#1159479 (C++23) No.3508 OR Mapping

• 問題: No.3508 OR Mapping
• ユーザー: Azaki
• 提出日時: 2026-04-18 11:54:11
• 言語: C++23 (gcc 15.2.0 + boost 1.89.0)
• 結果: AC
• 実行時間: 432 ms / 2,000 ms
• コード長: 5,063 bytes
• コンパイル時間: 4,785 ms
• コンパイル使用メモリ: 362,504 KB
• 実行使用メモリ: 155,728 KB
• 最終ジャッジ日時: 2026-04-18 11:54:39
• 合計ジャッジ時間: 25,829 ms
• ジャッジサーバーID （参考情報）: judge3_0 / judge2_1

ファイルパターン	結果
sample	AC * 2
other	AC * 65

ソースコード

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

using ll = long long;

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

    int N, M;
    long long K;
    cin >> N >> M >> K;

    vector<vector<int>> g(N), rg(N);
    vector<pair<int,int>> edges;
    edges.reserve(M);

    for (int i = 0; i < M; i++) {
        int u, v;
        cin >> u >> v;
        --u; --v;
        g[u].push_back(v);
        rg[v].push_back(u);
        edges.push_back({u, v});
    }

    // Kosaraju
    vector<int> used(N, 0), order;
    order.reserve(N);

    for (int s = 0; s < N; s++) {
        if (used[s]) continue;
        stack<pair<int,int>> st;
        st.push({s, 0});
        used[s] = 1;
        while (!st.empty()) {
            auto &[v, idx] = st.top();
            if (idx < (int)g[v].size()) {
                int to = g[v][idx++];
                if (!used[to]) {
                    used[to] = 1;
                    st.push({to, 0});
                }
            } else {
                order.push_back(v);
                st.pop();
            }
        }
    }

    vector<int> comp(N, -1);
    vector<vector<int>> members;
    int C = 0;

    for (int i = N - 1; i >= 0; i--) {
        int s = order[i];
        if (comp[s] != -1) continue;
        members.push_back({});
        stack<int> st;
        st.push(s);
        comp[s] = C;
        while (!st.empty()) {
            int v = st.top(); st.pop();
            members[C].push_back(v);
            for (int to : rg[v]) {
                if (comp[to] == -1) {
                    comp[to] = C;
                    st.push(to);
                }
            }
        }
        C++;
    }

    vector<int> sz(C, 0);
    for (int c = 0; c < C; c++) sz[c] = (int)members[c].size();

    vector<vector<int>> dag(C);
    vector<vector<pair<int,int>>> inner_edges(C);
    vector<vector<int>> in_adj(N);

    for (auto [u, v] : edges) {
        int cu = comp[u], cv = comp[v];
        if (cu == cv) {
            inner_edges[cu].push_back({u, v});
            in_adj[u].push_back(v);
        } else {
            dag[cu].push_back(cv);
        }
    }

    for (int c = 0; c < C; c++) {
        sort(dag[c].begin(), dag[c].end());
        dag[c].erase(unique(dag[c].begin(), dag[c].end()), dag[c].end());
    }

    // type:
    // 0 = bad
    // 1 = singleton
    // 2 = odd-period nontrivial SCC
    vector<int> type(C, 0);

    vector<int> seen(N, 0);
    vector<ll> dist(N, 0);

    for (int c = 0; c < C; c++) {
        if (sz[c] == 1) {
            type[c] = 1; // singleton
            continue;
        }

        int root = members[c][0];
        stack<int> st;
        st.push(root);
        seen[root] = 1;
        dist[root] = 0;

        while (!st.empty()) {
            int v = st.top(); st.pop();
            for (int to : in_adj[v]) {
                if (!seen[to]) {
                    seen[to] = 1;
                    dist[to] = dist[v] + 1;
                    st.push(to);
                }
            }
        }

        ll gg = 0;
        for (auto [u, v] : inner_edges[c]) {
            ll x = dist[u] + 1 - dist[v];
            if (x < 0) x = -x;
            gg = std::gcd(gg, x);
        }

        for (int v : members[c]) seen[v] = 0;

        if (gg % 2 == 1) type[c] = 2; // good nontrivial SCC
        else type[c] = 0;             // impossible SCC
    }

    for (int c = 0; c < C; c++) {
        if (type[c] == 0) {
            cout << "No\n";
            return 0;
        }
    }

    int start = comp[0];
    if (type[start] != 2) { // start SCC must be good nontrivial
        cout << "No\n";
        return 0;
    }

    // Topological order
    vector<int> indeg(C, 0);
    for (int c = 0; c < C; c++) {
        for (int to : dag[c]) indeg[to]++;
    }

    queue<int> q;
    for (int c = 0; c < C; c++) {
        if (indeg[c] == 0) q.push(c);
    }

    vector<int> topo;
    topo.reserve(C);
    while (!q.empty()) {
        int v = q.front(); q.pop();
        topo.push_back(v);
        for (int to : dag[v]) {
            if (--indeg[to] == 0) q.push(to);
        }
    }

    // longest path from start, also restore one such path
    const int NEG = -1e9;
    vector<int> dp(C, NEG), prv(C, -1);
    dp[start] = 1;

    for (int v : topo) {
        if (dp[v] < 0) continue;
        for (int to : dag[v]) {
            if (dp[to] < dp[v] + 1) {
                dp[to] = dp[v] + 1;
                prv[to] = v;
            }
        }
    }

    int end = -1, best = -1;
    for (int c = 0; c < C; c++) {
        if (dp[c] > best) {
            best = dp[c];
            end = c;
        }
    }

    if (best != C) {
        cout << "No\n";
        return 0;
    }

    vector<int> path;
    for (int cur = end; cur != -1; cur = prv[cur]) path.push_back(cur);
    reverse(path.begin(), path.end());

    // singleton SCC must not be consecutive
    for (int i = 0; i + 1 < C; i++) {
        if (type[path[i]] == 1 && type[path[i + 1]] == 1) {
            cout << "No\n";
            return 0;
        }
    }

    cout << "Yes\n";
    return 0;
}