Answer
See the explanation
Work Step by Step
Charlie Programmer's solution involves forming all possible subgroup pairs, which would require generating \( \frac{n}{2} \) subsets for a group of \( n \) people and computing the difference between the age totals for each pair. This approach would have a complexity of \( O(2^{n/2}) \), as it involves considering all possible combinations. This is exponential.
Mary Programmer's solution, on the other hand, involves sorting the group by age, which has a complexity of \( O(n \log n) \), and then dividing the group into two equal-sized subgroups. This step would have a complexity of \( O(n) \). Therefore, the overall complexity of Mary Programmer's solution is \( O(n \log n) \). This is polynomial
The problem itself can be classified as nonpolynomial (NP) complexity, as the Charlie Programmer's solution involves generating all possible combinations, which grows exponentially with the input size.
