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QOJ

IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#132377#6329. Colorful GraphShuishuiWA 2500ms8896kbC++144.0kb2023-07-29 18:19:122023-07-29 18:19:13

Judging History

This is the latest submission verdict.

  • [2023-08-10 23:21:45]
  • System Update: QOJ starts to keep a history of the judgings of all the submissions.
  • [2023-07-29 18:19:13]
  • Judged
  • Verdict: WA
  • Time: 2500ms
  • Memory: 8896kb
  • [2023-07-29 18:19:12]
  • Submitted

answer

#include <bits/stdc++.h>
using namespace std;
using ll = long long;

const int N = 7e3 + 2;
const int V = 1e5, E = 1e5;
template<typename T>
struct MinGraph {
	int s, t, vtot;
	int head[V], etot;
	T dis[V], flow, cost, pf[V]; 
	int pre[V];
	bool vis[V];
	struct edge{
		int v, nxt;
		T f, c;
	} e[E * 2];

	void addedge(int u, int v, T f, T c, T f2 = 0)
	{
		e[etot] = {v, head[u], f, c}; head[u] = etot++;
		e[etot] = {u, head[v], f2, -c}; head[v] = etot++;
	}

	bool spfa()
	{	
		T inf = numeric_limits<T>::max() / 2;
		for (int i = 1; i <= vtot; i++)
		{
			dis[i] = inf;
			vis[i] = false;
			pre[i] = -1;
			pf[i] = inf;
		}

		dis[s] = 0;
		vis[s] = true;
		queue<int> q;
		q.push(s);
		while (!q.empty())
		{
			int u = q.front();;
			for (int i = head[u]; ~i; i = e[i].nxt)
			{
				int v = e[i].v;
				if (e[i].f && dis[v] > dis[u] + e[i].c)
				{
					dis[v] = dis[u] + e[i].c;
					pre[v] = i;
					pf[v] = min(pf[u], e[i].f);
					if (!vis[v]) 
					{
						vis[v] = 1;
						q.push(v);
					}
				}
			}
			q.pop();
			vis[u] = false;
		}
		return dis[t] != inf;
	}

	void augment()
	{
		int u = t;
		T f = pf[t];
		flow += f;
		cost += f * dis[t];
		while (~pre[u])
		{
			e[pre[u]].f -= f;
			e[pre[u]^1].f += f;
			u = e[pre[u]^1].v;
		}
	}

	pair<T, T> solve()
	{
		flow = 0;
		cost = 0;
		while (spfa()) augment();
		return {flow, cost};
	}

	void init(int s_, int t_, int vtot_)
	{
		s = s_, t = t_, vtot = vtot_;
		etot = 0;
		for (int i = 1; i <= vtot; i++) head[i] = -1;
	}
};

int dfn[N], low[N], bel[N], sz[N], tot, cnt;
bool ins[N];
stack<int> stk;
vector<int> scc[N];
vector<int> e[N];

void dfs(int x)
{
	dfn[x] = low[x] = ++tot;
	ins[x] = true;
	stk.push(x);
	for (auto y : e[x])
	{
		if (!dfn[y]) dfs(y);
		if (ins[y]) low[x] = min(low[x], low[y]);
	}

	if (dfn[x] == low[x])
	{
		vector<int> v;
		cnt++;
		while (true)
		{
			int y = stk.top();
			stk.pop();
			ins[y] = false;
			scc[cnt].push_back(y);
			bel[y] = cnt;
			sz[cnt]++;
			if (y == x) break;
		}
	}
}

MinGraph<ll> g;

void solve(void)
{
	int n, m;
	cin >> n >> m;
	for (int i = 1; i <= m; i++)
	{
		int u, v;
		cin >> u >> v;
		e[u].push_back(v);
	}

	for (int i = 1; i <= n; i++) if (!dfn[i]) dfs(i);
	
	// for (int i = 1; i <= n; i++)
	// 	cout << bel[i] << " ";
	// cout << "\n";
	// cout << cnt << "\n";
	int s = cnt * 2 + 1, t = cnt * 2 + 2;
	g.init(s, t, t);

	vector<array<int, 2>> used;

	for (int i = 1; i <= cnt; i++)
	{
		used.push_back({i, g.etot});
		g.addedge(s, i * 2 - 1, m, 1);
		g.addedge(i * 2 - 1, t, 1, 0);
		g.addedge(s, i * 2, 1, 0);
		g.addedge(i * 2 - 1, i * 2, m, 0);
	}

	for (int x = 1; x <= n; x++)
	{
		int i = bel[x];

		for (auto y : e[x])
		{
			int u = bel[x], v = bel[y];
			if (u == v)
				continue; 
			// cout << u << " " << v << "\n";
			g.addedge(u * 2, v * 2 - 1, m, 0);
		}
	}

	vector<int> ans(n + 2);

	auto [f, c] = g.solve();
	// cout << c << "\n";



	vector<int> vis(n * 2 + 2);
	int now = 0;
	for (auto [uid, eid] : used)
	{
		if (g.e[eid].f != m)
		{
			// cout << "\n";
			// cout << uid << "\n";
			now++;
			vis[uid * 2] = true;

			for (auto v : scc[uid])
			{
				// cout << v << "\n";
				ans[v] = now;
			}


			queue<int> q;
			q.push(uid * 2);
			while (!q.empty())
			{
				int u = q.front();
				// cout << u << "\n";
				for (int i = g.head[u]; ~i; i = g.e[i].nxt)
				{
					int v = g.e[i].v;
					if (v != t && v != s && g.e[i].f != m && !vis[v])
					{
						vis[v] = true;
						// cout << v << "\n";
						// cout << (v + 1) / 2 << "\n";
						for (auto nd : scc[(v + 1) / 2])
							ans[nd] = now;
					
						q.push(v + 1);
					}
				}
				q.pop();
			}
		}
	}

	for (int i = 1; i <= n; i++)
		cout << ans[i] << " ";
	cout << "\n";
}

int main()
{
	ios::sync_with_stdio(false);
	cin.tie(nullptr);
	cout.tie(nullptr);

	// int T;
	// cin >> T;
	// for (int i = 1; i <= T; i++)
		solve();

	return 0;
}

Details

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Test #1:

score: 100
Accepted
time: 2ms
memory: 7916kb

input:

5 5
1 4
2 3
1 3
2 5
5 1

output:

2 2 2 1 2 

result:

ok AC

Test #2:

score: 0
Accepted
time: 2ms
memory: 7644kb

input:

5 7
1 2
2 1
4 3
5 1
5 4
4 1
4 5

output:

1 1 2 2 2 

result:

ok AC

Test #3:

score: 0
Accepted
time: 2ms
memory: 7916kb

input:

8 6
6 1
3 4
3 6
2 3
4 1
6 4

output:

1 1 1 1 2 1 3 4 

result:

ok AC

Test #4:

score: -100
Wrong Answer
time: 2500ms
memory: 8896kb

input:

7000 6999
4365 4296
2980 3141
6820 4995
4781 24
2416 5844
2940 2675
3293 2163
3853 5356
262 6706
1985 1497
5241 3803
353 1624
5838 4708
5452 3019
2029 6161
3849 4219
1095 1453
4268 4567
1184 1857
2911 3977
1662 2751
6353 6496
2002 6628
1407 4623
425 1331
4445 4277
1259 3165
4994 1044
2756 5788
5496 ...

output:

1 1 1 1 3 2 3 1 1 1 1 1 4 1 1 5 1 6 1 1 1 1 2 1 1 7 8 6 1 9 1 1 10 11 1 1 1 12 2 13 1 1 14 1 15 1 16 2 17 18 1 19 1 3 1 1 1 20 1 21 1 3 3 2 1 22 2 2 1 23 24 1 25 1 26 1 6 1 1 2 2 2 1 1 1 1 1 1 1 2 1 6 122 1 2 1 1 1 27 1 3 3 1 1 1 28 1 3 1 29 3 1 30 1 1 1 1 31 3 2 3 32 33 3 1 1 34 1 1 35 1 1 36 1 37 ...

result:

wrong answer 10 and 3 are not connected