Python | Mutual tuple subtraction in list

Sometimes, while working with data, we can have a problem in which we need to perform tuple subtraction among all the tuples in list. This can have application in many domains. Let’s discuss certain ways in which this task can be performed. 

Method #1 : Using combinations() + list comprehension This problem can be solved using combinations of above functions. In this, we use combinations() to generate all possible combination among tuples and list comprehension is used to feed subtraction logic. 

Python3

# Python3 code to demonstrate working of
# Mutual tuple subtraction in list
# Using list comprehension + combinations
from itertools import combinations

# initialize list
test_list = [(2, 4), (6, 7), (5, 1), (6, 10)]

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

# Mutual tuple subtraction in list
# Using list comprehension + combinations
res = [(b1 - a1, b2 - a2) for (a1, a2), (b1, b2) in combinations(test_list, 2)]

# printing result
print("The mutual subtraction tuples are : " + str(res))

Output : 

The original list : [(2, 4), (6, 7), (5, 1), (6, 10)]
The mutual subtraction tuples are : [(4, 3), (3, -3), (4, 6), (-1, -6), (0, 3), (1, 9)]

Time Complexity: O(n), where n is the length of the list test_list 
Auxiliary Space: O(n) additional space of size n is created where n is the number of elements in the res list 

Method #2 : Using list comprehension + zip() + operator.sub + combinations() The combinations of above methods can also solve this problem. In this, we perform the task of subtraction using sub() and the like indexed elements are linked using zip(). 

Python3

# Python3 code to demonstrate working of
# Mutual tuple subtraction in list
# Using list comprehension + zip() + operator.sub + combinations()
from itertools import combinations
import operator

# initialize list
test_list = [(2, 4), (6, 7), (5, 1), (6, 10)]

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

# Mutual tuple subtraction in list
# Using list comprehension + zip() + operator.sub + combinations()
res = [(operator.sub(*a), operator.sub(*b))\
      for a, b in (zip(y, x) for x, y in combinations(test_list, 2))]

# printing result
print("The mutual subtraction tuples are : " + str(res))

Output : 

The original list : [(2, 4), (6, 7), (5, 1), (6, 10)]
The mutual subtraction tuples are : [(4, 3), (3, -3), (4, 6), (-1, -6), (0, 3), (1, 9)]

 Using nested for loops:

Approach:

Initialize an empty list result.
Using a list comprehension with two nested loops, iterate over all pairs of tuples in the input list, except pairs of identical tuples.
For each pair of tuples, subtract the first element of the second tuple from the first element of the first tuple, and subtract the second element of the second tuple from the second element of the first tuple.
Append the resulting tuple to result.
Return result.

Python3

def subtract_tuples(tuples):
    result = []
    for t1 in tuples:
        for t2 in tuples:
            if t1 != t2:
                result.append((t1[0] - t2[0], t1[1] - t2[1]))
    return result

tuples = [(1, 2), (3, 4), (5, 6)]
print(subtract_tuples(tuples))
# Output: [(-2, -2), (-4, -4), (2, 2), (4, 4), (0, 0), (-2, -2), (2, 2), (0, 0), (4, 4)]

Output

[(-2, -2), (-4, -4), (2, 2), (-2, -2), (4, 4), (2, 2)]

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