POI2004MAK

dp #贪心 #构造 #POI #Year2004

order 等于所有环的长度的 \(lcm\)

\(dp_{i,j}\) 表示前 \(i\) 个质数组成和为 \(j\) 的最大 \(lcm\) 每个数一定是 \(p^k\)，其它方案在贪心上都是不优的

在 \(dp\) 的时候记录方案，尽可能优先选择较大的

然后构造方案，将较小的环贪心的往前放

// Author: xiaruize
#ifndef ONLINE_JUDGE
bool start_of_memory_use;
#endif
#include <bits/stdc++.h>
using namespace std;
#ifndef ONLINE_JUDGE
clock_t start_clock = clock();
#endif
#define double long double
#define int long long
#define ull unsigned long long
#define ALL(a) (a).begin(), (a).end()
#define pb push_back
#define mk make_pair
#define pii pair<int, int>
#define pis pair<int, string>
#define sec second
#define fir first
#define sz(a) int((a).size())
#define Yes cout << "Yes" << endl
#define YES cout << "YES" << endl
#define No cout << "No" << endl
#define NO cout << "NO" << endl
#define mms(arr, n) memset(arr, n, sizeof(arr))
#define rep(i, a, n) for (int i = (a); i <= (n); ++i)
#define per(i, n, a) for (int i = (n); i >= (a); --i)
int max(int a, int b)
{
	if (a > b)
		return a;
	return b;
}
int min(int a, int b)
{
	if (a < b)
		return a;
	return b;
}
const int INF = 0x3f3f3f3f3f3f3f3f;
const int MOD = 1000000007;
const int N = 1e4 + 10;

double dp[205][N];
int pre[205][N];
bool ntpr[N];
vector<int> pr;
int n;

void init()
{
	rep(i, 2, 1e4)
	{
		if (!ntpr[i])
			pr.push_back(i);
		if (pr.size() > 200)
			break;
		for (auto v : pr)
		{
			if (v * i > 1e4)
				break;
			ntpr[i * v] = true;
			if (i % v == 0)
				break;
		}
	}
	// cerr << pr.size() << endl;
	rep(i, 0, 1e4) dp[0][i] = 1;
	rep(i, 0, pr.size() - 1)
	{
		int x = pr[i];
		// cerr << x << endl;
		// double cnt = log2(x);
		memcpy(dp[i + 1], dp[i], sizeof(dp[i]));
		// cerr << cnt << endl;
		rep(j, 0, 1e4)
		{
			for (int cur = x, p = 1; cur + j <= 1e4; cur *= x, p++)
			{
				if (dp[i + 1][j + cur] <= dp[i][j] * cur)
				{
					dp[i + 1][j + cur] = dp[i][j] * cur;
					pre[i + 1][j + cur] = cur;
				}
			}
		}
	}
}

void solve()
{
	cin >> n;
	int cur = n;
	vector<int> res;
	per(i, pr.size(), 1)
	{
		int x = pre[i][cur];
		// cerr << i << ' ' << cur << endl;
		if (x)
			res.push_back(x);
		cur -= x;
	}
	while (cur--)
		res.push_back(1);
	sort(ALL(res));
	// for (auto v : res)
	// 	cerr << v << ' ';
	int sum = 1;
	for (auto v : res)
	{
		// cerr << v << ' ';
		rep(i, sum + 1, sum + v - 1) cout << i << ' ';
		cout << sum << ' ';
		sum += v;
	}
	// cerr << endl;
	cout << endl;
}

#ifndef ONLINE_JUDGE
bool end_of_memory_use;
#endif

signed main()
{
	// freopen(".in","r",stdin);
	// freopen(".out","w",stdout);
	ios::sync_with_stdio(false);
	cin.tie(0);
	cout.tie(0);
	init();
	int testcase = 1;
	cin >> testcase;
	while (testcase--)
		solve();
#ifndef ONLINE_JUDGE
	cerr << "Memory use:" << (&end_of_memory_use - &start_of_memory_use) / 1024.0 / 1024.0 << "MiB" << endl;
	cerr << "Time use:" << (double)clock() / CLOCKS_PER_SEC * 1000.0 << "ms" << endl;
#endif
	return 0;
}