Python – Incremental List Extension

Sometimes, while working with Python list, we can have a problem in which we need to extend a list in a very customized way. We may have to repeat the contents of the list and while doing that, each time new list must add a number to original list. This incremental expansion has applications in many domains. Let’s discuss a way in which this task can be performed. 

Method: Using list comprehension 

This task can be performed in a brute manner, but having a shorter implementation using list comprehension always is better. In this, we perform task in 2 steps, first we make a helper list to form an addition factor list and then cumulate the result using original list. 

The original list is : [7, 8, 9]
List after extension and addition : [7, 8, 9, 10, 11, 12, 16, 17, 18, 34, 35, 36]

Time complexity: O(N*M), where N is the extension factor and M is the addition factor.
Auxiliary space: O(N), where N is the extension factor, for the temporary list ‘temp’.

Method 2:  using the map() and zip() functions:

In this implementation, we use the map() function to apply a lambda function to each element of the range(N) and test_list lists to generate the temp and res lists, respectively. The zip() function is then used to combine the elements of test_list and temp into pairs, which are then added together using another map() function with a lambda function that adds its two arguments.

1. Create a list test_list containing integers 7, 8, and 9.
2. Print the original list test_list.
3. Set the extension factor N to 4 and the addition factor M to 3.
4. Create a list temp using map() and a lambda function that raises M to the power of each element in the range range(N), except for the first element which is set to 0.
5. Create a list res using map(), zip(), and another lambda function that adds the corresponding elements of test_list and temp.
6. Print the final list res.

The original list is : [7, 8, 9]
List after extension and addition : [7, 11, 18, 34, 8, 12, 16, 35, 9, 10, 17, 36]

Time complexity: O(N), where N is the size of the output list res. 

Auxiliary space: O(N), where N is the size of the output list res.

Method 3: Using a loop to extend the list and then adding a constant value to each element.

Approach:

1. Create an empty list named temp to store the values of the incremental list extension.
2. Use a loop to create an incremental list of length N using the formula 1 * M**i, where i is the index of the current element. Store the values in the list temp. The first element of the list is set to 0.
3. Create an empty list named res to store the final result.
4. Use two nested loops to add each element of the test_list with each element of the temp list, and store the result in the res list.
5. Print the final list after extension and addition using the print() function.

Below is the implementation of the above approach:

The original list is : [7, 8, 9]
List after extension and addition : [7, 8, 9, 10, 11, 12, 16, 17, 18, 34, 35, 36]

Time Complexity: O(N^2), where N is the extension factor. The loop used to create the incremental list has a time complexity of O(N), and the nested loop used to add each element of test_list with each element of temp has a time complexity of O(N^2).

Auxiliary Space: O(N), where N is the extension factor. The space required for the temp list is O(N), as it stores the incremental list. The space required for the res list is also O(N^2), as it stores the final result after extension and addition.

Method 4: use the itertools library’s

1. Initialize a list of integers called test_list with values [7, 8, 9].
2. Print the original list by converting it to a string and adding it to a string message.
3. Set two variables called N and M to the values 4 and 3, respectively. These variables are used to determine how much to extend the list and how much to increment each element in the list.
4. Generate a list called powers_of_m using a list comprehension that calculates M raised to the power of each integer in the range 0 to N-1. The first element of the list is set to 0 because it will not be used in the final calculation.
5. Generate all possible combinations of elements from test_list and powers_of_m using a nested list comprehension. Each combination is formed by adding an element from test_list and an element from powers_of_m. The resulting list of combinations is assigned to a variable called combinations.
6. Print the resulting list by converting it to a string and adding it to a string message.

The original list is : [7, 8, 9]
List after extension and addition : [7, 10, 16, 34, 8, 11, 17, 35, 9, 12, 18, 36]

Time Complexity :O(N^2)
Auxiliary Space:  O(N^2)

Method 5: Using numpy to perform vectorized operations.

Step-by-step approach:

Import the numpy library.
Convert the original list to a numpy array.
Create an array of powers of M using numpy’s power function.
Set the first element of the powers of M array to 0.
Use numpy’s broadcasting feature to add the original array to the powers of M array.
Return the resulting array.

OUTPUT:
The original list is : [7, 8, 9]
List after extension and addition : [7, 10, 16, 34, 8, 11, 17, 35, 9, 12, 18, 36]

Time complexity: O(N), where N is the extension factor.
Auxiliary space: O(N), for the array of powers of M created using numpy.