Python – Extract element with relative difference greater than K

Given a list of numbers, the task is to write a Python program to extract all numbers with differences of the next and previous elements with a current greater than K.

Input : test_list = [2, 7, 4, 1, 9, 2, 3, 10, 1, 5], K = 4
Output : [9, 10]
Explanation : 9 has 1 as preceding element and 2 as succeeding. 8 and 7 are its difference respectively which are greater than 4.

Input : test_list = [2, 7, 4, 1, 9, 2], K = 4
Output : [9]
Explanation : 9 has 1 as preceding element and 2 as succeeding. 8 and 7 are its difference respectively which are greater than 4.

Method #1: Using loop

In this, we check using brute force if the next or previous element has elements less than K difference and omit them. Loop is used for the iteration of all the elements.

Python3

# Python3 code to demonstrate working of
# Extract element with relative difference
# greater than K Using loop

# initializing list
test_list = [2, 7, 4, 1, 9, 2, 3, 10, 1, 5]

# printing original list
print("The original list is : " + str(test_list))

# initializing K
K = 4

res = []
for idx in range(1, len(test_list)):

    # using abs to get absolute difference
    if abs(test_list[idx - 1] - test_list[idx]) > K\
            and abs(test_list[idx + 1] - test_list[idx]) > K:
        res.append(test_list[idx])

# printing result
print("The extracted difference elements : " + str(res))

Output

The original list is : [2, 7, 4, 1, 9, 2, 3, 10, 1, 5]
The extracted difference elements : [9, 10]

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

Method #2: Using list comprehension

This is similar to the above method, the difference only being the usage of list comprehension for availing a shorthand to solving the issue. 

Python3

# Python3 code to demonstrate working of
# Extract element with relative difference
# greater than K Using list comprehension

# initializing list
test_list = [2, 7, 4, 1, 9, 2, 3, 10, 1, 5]

# printing original list
print("The original list is : " + str(test_list))

# initializing K
K = 4

# using abs to get absolute difference
# list comprehension provides shorthand
res = [test_list[idx] for idx in range(
  1, len(test_list)) if abs(test_list[idx - 1] - test_list[idx]) > K
       and abs(test_list[idx + 1] - test_list[idx]) > K]

# printing result
print("The extracted difference elements : " + str(res))

Output

The original list is : [2, 7, 4, 1, 9, 2, 3, 10, 1, 5]
The extracted difference elements : [9, 10]

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

Method #3: Using numpy

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

Python3

#importing numpy
import numpy as np

# initializing list
test_list = [2, 7, 4, 1, 9, 2, 3, 10, 1, 5]

# printing original list
print("The original list is : " + str(test_list))

# initializing K
K = 4

# using np.diff to get absolute difference
res = [test_list[idx] for idx in range(1, len(test_list))
       if np.diff([test_list[idx - 1], test_list[idx]])[0] > K
       and np.diff([test_list[idx + 1], test_list[idx]])[0] > K]

# printing result
print("The extracted difference elements : " + str(res))

Output:

The original list is : [2, 7, 4, 1, 9, 2, 3, 10, 1, 5]
The extracted difference elements : [9, 10]

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

Method #4: Using filter()

• Use filter() to iterate through all the elements in the test_list except the first and the last element (since we are checking the relative difference between adjacent elements).
• The lambda function inside filter() checks whether the absolute difference between the current element and its adjacent elements is greater than K.
• The resulting elements that satisfy the condition are stored in the list res.

Python3

test_list = [2, 7, 4, 1, 9, 2, 3, 10, 1, 5]
K = 4

res = list(filter(lambda x: abs(x - test_list[test_list.index(x) - 1]) > K and abs(x - test_list[test_list.index(x) + 1]) > K, test_list[1:-1]))

print("The extracted difference elements : " + str(res))

Output

The extracted difference elements : [9, 10]

Time Complexity: O(n)
Auxiliary Space: O(n), for storing the result in the list res