結果

問題 No.1194 Replace
ユーザー T1610T1610
提出日時 2020-08-23 23:19:02
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 1,286 ms / 2,000 ms
コード長 10,618 bytes
コンパイル時間 3,250 ms
コンパイル使用メモリ 239,788 KB
実行使用メモリ 94,516 KB
最終ジャッジ日時 2024-10-15 19:27:22
合計ジャッジ時間 22,121 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge2
このコードへのチャレンジ
（要ログイン）

テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 801 ms
61,408 KB
testcase_01 AC 832 ms
64,920 KB
testcase_02 AC 644 ms
53,712 KB
testcase_03 AC 502 ms
46,052 KB
testcase_04 AC 846 ms
64,912 KB
testcase_05 AC 796 ms
60,836 KB
testcase_06 AC 744 ms
57,124 KB
testcase_07 AC 1,286 ms
93,964 KB
testcase_08 AC 1,200 ms
94,368 KB
testcase_09 AC 1,207 ms
94,392 KB
testcase_10 AC 1,193 ms
94,516 KB
testcase_11 AC 1,183 ms
94,324 KB
testcase_12 AC 1,159 ms
94,320 KB
testcase_13 AC 549 ms
38,432 KB
testcase_14 AC 444 ms
32,060 KB
testcase_15 AC 404 ms
34,688 KB
testcase_16 AC 539 ms
38,456 KB
testcase_17 AC 357 ms
31,624 KB
testcase_18 AC 354 ms
28,248 KB
testcase_19 AC 567 ms
39,848 KB
testcase_20 AC 2 ms
5,248 KB
testcase_21 AC 2 ms
5,248 KB
testcase_22 AC 2 ms
5,248 KB
testcase_23 AC 138 ms
17,588 KB
testcase_24 AC 41 ms
9,556 KB
testcase_25 AC 16 ms
5,248 KB
testcase_26 AC 165 ms
15,340 KB
testcase_27 AC 24 ms
5,320 KB
testcase_28 AC 67 ms
9,404 KB
testcase_29 AC 8 ms
5,248 KB
権限があれば一括ダウンロードができます

ソースコード

diff # 

#include <bits/stdc++.h>
using namespace std;
#define rep(i,n) REP(i,0,n)
#define REP(i,s,e) for(int i=(s); i<(int)(e); i++)
#define repr(i, n) REPR(i, n, 0)
#define REPR(i, s, e) for(int i=(int)(s-1); i>=(int)(e); i--)
#define all(r) r.begin(),r.end()
#define rall(r) r.rbegin(),r.rend()

typedef long long ll;
typedef vector<int> vi;
typedef vector<ll> vl;

const ll INF = 1e18;
const ll MOD = 1e9 + 7;

template<typename T> T chmax(T& a, const T& b){return a = (a > b ? a : b);}
template<typename T> T chmin(T& a, const T& b){return a = (a < b ? a : b);}

//有向、無向グラフ共通クラス(隣接リスト)
struct Graph {
    int n;
    using WEIGHT_TYPE = long long;
    const WEIGHT_TYPE INF = 1e18;
    struct Edge {
        int to;
        WEIGHT_TYPE weight;
    };
    struct Edge2 {
        int from;
        int to;
        WEIGHT_TYPE weight;
    };
    vector<vector<Edge>> es;
    Graph(int n) : n(n), es(n) {}

    // dijkstra O(E log V)
    vector<WEIGHT_TYPE> dijkstra(int s) {
        vector<WEIGHT_TYPE> d(n, INF);
        d[s] = 0;
        using P = pair<WEIGHT_TYPE, int>;
        priority_queue<P, vector<P>, greater<P>> q;
        q.push({0LL, s});
        while(!q.empty()) {
            auto p = q.top();
            q.pop();
            int cur = p.second;
            auto cost = p.first;
            if(d[cur] < p.first) continue;
            for(auto &e : es[cur]) {
                int to = e.to;
                auto dist = e.weight + cost;
                if(dist < d[to]) {
                    d[to] = dist;
                    q.push({dist, to});
                }
            }
        }
        return d;
    }
    // dijkstra O(V^2)
    vector<WEIGHT_TYPE> dijkstra2(int s) {
        vector<WEIGHT_TYPE> d(n, INF);
        d[s] = 0;
        vector<int> used(n);
        auto mat = getEdgeMat();
        while(1) {
            int cur = -1;
            rep(i, n) {
                if(used[i]) continue;
                if(cur == -1 || d[i] < d[cur]) cur = i;
            }
            if(cur == -1) break;
            used[cur] = 1;
            rep(i, n) { chmin(d[i], d[cur] + mat[cur][i]); }
        }
        return d;
    }
    // warshall_floyd O(n^3)
    vector<vector<WEIGHT_TYPE>> warshall_floyd() {
        // vector<vector<WEIGHT_TYPE>> d(n, vector<WEIGHT_TYPE>(n, INF));
        // rep(i, n) d[i][i] = 0LL;
        // rep(i, n) for (auto && e : es[i]) {
        //     int j = e.to;
        //     chmin(d[i][j], e.weight);
        // }
        auto d = getEdgeMat();
        rep(k, n) rep(i, n) rep(j, n) { chmin(d[i][j], d[i][k] + d[k][j]); }
        return d;
    }
    // 頂点sから到達できるか
    vector<bool> getVisitable(int s) {
        vector<bool> ret(n);
        queue<int> q;
        q.push(s);
        ret[s] = true;
        while(!q.empty()) {
            auto cur = q.front();
            q.pop();
            for(auto &&e : es[cur]) {
                if(!ret[e.to]) {
                    ret[e.to] = true;
                    q.push(e.to);
                }
            }
        }
        return ret;
    }
    // 2部グラフ判定
    bool isBipartile() {
        vector<int> memo(n, -1);
        rep(i, n) {
            if(memo[i] != -1) continue;
            queue<int> q;
            q.push(i);
            memo[i] = 0;
            while(!q.empty()) {
                auto v = q.front();
                q.pop();
                for(auto &&e : es[v]) {
                    auto u = e.to;
                    if(memo[u] == -1) {
                        memo[u] = !memo[v];
                        q.push(u);
                    } else if(memo[u] == memo[v]) {
                        return false;
                    }
                }
            }
        }
        return true;
    }
    vector<vector<WEIGHT_TYPE>> getEdgeMat() {
        vector<vector<WEIGHT_TYPE>> mat(n, vector<WEIGHT_TYPE>(n, INF));
        rep(i, n) mat[i][i] = 0;
        rep(i, n) {
            for(auto &&e : es[i]) chmin(mat[i][e.to], e.weight);
        }
        return mat;
    }
};

// 無向グラフ
struct GraphUD : public Graph {
    GraphUD(int n) : Graph(n) {}
    void add_edge(int from, int to, WEIGHT_TYPE weight) {
        es[from].push_back({to, weight});
        es[to].push_back({from, weight});
    }
    vector<Edge2> getEdge2() {
        vector<Edge2> ret;
        rep(i, n) for(auto &&e : es[i]) {
            if(i < e.to) ret.push_back({i, e.to, e.weight});
        }
        return ret;
    }
    // 橋の検出
    // http://nupioca.hatenadiary.jp/entry/2013/11/03/200006
    // Calculate bridges in a undirected graph.
    // Assume graph is connected and has no parallel edges or self-loops.
    vector<Edge2> getBridges() {
        int V = n;
        // res: bridges
        vector<Edge2> res;
        // assume at least the first vertex exists
        vector<int> low(V, -1); // lowest reacheable index
        vector<int> pre(V, -1); // pre-order index
        int count = 0;          // pre-order index counter

        // v: current node
        // from: parent node
        function<int(int, int)> dfs = [&](int v, int from) {
            pre[v] = count++;
            low[v] = pre[v];
            for(auto &&e : es[v]) {
                int to = e.to;
                if(pre[to] == -1) {
                    // destination has not been visited
                    // visit destination and update low[v]
                    low[v] = min(low[v], dfs(to, v));
                    if(low[to] == pre[to]) {
                        // edge is not contained in a closed path -> bridge
                        res.push_back({v, to, e.weight});
                    }
                } else {
                    if(from == to) {
                        // ignore a path to parent
                        continue;
                    }
                    low[v] = min(low[v], low[to]);
                }
            }
            return low[v];
        };

        dfs(0, -1); // start dfs from vertex 0

        return res;
    }
};

// 有向グラフ
struct GraphD : public Graph {
    GraphD(int n) : Graph(n) {}
    void add_edge(int from, int to, WEIGHT_TYPE weight) {
        es[from].push_back({to, weight});
    }
    vector<Edge2> getEdge2() {
        vector<Edge2> ret;
        rep(i, n) for(auto &&e : es[i]) { ret.push_back({i, e.to, e.weight}); }
        return ret;
    }
    GraphD getReverseGraph() {
        GraphD g(n);
        rep(i, n) for(auto &&e : es[i]) { g.add_edge(e.to, i, e.weight); }
        return g;
    }
    vector<vector<int>> scc() {
        vector<vector<int>> res;
        vector<int> cmp(n);
        vector<int> vs;
        vector<vector<int>> r_es(n);
        rep(i, n) for(auto &&e : es[i]) {
            int j = e.to;
            r_es[j].push_back(i);
        }

        vector<bool> used(n);
        function<void(int)> dfs = [&](int v) {
            used[v] = true;
            for(auto &&e : es[v]) {
                int to = e.to;
                if(!used[to]) dfs(to);
            }
            vs.push_back(v);
        };
        function<void(int, int)> rdfs = [&](int v, int k) {
            used[v] = true;
            cmp[v] = k;
            for(auto &&to : r_es[v]) {
                if(!used[to]) rdfs(to, k);
            }
        };

        fill(all(used), 0);
        vs.clear();
        for(int v = 0; v < n; v++) {
            if(!used[v]) dfs(v);
        }
        fill(all(used), 0);
        int k = 0;
        for(int i = vs.size() - 1; i >= 0; i--) {
            if(!used[vs[i]]) rdfs(vs[i], k++);
        }
        res.clear();
        res.resize(k);
        for(int i = 0; i < n; i++) {
            res[cmp[i]].push_back(i);
        }
        return res;
    }
    // bellmanFord 負閉路があるなら, dist[s] = INF | O(VE)
    vector<WEIGHT_TYPE> bellmanFord(int s) {
        vector<WEIGHT_TYPE> dist(n, INF);
        dist[s] = 0;
        auto es = getEdge2();
        rep(i, n) {
            for(auto &&e : es) {
                if(dist[e.to] > dist[e.from] + e.weight) {
                    dist[e.to] = dist[e.from] + e.weight;
                    if(i == n - 1) {
                        dist[s] = INF;
                        return dist;
                    }
                }
            }
        }
        return dist;
    }
    // bellmanFord s->tの経路上に負閉路があるなら, dist[s] = INF | O(VE)
    vector<WEIGHT_TYPE> bellmanFord2(int s, int t) {
        vector<WEIGHT_TYPE> dist(n, INF);
        auto f1 = getVisitable(s);
        auto f2 = getReverseGraph().getVisitable(t);
        dist[s] = 0;
        auto es = getEdge2();
        rep(i, n) {
            for(auto &&e : es) {
                if(!(f1[e.from] && f2[e.to])) continue;
                if(dist[e.to] > dist[e.from] + e.weight) {
                    dist[e.to] = dist[e.from] + e.weight;
                    if(i == n - 1) {
                        dist[s] = INF;
                        return dist;
                    }
                }
            }
        }
        return dist;
    }
};

#define DEBUG_MODE
#ifdef DEBUG_MODE
#define dump(x) cout << #x << " : " << x << " "
#define dumpL(x) cout << #x << " : " << x << '\n'
#define LINE cout << "line : " << __LINE__ << " "
#define LINEL cout << "line : " << __LINE__ << '\n'
#define dumpV(v) cout << #v << " : ["; for(auto& t : v) cout << t << ", "; cout<<"]" << " "
#define dumpVL(v) cout << #v << " : ["; for(auto& t : v) cout << t << ", "; cout<<"]" << endl
#define STOP assert(false)
#else
#define dump(x) 
#define dumpL(x) 
#define LINE 
#define LINEL 
#define dumpV(v) 
#define dumpVL(v) 
#define STOP assert(false)
#endif
 



template<typename T>
tuple<map<T, int>, vector<T>> zaatu(const vector<vector<T>>& v) {
    map<T, int> mp;
    for(auto&& u: v) for(auto&& x: u) mp[x] = 0;
    vector<T> r;
    for(auto& p: mp) {
        p.second = r.size();
        r.emplace_back(p.first);
    }
    return {mp, r};
}

int main(){
    ll n, m;
    cin >> n >> m;
    vl x(m), y(m);
    rep(i, m) {
        cin >> x[i] >> y[i];
        --x[i];
        --y[i];
    }
    ll ans = n*(n+1)/2;

    vector<vl> z = {x, y};

    auto [mp, r_mp] = zaatu(z);
    for(auto&& p: mp) ans -= p.first+1;

    n = mp.size();
    GraphD g(n);
    rep(i, m) g.add_edge(mp[x[i]], mp[y[i]], 1);
    auto scc = g.scc();
    vl d(n);
    rep(i, n) d[i] = r_mp[i]+1;
    repr(i, scc.size()) {
        ll ma = 0;
        for(auto&& x: scc[i]) for(auto&& y: g.es[x]) chmax(ma, d[y.to]);
        for(auto&& x: scc[i]) chmax(d[x], ma);
    }
    cout << ans + accumulate(all(d), 0LL) << '\n';
    // dumpL(ans);
    return 0;
}
0