#206416 (C++17) No.19 ステージの選択

• 問題: No.19 ステージの選択
• ユーザー: mai
• 提出日時: 2017-09-24 21:39:55
• 言語: C++17 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 2 ms / 5,000 ms
• コード長: 7,489 bytes
• コンパイル時間: 3,587 ms
• コンパイル使用メモリ: 232,688 KB
• 実行使用メモリ: 5,376 KB
• 最終ジャッジ日時: 2024-06-02 13:02:46
• 合計ジャッジ時間: 4,148 ms
• ジャッジサーバーID （参考情報）: judge4 / judge2

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	2 ms; 5,248 KB
testcase_01	AC	1 ms; 5,376 KB
testcase_02	AC	2 ms; 5,376 KB
testcase_03	AC	2 ms; 5,376 KB
testcase_04	AC	2 ms; 5,376 KB
testcase_05	AC	1 ms; 5,376 KB
testcase_06	AC	2 ms; 5,376 KB
testcase_07	AC	1 ms; 5,376 KB
testcase_08	AC	2 ms; 5,376 KB
testcase_09	AC	1 ms; 5,376 KB
testcase_10	AC	2 ms; 5,376 KB
testcase_11	AC	2 ms; 5,376 KB
testcase_12	AC	2 ms; 5,376 KB
testcase_13	AC	2 ms; 5,376 KB
testcase_14	AC	1 ms; 5,376 KB
testcase_15	AC	2 ms; 5,376 KB
testcase_16	AC	1 ms; 5,376 KB
testcase_17	AC	2 ms; 5,376 KB
testcase_18	AC	2 ms; 5,376 KB
testcase_19	AC	1 ms; 5,376 KB
testcase_20	AC	1 ms; 5,376 KB
testcase_21	AC	1 ms; 5,376 KB
testcase_22	AC	1 ms; 5,376 KB
testcase_23	AC	2 ms; 5,376 KB

ソースコード

#pragma GCC optimize ("O3")
#pragma GCC target ("avx")
#include "bits/stdc++.h" // define macro "/D__MAI"

using namespace std;
typedef long long int ll;

#define xprintf(fmt,...) fprintf(stderr,fmt,__VA_ARGS__)
#define debugv(v) {printf("L%d %s > ",__LINE__,#v);for(auto e:v){cout<<e<<" ";}cout<<endl;}
#define debuga(m,w) {printf("L%d %s > ",__LINE__,#m);for(int x=0;x<(w);x++){cout<<(m)[x]<<" ";}cout<<endl;}
#define debugaa(m,h,w) {printf("L%d %s >\n",__LINE__,#m);for(int y=0;y<(h);y++){for(int x=0;x<(w);x++){cout<<(m)[y][x]<<" ";}cout<<endl;}}
#define ALL(v) (v).begin(),(v).end()
#define repeat(cnt,l) for(auto cnt=0ll;cnt<(l);++cnt)
#define iterate(cnt,b,e) for(auto cnt=(b);cnt!=(e);++cnt)
#define MD 1000000007ll
#define PI 3.1415926535897932384626433832795
#define EPS 1e-12
template<typename T1, typename T2> ostream& operator <<(ostream &o, const pair<T1, T2> p) { o << "(" << p.first << ":" << p.second << ")"; return o; }
template<typename iterator> inline size_t argmin(iterator begin, iterator end) { return distance(begin, min_element(begin, end)); }
template<typename iterator> inline size_t argmax(iterator begin, iterator end) { return distance(begin, max_element(begin, end)); }
template<typename T> T& maxset(T& to, const T& val) { return to = max(to, val); }
template<typename T> T& minset(T& to, const T& val) { return to = min(to, val); }

mt19937_64 randdev(8901016);
inline ll rand_range(ll l, ll h) {
    return uniform_int_distribution<ll>(l, h)(randdev);
}

#ifdef __MAI
#define getchar_unlocked getchar
#define putchar_unlocked putchar
#endif
#ifdef __VSCC
#define getchar_unlocked _getchar_nolock
#define putchar_unlocked _putchar_nolock
#endif
namespace {
#define isvisiblechar(c) (0x21<=(c)&&(c)<=0x7E)
    class MaiScanner {
    public:
        template<typename T> void input_integer(T& var) {
            var = 0;
            T sign = 1;
            int cc = getchar_unlocked();
            for (; cc<'0' || '9'<cc; cc = getchar_unlocked())
                if (cc == '-') sign = -1;
            for (; '0' <= cc&&cc <= '9'; cc = getchar_unlocked())
                var = (var << 3) + (var << 1) + cc - '0';
            var = var*sign;
        }
        inline int c() { return getchar_unlocked(); }
        inline MaiScanner& operator>>(int& var) {
            input_integer<int>(var);
            return *this;
        }
        inline MaiScanner& operator>>(long long& var) {
            input_integer<long long>(var);
            return *this;
        }
        inline MaiScanner& operator>>(string& var) {
            int cc = getchar_unlocked();
            for (; !isvisiblechar(cc); cc = getchar_unlocked());
            for (; isvisiblechar(cc); cc = getchar_unlocked())
                var.push_back(cc);
            return *this;
        }
        template<typename IT> void in(IT begin, IT end) {
            for (auto it = begin; it != end; ++it) *this >> *it;
        }
    };
}
MaiScanner scanner;




class unionfind {
public:
    vector<int> data;
    unionfind(int size) : data(size, -1) { }
    bool union_set(int x, int y) {
        x = root(x); y = root(y);
        if (x != y) {
            if (data[y] < data[x]) swap(x, y);
            data[x] += data[y]; data[y] = x;
        }
        return x != y;
    }
    inline bool find_set(int x, int y) {
        return root(x) == root(y);
    }
    inline int root(int x) {
        return data[x] < 0 ? x : data[x] = root(data[x]);
    }
    inline int size(int x) {
        return -data[root(x)];
    }
};

class DGraph {
public:
    size_t n;
    vector<vector<int>> vertex_to;
    vector<vector<int>> vertex_from;

    DGraph(size_t n) :n(n), vertex_to(n), vertex_from(n) {}

    void connect(int from, int to) {
        vertex_to[from].emplace_back(to);
        vertex_from[to].emplace_back(from);
    }
    void resize(size_t _n) {
        n = _n;
        vertex_to.resize(_n);
        vertex_from.resize(_n);
    }
};

int strongly_connected_components(const DGraph& graph, unionfind& result) {
    stack<int> s;
    int size = graph.n;
    vector<int> num(size), low(size);
    vector<int> flg(size);
    int count = 0;
    int n_components = graph.n;

    function<void(int)> dfs = [&](int idx) {
        low[idx] = num[idx] = ++count;
        s.push(idx);
        flg[idx] = true;

        for (int w : graph.vertex_to[idx]) {
            if (num[w] == 0) {
                dfs(w);
                low[idx] = min(low[idx], low[w]);
            }
            else if (flg[w]) { // ?
                low[idx] = min(low[idx], num[w]);
            }
        }
        if (low[idx] == num[idx]) {
            while (!s.empty()) {
                int w = s.top(); s.pop();
                flg[w] = false;
                if (idx == w) break;
                n_components -= result.union_set(idx, w);
            }
        }
    };
    for (int i = 0; i < graph.n; ++i) {
        if (num[i] == 0) dfs(i);
    }
    return n_components;
}

class scc_DGraph {
public:
    const DGraph& orig;
    DGraph sccg;
    vector<int> ori2scc;
    vector<vector<int>> scc2ori;

    scc_DGraph(const DGraph& g) :orig(g), sccg(1), ori2scc(g.n, -1) { build(); }

    void build() {
        unionfind uf(orig.n);
        strongly_connected_components(orig, uf);

        int n_vtx = 0;
        for (int i = 0; i < orig.n; ++i) {
            int r = uf.root(i);
            if (ori2scc[r] == -1) {
                ori2scc[r] = n_vtx++;
                scc2ori.emplace_back();
            }
            ori2scc[i] = ori2scc[r];
            scc2ori[ori2scc[i]].push_back(i);
        }
        sccg.resize(n_vtx);

        for (int i = 0; i < orig.n; ++i) {
            for (int to : orig.vertex_to[i]) {
                if (ori2scc[i] == ori2scc[to]) continue;
                sccg.connect(ori2scc[i], ori2scc[to]);
            }
        }
    }

    inline const vector<int>& vertex_to(int v) const { return sccg.vertex_to[v]; }
    inline const vector<int>& vertex_from(int v) const { return sccg.vertex_from[v]; }
    inline int size() const { return sccg.n; }

};



ll m, n, kei;

pair<int, int> stages[110];

int main() {

    scanner >> n;

    DGraph graph(n);

    repeat(i, n) {
        int l, s;
        scanner >> l >> s;
        l *= 2;
        --s;
        stages[i] = make_pair(l, s);

        if (s != i) {
            graph.connect(s, i);
        }
    }

    scc_DGraph scc(graph);

    // 強連結成分の難易度は，「強連結成分の難易度の総和/2 + 強連結成分内の最も簡単な難易度/2」

    // 制約(入次数が高々1)より，強連結成分は弱連結成分でもある
    
    // つまり，弱連結成分は，サイクルか根付き木のどちらか．

    // もしかして，サイクル検出だけで十分？SCC要らない？


    int result = 0;

    for (auto& lis : scc.scc2ori) {
        if (lis.size() >= 2) {

            int easy = 1e9;
            int sum = 0;

            for (int u : lis) {
                int d = stages[u].first;
                sum += d;
                minset(easy, d);
            }
            result += sum / 2 + easy / 2;

        }
        else if (lis.size() == 1) {
            int u = lis[0];
            int d = stages[u].first;

            if (graph.vertex_from[u].size() == 0) { // 入次数が0
                result += d;
            }
            else {
                result += d / 2;
            }
        }

    }

    printf("%.1f\n", (double)result / 2);


    return 0;
}