# Python program to extract rows with common difference elements

Given a Matrix, extract rows with AP sequence.

Input : test_list = [[4, 7, 10], [8, 10, 12], [10, 11, 13], [6, 8, 10]]
Output : [[4, 7, 10], [8, 10, 12], [6, 8, 10]]
Explanation : 3, 4, and 2 are common difference in AP.

Input : test_list = [[4, 7, 10], [8, 10, 13], [10, 11, 13], [6, 8, 10]]
Output : [[4, 7, 10], [6, 8, 10]]
Explanation : 3 and 2 are common difference in AP.

Method #1: Using loop

In this, we check for all the elements having a common difference using a loop, if any element not found to be in sync, then the row is flagged off and not added to the result.

## Python3

 # Python3 code to demonstrate working of # Extract rows with common difference elements# Using loop # initializing listtest_list = [[4, 7, 10],             [8, 10, 12],             [10, 11, 13],              [6, 8, 10]] # printing original listprint("The original list is : " + str(test_list))         res = []for row in test_list:    flag = True    for idx in range(0, len(row) - 1):                 # check for common difference        if row[idx + 1] - row[idx] != row[1] - row[0]:            flag = False            break    if flag :        res.append(row) # printing result print("Filtered Matrix : " + str(res))

Output:

The original list is : [[4, 7, 10], [8, 10, 12], [10, 11, 13], [6, 8, 10]]
Filtered Matrix : [[4, 7, 10], [8, 10, 12], [6, 8, 10]]

Time Complexity: O(n*m)
Auxiliary Space: O(k)

Method #2: Using all() + list comprehension

In this, we check for all values to have common difference using all(), list comprehension is used to perform an iteration of rows.

## Python3

 # Python3 code to demonstrate working of # all() + list comprehension# Using list comprehension + all() # initializing listtest_list = [[4, 7, 10],             [8, 10, 12],             [10, 11, 13],              [6, 8, 10]] # printing original listprint("The original list is : " + str(test_list)) # checking for all values to have common difference         res = [row for row in test_list       if all(row[idx + 1] - row[idx] == row[1] - row[0]              for idx in range(0, len(row) - 1))] # printing result print("Filtered Matrix : " + str(res))

Output:

The original list is : [[4, 7, 10], [8, 10, 12], [10, 11, 13], [6, 8, 10]]
Filtered Matrix : [[4, 7, 10], [8, 10, 12], [6, 8, 10]]

Time Complexity: O(n*m)
Auxiliary Space: O(k)

Method 3 :  using the NumPy library.

we can use the numpy.diff() function to find the differences between consecutive elements in each row, and then use numpy.all() to check if all elements in the resulting array are equal.

## Python3

 import numpy as np # initializing listtest_list = [[4, 7, 10],             [8, 10, 12],             [10, 11, 13],              [6, 8, 10]] # convert list to numpy arrayarr = np.array(test_list) # calculate differences between consecutive elements in each rowdiffs = np.diff(arr, axis=1) # check if all elements in diffs are equalmask = np.all(diffs == diffs[:, 0][:, np.newaxis], axis=1) # filter rows that meet the criteriares = arr[mask].tolist() # printing result print("Filtered Matrix : " + str(res))

OUTPUT :
Filtered Matrix : [[4, 7, 10], [8, 10, 12], [6, 8, 10]]

The time complexity of this code is O(nm), where n is the number of rows and m is the number of columns in the input matrix.

The auxiliary space complexity of this code is O(nm), which includes the space required for the numpy array arr, the intermediate array diffs, the boolean mask mask, and the resulting filtered list res.

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