to see if it matches the i-th index. If no match and reach the end of the loop, the i-th pointer moves to the next index

this means that we examine each index twice in our algorithm. In this example, an array with a length of 9 takes, at worst, 81 (9 2 ). For small datasets , this runtime is okay. But when you dramatically increase the dataset (say 1,000,000,000 entries), the O (n x ) performance doesn’t look terrible.

Final thoughts on O (n x )

always try to create algorithms with a more optimal execution time than O (n x ) . There are chances that you’re dealing with a set of data much larger than the picture that we have here. Next, look at the reverse of an engine of execution polynomial:. logarithmic

O (log n)

Imagine a telephone directory. If n We need to give you the name of a person and what you need to look up, how are you going to do it?

An algorithm that is starts at the beginning of the book and goes through each name until it reaches the name it is looking for, runs in O (n) running - the worst case scenario is that the person you are looking for is just the last name .

What can we do to improve it? How can we do better than linear execution?

You can perform an algorithm called binary search. We won’t go into the details of how to code binary search, but if you understand how it works through a pseudo - code, you can see why it is a little better than O (n) .

for pseudo binary search - code

Consider this: an address book as an array of objects in which each object has a first name, last name, and phone number. Here is an excerpt:

  1. Since the address book is already sorted by name, we can check if the middle lastName property matches the family of the search term.
  2. Otherwise, and the first letter comes after the first letter of the current middle surname, we delete in the first half.
  3. If it comes first, remove the second half.
  4. If it is the same, look at the next letter and compare the substrings to each other by following steps 1-3.
  5. Continue to perform this action until we find the answer. If we can’t find the answer, say so.

    This is called binary search. It has an O (log n) execution because we delete a section of our entry each time until we find the answer.

    Final thoughts on O (log n)

    Remember our basic logarithmic equation . The result when we take a register of a number is always smaller. If O (n) is linear and O (n 2 ) requires more passes, then O (log n) is a little better than O (n) because when we take the log of n it is a smaller number.

    O (2 n )

    O (2 n) generally refers to recursive solutions that involve some type of operation. The Fibonacci sequence is the most popular example of this execution. This particular example returns the nth number in the Fibonacci sequence:

    This solution increases the amount of steps required to complete the problem exponentially. Avoid this particular execution at all costs.

    O (n log n)

    O (n log n) execution is very similar to O (log n) execution, except that it performs worse than a linear execution. Essentially, a O (n log n) execution algorithm has some kind of linear function that has a nested logarithmic function. Take this example:

    In this code snippet, we increment a counter starting at 0 and using a while loop in that counter to multiply j by two for each step - this makes it logarithmic since we do basically big jumps with each iteration using multiplication.

Since it is nested, we will multiply the values ‚Äã‚Äãtogether by Big O notation instead of adding. We add when we have code blocks. O (n) x O (log n) === O (n log n).

O (n!)

To have an autonomy of O (n!), the algorithm must be extremely slow , even on smaller inputs. One of the most famous simple examples of an algorithm with a slow execution engine is finding all the permutations in a string.

In this algorithm, like the input length increases, the return number of permutations is the input length! (factorial).

factorial, if you remember it is the nth number multiplied by each number before it up to 1.

If we look at a length of 3, for example, we multiply 3 x 2 x 1 === 6. Six is ‚Äã‚Äã3

There does not need to be very long or very large input for an algorithm to take a long time to complete when the execution time is so slow. At all costs, try to find something more effective if you can. This is fine for a naïve solution or the first step to a problem, but it really needs some revamping to be somehow better.

Ground Rules to Remember

There are a few basic things to remember when trying to understand the time complexity of a function:

  1. Constants are good to know, but don’t necessarily have to be considered. This includes declarations, arithmetic operations, and coefficients or multiples of the same execution ( i.e. if we have two loops stacked on top of each other with the same execution time, we do not count as O (2n) - it’s just O (n).
  1. Big O notation only deals with the upper bound, or worst case scenario when it comes to time complexity.
    1. when you have multiple blocks of code with different runtimes stacked on top of each other, keep only the worst case value and treat it as runtime. it is the largest block of code in your function which will have an effect on the overall complexity. notation

      Conclusion

      In summary, Big O can have two meanings of its own associated:. Time complexity and the complexity of space In this article, we have taken a close look at the complexity of time. it is calculated as the time it takes for the algorithm to complete when its input increases.This is important here Ndo we are interacting with very large datasets - as you are likely to do with an employer. an array that can serve as a cheat sheet until you know more about Big O notation:

      Graph showing how execution time increases as your algorithm input increases.
      As the size of the entry increases, you can take a visual look to see how the number of operations increases. This will give you an idea of ‚Äã‚Äãwhat an efficient runtime is for more basic algorithms.

      Know the notation Big O, the way it’s calculated and what would be considered an acceptable time complexity for an algorithm will give you an edge over other applicants when looking for a job.

      Javascript Time Complexity __del__: Questions

      How can I make a time delay in Python?

      5 answers

      I would like to know how to put a time delay in a Python script.

      2973

      Answer #1

      import time
      time.sleep(5)   # Delays for 5 seconds. You can also use a float value.
      

      Here is another example where something is run approximately once a minute:

      import time
      while True:
          print("This prints once a minute.")
          time.sleep(60) # Delay for 1 minute (60 seconds).
      

      2973

      Answer #2

      You can use the sleep() function in the time module. It can take a float argument for sub-second resolution.

      from time import sleep
      sleep(0.1) # Time in seconds
      

      How to delete a file or folder in Python?

      5 answers

      How do I delete a file or folder in Python?

      2639

      Answer #1


      Path objects from the Python 3.4+ pathlib module also expose these instance methods:

      Javascript Time Complexity __delete__: Questions

      2639

      Answer #2


      Path objects from the Python 3.4+ pathlib module also expose these instance methods:

      2639

      Answer #3

      Python syntax to delete a file

      import os
      os.remove("/tmp/<file_name>.txt")
      

      Or

      import os
      os.unlink("/tmp/<file_name>.txt")
      

      Or

      pathlib Library for Python version >= 3.4

      file_to_rem = pathlib.Path("/tmp/<file_name>.txt")
      file_to_rem.unlink()
      

      Path.unlink(missing_ok=False)

      Unlink method used to remove the file or the symbolik link.

      If missing_ok is false (the default), FileNotFoundError is raised if the path does not exist.
      If missing_ok is true, FileNotFoundError exceptions will be ignored (same behavior as the POSIX rm -f command).
      Changed in version 3.8: The missing_ok parameter was added.

      Best practice

      1. First, check whether the file or folder exists or not then only delete that file. This can be achieved in two ways :
        a. os.path.isfile("/path/to/file")
        b. Use exception handling.

      EXAMPLE for os.path.isfile

      #!/usr/bin/python
      import os
      myfile="/tmp/foo.txt"
      
      ## If file exists, delete it ##
      if os.path.isfile(myfile):
          os.remove(myfile)
      else:    ## Show an error ##
          print("Error: %s file not found" % myfile)
      

      Exception Handling

      #!/usr/bin/python
      import os
      
      ## Get input ##
      myfile= raw_input("Enter file name to delete: ")
      
      ## Try to delete the file ##
      try:
          os.remove(myfile)
      except OSError as e:  ## if failed, report it back to the user ##
          print ("Error: %s - %s." % (e.filename, e.strerror))
      

      RESPECTIVE OUTPUT

      Enter file name to delete : demo.txt
      Error: demo.txt - No such file or directory.
      
      Enter file name to delete : rrr.txt
      Error: rrr.txt - Operation not permitted.
      
      Enter file name to delete : foo.txt
      

      Python syntax to delete a folder

      shutil.rmtree()
      

      Example for shutil.rmtree()

      #!/usr/bin/python
      import os
      import sys
      import shutil
      
      # Get directory name
      mydir= raw_input("Enter directory name: ")
      
      ## Try to remove tree; if failed show an error using try...except on screen
      try:
          shutil.rmtree(mydir)
      except OSError as e:
          print ("Error: %s - %s." % (e.filename, e.strerror))
      

      Is there a simple way to delete a list element by value?

      5 answers

      I want to remove a value from a list if it exists in the list (which it may not).

      a = [1, 2, 3, 4]
      b = a.index(6)
      
      del a[b]
      print(a)
      

      The above case (in which it does not exist) shows the following error:

      Traceback (most recent call last):
        File "D:zjm_codea.py", line 6, in <module>
          b = a.index(6)
      ValueError: list.index(x): x not in list
      

      So I have to do this:

      a = [1, 2, 3, 4]
      
      try:
          b = a.index(6)
          del a[b]
      except:
          pass
      
      print(a)
      

      But is there not a simpler way to do this?

      1055

      Answer #1

      To remove an element"s first occurrence in a list, simply use list.remove:

      >>> a = ["a", "b", "c", "d"]
      >>> a.remove("b")
      >>> print(a)
      ["a", "c", "d"]
      

      Mind that it does not remove all occurrences of your element. Use a list comprehension for that.

      >>> a = [10, 20, 30, 40, 20, 30, 40, 20, 70, 20]
      >>> a = [x for x in a if x != 20]
      >>> print(a)
      [10, 30, 40, 30, 40, 70]
      

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