Python – Check if all tuples have element difference less than K

Given a Tuple list, check if each tuple has a difference less than K.

Input : test_list = [(3, 4), (1, 2), (7, 8), (9, 13)], K = 2 
Output : False 
Explanation : 13 – 9 = 4 > 2. 

Input : test_list = [(3, 4), (1, 2), (7, 8)], K = 2
Output : True 
Explanation : All have abs. diff 1 < 2.

Method #1 : Using loop

In this, we keep a boolean variable and check if any element is greater than or equal to K, then mark it False and break. 

Python3

# Python3 code to demonstrate working of
# Check if all tuples have element difference less than K
# Using loop

# initializing list
test_list = [(3, 4), (1, 2), (7, 8), (9, 8)]

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

# initializing K
K = 2

res = True
for ele1, ele2 in test_list:

    # using abs() to compute absolute difference
    if abs(ele1 - ele2) >= K:
        res = False

# printing result
print("Are all elements difference less than K ? : " + str(res))

Output

The original list is : [(3, 4), (1, 2), (7, 8), (9, 8)]
Are all elements difference less than K ? : True

Time complexity: O(n), where n is the number of tuples in the list.
Auxiliary space: O(1), as we are not using any extra data structures that depend on the size of the input.

Method #2 : Using all()

In this, we use all() to check if all the tuples have difference within K.

Python3

# Python3 code to demonstrate working of
# Check if all tuples have element difference less than K
# Using all()

# initializing list
test_list = [(3, 4), (1, 2), (7, 8), (9, 8)]

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

# initializing K
K = 2

# shorthand to solve this problem
res = all(abs(sub1 - sub2) < K for sub1, sub2 in test_list)

# printing result
print("Are all elements difference less than K ? : " + str(res))

Output

The original list is : [(3, 4), (1, 2), (7, 8), (9, 8)]
Are all elements difference less than K ? : True

Time complexity: O(n), where n is the number of tuples in the list.

Auxiliary space: O(1), as only constant extra space is used to store the value of K and the result.

Method#3: Using Recursive method.

Python3

# Python3 code to demonstrate working of
# Check if all tuples have element difference less than K
# Using recursive function
def is_lessthanK(lst,K,start=0):
  if start==len(lst):#base condition
    return True
  if abs(lst[start][0] - lst[start][1]) > K:
    return False
  return is_lessthanK(lst,K,start+1)

# initializing list
test_list = [(3, 4), (1, 2), (7, 8), (9, 8)]

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

# initializing K
K = 2

res = is_lessthanK(test_list,K)

# printing result
print("Are all elements difference less than K ? : " + str(res))
#this code contributed by tvsk

Output

The original list is : [(3, 4), (1, 2), (7, 8), (9, 8)]
Are all elements difference less than K ? : True

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

Method #4 using combinations

Approach

 Using combinations from the itertools module to generate all possible pairs of tuples.

Algorithm

1. Import the combinations function from the itertools module.
2. Generate all possible pairs of tuples using the combinations function.
3. Iterate through each pair of tuples and calculate the absolute difference between each pair of elements in the two tuples.
4. If the absolute difference is greater than or equal to K, return False.
5. If all pairs have absolute differences less than K, return True.

Python3

from itertools import combinations

def check_tuple_difference(test_list, K):
    for i, j in combinations(test_list, 2):
        diff = abs(i[0]-j[0]) + abs(i[1]-j[1])
        if diff >= K:
            return False
    return True

test_list = [(3, 4), (1, 2), (7, 8), (9, 13)]
K = 2
print(check_tuple_difference(test_list, K))

Output

False

Time complexity:  O(n^2) because we generate all possible pairs of tuples. 
Auxiliary Space: O(1)

Method #5: Using any() and filter() function

Step by step approach:

1. Initialize the test_list and K.
2. Use the filter() function to filter out the tuples from the test_list that have an element difference greater than or equal to K.
3. Check if any tuples are left in the filtered result using the any() function.
4. Negate the result using the not operator to get the final result.
5. Print the final result.

Python3

# initializing list
test_list = [(3, 4), (1, 2), (7, 8), (9, 8)]

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

# initializing K
K = 2

res = not any(filter(lambda x: abs(x[0]-x[1])>=K, test_list))

# printing result
print("Are all elements difference less than K ? : " + str(res))
#This code is contributed by Vinay Pinjala.

Output

The original list is : [(3, 4), (1, 2), (7, 8), (9, 8)]
Are all elements difference less than K ? : True

Time Complexity: O(n), where n is the length of test_list. The filter() function iterates over each tuple in the list once to check the element difference, and the any() function also iterates over the filtered result to check if any tuples are left.

Auxiliary Space: O(1), because we use only a single boolean variable to store the result. The filter() function and lambda function use negligible space, and the any() function does not create any additional data structure.