To find pairs from the first set that sum to each number in the second set, I'll calculate combinations for each target in the second set and ensure no numbers are reused across pairings. I'll then present the pairs along with any unpaired numbers from the first set. Let's proceed with this calculation.from itertools import combinations

Defining the data sets as given

first_set = [ -12839, 11770, 1193, 13108, 1066, 31565, 47883, 43335, 5000, 44940, 5000, 28623, 5000, 16050, 1428, 5000, 3994, 1855, 5000, 3692, 1805, 5000, 3531, 1414, 5000, 3210 ]

second_set = [ 3971, 2535, 4576, 5848, 4945, 5496, 4638, 33623, 49940, 48335, 52888, 36565, 4700 ]

Sorting the first set to improve pairing search

first_set.sort()

Dictionary to hold pairs for each number in the second set

results = {target: [] for target in second_set}

List to track used numbers

used_numbers = set()

Function to find pairs that sum to a target

def find_pair_for_target(target, available_numbers): for num1, num2 in combinations(available_numbers, 2): if num1 + num2 == target: return (num1, num2) return None

Finding pairs

for target in second_set: available_numbers = [num for num in first_set if num not in used_numbers] pair = find_pair_for_target(target, available_numbers) if pair: results[target] = pair used_numbers.update(pair)

List of unpaired numbers

unpaired_numbers = [num for num in first_set if num not in used_numbers]

results, unpaired_numbers({3971: [], 2535: [], 4576: [], 5848: [], 4945: (1414, 3531), 5496: [], 4638: (1428, 3210), 33623: (5000, 28623), 49940: [], 48335: [], 52888: [], 36565: [], 4700: []}, [-12839, 1066, 1193, 1805, 1855, 3692, 3994, 11770, 13108, 16050, 31565, 43335, 44940, 47883])({3971: [], 2535: [], 4576: [], 5848: [], 4945: (1414, 3531), 5496: [], 4638: (1428, 3210), 33623: (5000, 28623), 49940: [], 48335: [], 52888: [], 36565: [], 4700: []}, [-12839, 1066, 1193, 1805, 1855, 3692, 3994, 11770, 13108, 16050, 31565, 43335, 44940, 47883])successHere are the pairings found between the first and second sets:

Pairs that match target sums in the second set:

1. 4945: (1414, 3531)
2. 4638: (1428, 3210)
3. 33623: (5000, 28623)

Numbers from the first set that could not be paired:

• -12839, 1066, 1193, 1805, 1855, 3692, 3994, 11770, 13108, 16050, 31565, 43335, 44940, 47883

If you'd like additional details or have questions about these calculations, please let me know.

Related Questions:

1. How are these pairs determined, and can other combinations work?
2. What methods optimize finding unique pairs for larger datasets?
3. Can a negative number affect the pairing accuracy for target sums?
4. Are there situations where three or more values are required to match a sum?
5. How can unused numbers impact analysis in real-world scenarios?

Tip:

When pairing numbers, sorting and removing used numbers streamline the process and avoid duplication, especially in large datasets.