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IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#97670#6329. Colorful Graphyzc2005ML 2ms5808kbC++143.7kb2023-04-17 21:02:402023-04-17 21:02:42

Judging History

你现在查看的是最新测评结果

  • [2023-08-10 23:21:45]
  • System Update: QOJ starts to keep a history of the judgings of all the submissions.
  • [2023-04-17 21:02:42]
  • 评测
  • 测评结果:ML
  • 用时:2ms
  • 内存:5808kb
  • [2023-04-17 21:02:40]
  • 提交

answer

#include <bits/stdc++.h>
using namespace std;
mt19937_64 rnd(chrono::steady_clock::now().time_since_epoch().count());
using pii = pair<int, int>;
using i64 = long long;
#define rep(i, a, b) for (int i = a, I = b; i <= I; ++i)
#define per(i, a, b) for (int i = a, I = b; i >= I; --i)
template<typename T> void up(T &x, T y) { if (x < y) x = y; }
template<typename T> void down(T &x, T y) { if (x > y) x = y; }

const int N = 7005, inf = 1e9;
int n, m, a[N], b[N], c[N], bel[N], stk[N], to[N], top, cnt, d[N];
vector<int> e1[N], e2[N];
bool vis[N];

void dfs1(int u) {
    vis[u] = 1;
    for (auto v : e2[u]) if (!vis[v]) dfs1(v);
    stk[++top] = u;
}
void dfs2(int u, int c) {
    bel[u] = c;
    for (auto v : e1[u]) if (!bel[v]) dfs2(v, c);
}

vector<int> A, B;
namespace flow {
	const int N = 14005, M = 123456;
	int n, s, t, d[N], que[N], cap[M], res;
	int cnt = 1, head[N], cur[N], to[M], nxt[M], val[M];

	void addedge(int u, int v, int w) {
		to[++cnt] = v;
        cap[cnt] = val[cnt] = w;
		nxt[cnt] = head[u];
		head[u] = cnt;
	}
	void add(int u, int v, int w) {
		addedge(u, v, w);
		addedge(v, u, 0); 
	}
	bool bfs() {
		int l = 1, r = 0;
		rep(i, 0, n) cur[i] = head[i], d[i] = 0;
		que[++r] = s, d[s] = 1;
		while (l <= r) {
			int u = que[l++];
			for (int i = head[u]; i; i = nxt[i]) {
				int v = to[i], w = val[i];
				if (d[v] || !w) continue;
				d[v] = d[u] + 1;
				que[++r] = v;
			}
		} 
		return d[t];
	}
	int dfs(int u, int flow) {
		if (u == t) return flow;
		int rest = flow;
		for (int &i = cur[u]; i; i = nxt[i]) {
			int v = to[i], w = val[i];
			if (d[v] != d[u] + 1 || !w) continue;
			int k = dfs(v, min(flow, w));
			if (!k) d[v] = 0;
			rest -= k;
			val[i] -= k, val[i ^ 1] += k; 
			if (!rest) break;
		}
		return flow - rest;
	}
	int dinic() {
		res = 0;
		while (bfs()) res += dfs(s, inf); 
		return res;
	}

    struct edge {
        int to, nxt, val;
    } e[M];
    int hd[N], tot;
    void get_path(int u) {
        for (int &i = hd[u]; i; ) {
            int v = e[i].to;
            if (!--e[i].val) i = e[i].nxt;
            get_path(v);
            if (v == t) B.push_back(u);
            if (u == s) A.push_back(v);
        }
    }
    void solve() {
        rep(u, 0, n) {
            for (int i = head[u]; i; i = nxt[i]) {
                if (!cap[i]) continue;
                int f = cap[i] - val[i];
                if (!f) continue;
                int v = to[i];
                e[++tot] = {v, hd[u], f}, hd[u] = tot;
            }
        }
        e[++tot] = {s, hd[t], res}, hd[t] = tot;
        get_path(s);
    }
}

int main() {
    // freopen("1.in", "r", stdin);
    ios::sync_with_stdio(0), cin.tie(0);

    cin >> n >> m;
    rep(i, 1, m) {
        cin >> a[i] >> b[i];
        e1[a[i]].push_back(b[i]);
        e2[b[i]].push_back(a[i]);
    }
    rep(i, 1, n) if (!vis[i]) dfs1(i);
    per(i, n, 1) {
        int u = stk[i];
        if (!bel[u]) dfs2(u, ++cnt);
    }
    
    flow::t = flow::n = 2 * cnt + 1;
    rep(i, 1, cnt) flow::add(flow::s, i, 1), flow::add(i + cnt, flow::t, 1);
    rep(i, 1, cnt) flow::add(i + cnt, i, inf);
    rep(i, 1, m) {
        int u = bel[a[i]], v = bel[b[i]];
        if (u == v) continue;
        flow::add(u, v + cnt, inf);
    }

    int res = flow::dinic();
    flow::solve();
    assert((int) A.size() == res);
    rep(i, 0, res - 1) {
        to[A[i]] = B[i] - cnt, ++d[B[i] - cnt];
        assert(d[B[i] - cnt] == 1);
    }
    int col = 0;
    rep(u, 1, cnt) {
        if (d[u]) continue;
        c[u] = ++col;
        int x = u;
        while (to[x]) x = to[x], c[x] = col;
    }
    rep(i, 1, n) cout << c[bel[i]] << " \n"[i == n];

    return 0;
}

Details

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Test #1:

score: 100
Accepted
time: 2ms
memory: 5784kb

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: 5808kb

input:

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

output:

2 2 1 2 2

result:

ok AC

Test #3:

score: 0
Accepted
time: 2ms
memory: 5800kb

input:

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

output:

4 4 4 4 3 4 2 1

result:

ok AC

Test #4:

score: -100
Memory Limit Exceeded

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:


result: