Throughout the journey of learning Python, we have been using predefined Python functions like print(), input(), type(), etc. Python has a large number of functions, and not all of them are directly accessible from a new Python script. Instead, they are stored in separate files, called modules. To use these functions, we need to import the module that contains them. This is done using the import statement. Let's illustrate that:
import math           # Importing the math module

print(math.pi)        # Accessing the constant pi from the math module
print(math.sqrt(16))  # Accessing the square root function from the math module
This program will print the value of pi (3.141592653589793) and the square root of 16 (4.0).
We can also import specific attributes or functions from a module using the from...import statement:
from math import pi, sqrt  # Importing only pi and sqrt from the math module

print(pi)                  # We can use pi directly without prefixing it with the module name
print(sqrt(16))            # Similarly, we can use sqrt directly
The output of the program will be the same as the previous one.
Sometimes, modules have long names, and typing the entire name every time we want to use a function can be laborious. To avoid this, we can use the as keyword to assign a different name (alias) to the module.
import math as m   # Importing the math module and renaming it as m

print(m.pi)        # Now we can use the short alias
print(m.sqrt(16))  # Using the sqrt function using the alias
The output will also be 3.141592653589793 and 4.0, just like before.
In conclusion, modules in Python are like toolboxes that contain predefined functions and variables which we can import and use in our programs. They help in organizing the code and making it more efficient.
How Modules Work Under the Hood
When you import a module, Python does some behind-the-scenes work that might not be immediately apparent. Here's an overview of what happens when you use the import statement:
  1. Locating the Module: Python first looks for the module by checking the locations specified in its sys.path list. This list includes the current directory, the built-in Python packages directory, and any paths specified in the PYTHONPATH environment variable. If Python finds the module, it proceeds to the next steps. If not, it throws a ModuleNotFoundError.
  1. Initialization of the Module: Once the module file is located, Python creates a new module object (types.ModuleType). Then it loads the module's content into this new module object, executing all the top-level code in the module file. This includes definitions of functions, classes, variables, and the execution of initialization code.
  1. Caching the Module: After initialization, the module is cached in sys.modules (a dictionary). This step ensures that when the same module is imported again in the script (or by other scripts), Python doesn't need to locate and initialize the module again. Instead, it can use the cached version. The key in this dictionary is the module name, and the value is the module object.
  1. Adding the Module to the Importer's Namespace: Finally, Python adds the name of the module to the namespace of the script or module that imported it. The name refers to the module object, so you can access the module's functions and variables using the dot notation.
Let's illustrate this with some code:
import sys
import math

print(sys.path)       # The path where Python searches for modules
print(sys.modules)    # The cached modules
print(math.sqrt(16))  # Accessing a function from the math module
The sys.path prints a list of directories where Python searches for modules. The sys.modules prints a dictionary of module names (keys) and their respective module objects (values).

Challenge: Random Numbers

In the world of cryptography, random numbers play an incredibly crucial role. Cryptographic algorithms often rely on generating a sequence of random numbers to keep the data secure.
In this challenge, you are tasked to simulate a simple random number generator that will help us understand the randomness in a more tangible form. Python comes with a built-in module named random that has various functions to generate random numbers. You are asked to use this module to generate a list of n random integers between two given numbers a and b. The randomness, however, should not be truly random - we need to fix the seed to 42 for the repeatability of the experiment. You can use the seed() function to fix the seed and randint() to generate a random number.
The first line of the input contains three space-separated integers: n, a, and b. The numbers a and b determine the range (inclusive) from which the random numbers should be picked, and n determines how many such numbers you need to generate.
The program should print n space-separated random numbers generated within the range [a, b] with the random seed fixed at 42.
10 1 100
82 15 4 95 36 32 29 18 95 14
5 1 5
1 1 3 2 2
3 10 20
20 11 10
Note: As we set the random seed to 42, the sequence of the output should remain the same across multiple runs of the program. This is a feature we exploit in testing, debugging, and other scenarios where deterministic output is necessary.


Time limit: 2.4 seconds

Memory limit: 512 MB

Output limit: 1 MB

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