Python program to create a list centered on zero

Given two integer variables, limit and diff, write a Python program to create a list that is centered on zero, using limit, which specifies limit of the list and diff that specifies the common difference between integers. 

Examples:

Input : limit = 1, diff = 0.5
Output : [-1, -0.5, 0.0, 0.5, 1]

Input : limit = 25, diff = 5
Output : [-25, -20, -15, -10, -5, 0, 5, 10, 15, 20, 25]

Approach #1: Naive Approach 

This is a naive approach to the above problem. First, create an empty list 'lst', and then we use a while loop to append the next integer with a difference equal to 'diff'. 

[-1, -0.5, 0.0, 0.5, 1]

Time Complexity: O(n), where n is the number of elements in the list
Auxiliary Space: O(n), where n is the number of elements in the list 

Approach #2: Using Python Numpy 

Using Numpy module makes the solution a lot easier. In this method, we use np.arange which return evenly spaced values within a given interval 'diff'. 

[-1.0, -0.5, 0.0, 0.5, 1.0]

Approach #3: list comprehension 

[-1.0, -0.5, 0.0, 0.5, 1.0]

Approach #4: Using recursion

This approach uses recursion to generate the list of integers. It has a base case when limit is 0, and in that case it returns an list with 0. Otherwise, it generates the list by appending -limit to the result of a recursive call to the function with limit set to limit-diff, and then appending limit to the result.

[-25, -20, -15, -10, -5, 0, 5, 10, 15, 20, 25]

Time complexity: O(n), where n is the length of the list
Auxiliary Space: O(n)