Write a function that takes in an array of integers, which can be both positive and negative, along with a target integer. The function should return all unique pairs of integers from the array that sum up to the target integer.

def find_pairs_with_sum(arr: List[int], target: int) -> List[Tuple[int, int]]:

    pass

Inputs
The inputs are defined as follows:

• arr: A list of integers containing both positive and negative numbers. The array may have duplicate values.
• target: An integer that we are interested in finding pairs for.

Output
Return a list of tuples, where each tuple contains a pair of integers that sum up to the target integer.

Example Tests

• find_pairs_with_sum([3, 4, 2, 5], 7) should return [(3, 4), (2, 5)]
• find_pairs_with_sum([2, 4, 1, 5], 9) should return [(4, 5)]
• find_pairs_with_sum([7, 1, 2, 3, 4, -2], 5) should return [(1, 4), (2, 3), (7, -2)]

Hint

Make sure that your function returns unique combinations. If the array [2, 3, 4, 6] has assigned number 5, only return (2, 3), not (2, 3), (3, 2)

Answer

from typing import List, Tuple, Set



def find_pairs_with_sum(arr: List[int], target: int) -> List[Tuple[int, int]]:

    # Initialize an empty set to store unique pairs

    result_set = set()

    

    # Create a set for quick lookups

    complementary_set = set()

    

    # Iterate through the array to find pairs that sum up to the target

    for num in arr:

        complement = target - num

        if complement in complementary_set:

            # Sort the pair (smaller, larger) before adding to result set for uniqueness

            result_set.add(tuple(sorted((num, complement))))

        complementary_set.add(num)

    

    # Convert the set to a list of tuples

    return list(result_set)



# Test the function with the given test cases

test_cases = [

    ([3, 4, 2, 5], 7), 

    ([2, 4, 1, 5], 9), 

    ([7, 1, 2, 3, 4, -2], 5)

]



for arr, target in test_cases:

    print(f"find_pairs_with_sum({arr}, {target}) = {find_pairs_with_sum(arr, target)}")

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