Python program to test if all elements in list are maximum of K apart

Given a list of numbers, the task is to write a Python program to test if all elements are maximum of K apart.

Examples:

Input : test_list = [475, 503, 425, 520, 470, 500], K = 100
Output : True 
Explanation : Maximum element is 520 and minimum is 425, 520-425 = 95, which is less than 100, hence elements are in range.

Input : test_list = [475, 503, 425, 540, 470, 500], K = 100
Output : False 
Explanation : Maximum element is 540 and minimum is 425, 520-425 = 115, which is more than 100, hence elements are not in range.

Method #1 : Using sort()

In this, we perform the task of sorting elements to get the min and max elements accessible using sort(). The next step is to get the difference among them, if less than the range, True is returned.

The original list is : [475, 503, 425, 520, 470, 500]
Are elements in range ? : True

Time Complexity: O(n log(n))
Auxiliary Space: O(1)

Method #2 : Using min() + max()

Instead of changing the ordering or original list, min() and max() are used to get minimum and maximum elements respectively, and the difference between them gets the required result.

The original list is : [475, 503, 425, 520, 470, 500]
Are elements in range ? : True

Time Complexity: O(n)
Auxiliary Space: O(1)

Method #3: Using numpy.ptp() to find range

Note: Install numpy module using command “pip install numpy”

Output:

The original list is : [475, 503, 425, 520, 470, 500]
Are elements in range ? : True

Time Complexity: O(n)
Auxiliary Space: O(1)

Method #4: Using a for loop to check if all elements are in range

• Initialize a boolean variable flag as True
• Loop through each element elem in the list test_list
• Check if the absolute difference between elem and min(test_list) is greater than K. If yes, set flag to False and break out of the loop.
• Check if the absolute difference between elem and max(test_list) is greater than K. If yes, set flag to False and break out of the loop.
• After the loop, if flag is still True, then all elements are within the range K.

The original list is : [475, 503, 425, 520, 470, 500]
Are elements in range ? : True

Time complexity: O(n), where n is the length of test_list.
Auxiliary space: O(1)

Method #5: using the built-in function all() and a list comprehension.

Step-by-step approach:

• Define a function in_range() that takes two arguments: a list of integers and the range limit K.
• Use a list comprehension to create a list of Boolean values indicating whether each element in the list is within the range [min(test_list) – K, max(test_list) + K].
• Use the built-in function all() to check if all the Boolean values are True. If they are, return True; otherwise, return False.

True

Time complexity: O(n), where n is the length of the input list.
Auxiliary space: O(n), because we are creating a new list of Boolean values with the same length as the input list.