Summat

#include <iostream>
#include <vector>
#include <algorithm>

void print(const std::vector<int>& vals)
{
	for (unsigned i = 0; i < vals.size(); i++)
	{
		std::cout << vals[i];
		if (i < vals.size() - 1)
			std::cout << " ";
	}
	std::cout << "\n";
}

std::vector<int> pairs(const std::vector<int>& numbers)
{
	std::vector<int> results;
	for (unsigned i = 0; i < numbers.size() - 1; i++)
	{
		for (unsigned j = i + 1; j < numbers.size(); j++)
		{
			results.emplace_back(numbers[i] + numbers[j]);
		}
	}
	std::sort(results.begin(), results.end());
	return results;
}

int test(int idx, int value, const std::vector<int>& numbers, std::vector<bool>& used)
{
	for (unsigned i = idx; i < numbers.size(); i++)
	{
		if (used[i])
			continue;

		if (value < numbers[i])
			return 0;
		if (value == numbers[i])
		{
			return i;
		}
	}

	return 0;
}



std::vector<int> solve(unsigned n, const std::vector<int>& numbers)
{
	std::vector<bool> used;
	used.resize(numbers.size());
	std::vector<int> solved;
	solved.resize(numbers.size());
	int min_unused = 2;
	int a_max = numbers[0];
	std::vector<int> tests;

	auto testAndMark = [&](int idx, int value) -> bool
	{
		for (unsigned i = 1; i < solved.size(); i++)
		{
			int val = solved[i] + value;
			int foundIdx = test(min_unused, val, numbers, used);
			if (!foundIdx)
			{
				for (int f : tests)
					used[f] = false;
				return false;
				break;
			}
			used[foundIdx] = true;
			tests.emplace_back(foundIdx);
		}
		return true;
	};

	auto testFirst = [&](int b, int c)
	{
		int val = b + c;

		for (unsigned i = 1; i < numbers.size(); i++)
		{

			if (val < numbers[i])
				return false;
			if (val == numbers[i])
			{
				return true;
			}
		}

		return false;
	};

	for (int a = 1; a < a_max; a++)
	{
		int b = numbers[0] - a;
		int next = numbers[1] - a;

		
		if (!testFirst(b, next))
		{
			continue;
		}
		
		solved.clear();
		solved.emplace_back(a);
		solved.emplace_back(b);
		used.clear();
		used.resize(numbers.size());
		min_unused = 2;

		
		tests.clear();
		if (!testAndMark(min_unused, next))
		{
			continue;
		}
		solved.emplace_back(next);


		while (solved.size() < n)
		{

			for (unsigned i = min_unused; i < numbers.size(); i++)
			{
				if (!used[i])
				{
					min_unused = i;
					break;
				}
			}
			next = numbers[min_unused] - a;
			used[min_unused++] = true;
			tests.clear();
			if (!testAndMark(min_unused, next))
			{
				break;
			}
			solved.emplace_back(next);
		}
		if (solved.size() == n)
			break;
	}
	return solved;
}
std::vector<int> readInput(unsigned& n)
{
	std::vector<int> inputs;
	std::cin >> n;
	unsigned reads = (n*(n - 1)) / 2;
	for (unsigned i = 0; i < reads; i++)
	{
		int v;
		std::cin >> v;
		inputs.emplace_back(v);
	}
	return inputs;
}
std::vector<int> testInputs(unsigned &n)
{
	std::vector<int> test = { 134123123,26365345,31231231,123123123, 123120000,123125151 };
	std::sort(test.begin(), test.end());
	n = test.size();
	print(test);
	auto vec = pairs(test);
	print(vec);
	return vec;
}
int main()
{
	unsigned n;
	std::vector<int> vec = readInput(n);
	//std::vector<int> vec = testInputs(n);
	std::sort(vec.begin(), vec.end());
	print(solve(n, vec));


}

Test 1

Group: 1, 2, 3

Verdict: ACCEPTED

Test 2

Group: 1, 2, 3

Verdict: ACCEPTED

Test 3

Group: 1, 2, 3

Verdict: ACCEPTED

Test 4

Group: 1, 2, 3

Verdict: ACCEPTED

Test 5

Group: 1, 2, 3

Verdict: ACCEPTED

Test 6

Group: 2, 3

Verdict: ACCEPTED

Test 7

Group: 2, 3

Verdict: ACCEPTED

Test 8

Group: 2, 3

Verdict: ACCEPTED

Test 9

Group: 2, 3

Verdict: ACCEPTED

Test 10

Group: 2, 3

Verdict: ACCEPTED

Test 11

Group: 3

Verdict: ACCEPTED

Test 12

Group: 3

Verdict: ACCEPTED

Test 13

Group: 3

Verdict: ACCEPTED

Test 14

Group: 3

Verdict: ACCEPTED

Test 15

Group: 3

Verdict: ACCEPTED