#604548 (C++17) No.1341 真ん中を入れ替えて門松列

提出ソース
結果

問題	No.1341 真ん中を入れ替えて門松列
ユーザー	hitonanode
提出日時	2021-01-15 22:44:53
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	TLE
実行時間	-
コード長	20,465 bytes
コンパイル時間	3,195 ms
コンパイル使用メモリ	246,000 KB
実行使用メモリ	11,392 KB
最終ジャッジ日時	2024-05-05 00:45:00
合計ジャッジ時間	6,710 ms
ジャッジサーバーID （参考情報）	judge5 / judge1
このコードへのチャレンジ
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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	2 ms 10,752 KB
testcase_01	AC	2 ms 5,376 KB
testcase_02	AC	2 ms 5,376 KB
testcase_03	AC	1 ms 5,376 KB
testcase_04	AC	2 ms 5,376 KB
testcase_05	AC	2 ms 5,376 KB
testcase_06	AC	20 ms 5,376 KB
testcase_07	TLE	-
testcase_08	--	-
testcase_09	--	-
testcase_10	--	-
testcase_11	--	-
testcase_12	--	-
testcase_13	--	-
testcase_14	--	-
testcase_15	--	-
testcase_16	--	-
testcase_17	--	-
testcase_18	--	-
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ソースコード

raw source code
#pragma GCC optimize("O3")
// #pragma GCC optimize("unroll-loops")
#include <bits/stdc++.h>
using namespace std;
using lint = long long;
using pint = pair<int, int>;
using plint = pair<lint, lint>;
struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_;
#define ALL(x) (x).begin(), (x).end()
#define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i<i##_end_;i++)
#define IFOR(i, begin, end) for(int i=(end)-1,i##_begin_=(begin);i>=i##_begin_;i--)
#define REP(i, n) FOR(i,0,n)
#define IREP(i, n) IFOR(i,0,n)
template <typename T, typename V>
void ndarray(vector<T>& vec, const V& val, int len) { vec.assign(len, val); }
template <typename T, typename V, typename... Args> void ndarray(vector<T>& vec, const V& val, int len, Args... args) { vec.resize(len), for_each(begin(vec), end(vec), [&](T& v) { ndarray(v, val, args...); }); }
template <typename T> bool chmax(T &m, const T q) { if (m < q) {m = q; return true;} else return false; }
template <typename T> bool chmin(T &m, const T q) { if (m > q) {m = q; return true;} else return false; }
int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); }
template <typename T1, typename T2> pair<T1, T2> operator+(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first + r.first, l.second + r.second); }
template <typename T1, typename T2> pair<T1, T2> operator-(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first - r.first, l.second - r.second); }
template <typename T> vector<T> sort_unique(vector<T> vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; }
template <typename T> istream &operator>>(istream &is, vector<T> &vec) { for (auto &v : vec) is >> v; return is; }
template <typename T> ostream &operator<<(ostream &os, const vector<T> &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <typename T, size_t sz> ostream &operator<<(ostream &os, const array<T, sz> &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; }
#if __cplusplus >= 201703L
template <typename... T> istream &operator>>(istream &is, tuple<T...> &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; }
template <typename... T> ostream &operator<<(ostream &os, const tuple<T...> &tpl) { std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os; }
#endif
template <typename T> ostream &operator<<(ostream &os, const deque<T> &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <typename T> ostream &operator<<(ostream &os, const set<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T, typename TH> ostream &operator<<(ostream &os, const unordered_set<T, TH> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T> ostream &operator<<(ostream &os, const multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T> ostream &operator<<(ostream &os, const unordered_multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &pa) { os << '(' << pa.first << ',' << pa.second << ')'; return os; }
template <typename TK, typename TV> ostream &operator<<(ostream &os, const map<TK, TV> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
template <typename TK, typename TV, typename TH> ostream &operator<<(ostream &os, const unordered_map<TK, TV, TH> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
#ifdef HITONANODE_LOCAL
const string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m", BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9;37m", RED_BACKGROUND = "\033[1;41m", NORMAL_FAINT = "\033[0;2m";
#define dbg(x) cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << endl
#else
#define dbg(x) (x)
#endif

// MaxFlow based and AtCoder Library, single class, no namespace, no private variables, compatible with C++11
// Reference: <https://atcoder.github.io/ac-library/production/document_ja/maxflow.html>
template <class Cap> struct mf_graph {
    struct simple_queue_int {
        std::vector<int> payload;
        int pos = 0;
        void reserve(int n) { payload.reserve(n); }
        int size() const { return int(payload.size()) - pos; }
        bool empty() const { return pos == int(payload.size()); }
        void push(const int &t) { payload.push_back(t); }
        int &front() { return payload[pos]; }
        void clear() {
            payload.clear();
            pos = 0;
        }
        void pop() { pos++; }
    };

    mf_graph() : _n(0) {}
    mf_graph(int n) : _n(n), g(n) {}

    int add_edge(int from, int to, Cap cap) {
        assert(0 <= from && from < _n);
        assert(0 <= to && to < _n);
        assert(0 <= cap);
        int m = int(pos.size());
        pos.push_back({from, int(g[from].size())});
        int from_id = int(g[from].size());
        int to_id = int(g[to].size());
        if (from == to) to_id++;
        g[from].push_back(_edge{to, to_id, cap});
        g[to].push_back(_edge{from, from_id, 0});
        return m;
    }

    struct edge {
        int from, to;
        Cap cap, flow;
    };

    edge get_edge(int i) {
        int m = int(pos.size());
        assert(0 <= i && i < m);
        auto _e = g[pos[i].first][pos[i].second];
        auto _re = g[_e.to][_e.rev];
        return edge{pos[i].first, _e.to, _e.cap + _re.cap, _re.cap};
    }
    std::vector<edge> edges() {
        int m = int(pos.size());
        std::vector<edge> result;
        for (int i = 0; i < m; i++) { result.push_back(get_edge(i)); }
        return result;
    }
    void change_edge(int i, Cap new_cap, Cap new_flow) {
        int m = int(pos.size());
        assert(0 <= i && i < m);
        assert(0 <= new_flow && new_flow <= new_cap);
        auto &_e = g[pos[i].first][pos[i].second];
        auto &_re = g[_e.to][_e.rev];
        _e.cap = new_cap - new_flow;
        _re.cap = new_flow;
    }

    std::vector<int> level, iter;
    simple_queue_int que;

    void _bfs(int s, int t) {
        std::fill(level.begin(), level.end(), -1);
        level[s] = 0;
        que.clear();
        que.push(s);
        while (!que.empty()) {
            int v = que.front();
            que.pop();
            for (auto e : g[v]) {
                if (e.cap == 0 || level[e.to] >= 0) continue;
                level[e.to] = level[v] + 1;
                if (e.to == t) return;
                que.push(e.to);
            }
        }
    }
    Cap _dfs(int v, int s, Cap up) {
        if (v == s) return up;
        Cap res = 0;
        int level_v = level[v];
        for (int &i = iter[v]; i < int(g[v].size()); i++) {
            _edge &e = g[v][i];
            if (level_v <= level[e.to] || g[e.to][e.rev].cap == 0) continue;
            Cap d = _dfs(e.to, s, std::min(up - res, g[e.to][e.rev].cap));
            if (d <= 0) continue;
            g[v][i].cap += d;
            g[e.to][e.rev].cap -= d;
            res += d;
            if (res == up) return res;
        }
        level[v] = _n;
        return res;
    }

    Cap flow(int s, int t) { return flow(s, t, std::numeric_limits<Cap>::max()); }
    Cap flow(int s, int t, Cap flow_limit) {
        assert(0 <= s && s < _n);
        assert(0 <= t && t < _n);
        assert(s != t);

        level.assign(_n, 0), iter.assign(_n, 0);
        que.clear();

        Cap flow = 0;
        while (flow < flow_limit) {
            _bfs(s, t);
            if (level[t] == -1) break;
            std::fill(iter.begin(), iter.end(), 0);
            Cap f = _dfs(t, s, flow_limit - flow);
            if (!f) break;
            flow += f;
        }
        return flow;
    }

    std::vector<bool> min_cut(int s) {
        std::vector<bool> visited(_n);
        simple_queue_int que;
        que.push(s);
        while (!que.empty()) {
            int p = que.front();
            que.pop();
            visited[p] = true;
            for (auto e : g[p]) {
                if (e.cap && !visited[e.to]) {
                    visited[e.to] = true;
                    que.push(e.to);
                }
            }
        }
        return visited;
    }

    int _n;
    struct _edge {
        int to, rev;
        Cap cap;
    };
    std::vector<std::pair<int, int>> pos;
    std::vector<std::vector<_edge>> g;
};

// MinCostFlow based on AtCoder Library, no namespace, no private variables, compatible with C++11
// Reference: <https://atcoder.github.io/ac-library/production/document_ja/mincostflow.html>
// **NO NEGATIVE COST EDGES**
template <class Cap, class Cost> struct mcf_graph {
    mcf_graph() {}
    mcf_graph(int n) : _n(n), g(n) {}

    int add_edge(int from, int to, Cap cap, Cost cost) {
        assert(0 <= from && from < _n);
        assert(0 <= to && to < _n);
        assert(0 <= cap);
        assert(0 <= cost);
        int m = int(pos.size());
        pos.push_back({from, int(g[from].size())});
        int from_id = int(g[from].size());
        int to_id = int(g[to].size());
        if (from == to) to_id++;
        g[from].push_back(_edge{to, to_id, cap, cost});
        g[to].push_back(_edge{from, from_id, 0, -cost});
        return m;
    }

    struct edge {
        int from, to;
        Cap cap, flow;
        Cost cost;
    };

    edge get_edge(int i) {
        int m = int(pos.size());
        assert(0 <= i && i < m);
        auto _e = g[pos[i].first][pos[i].second];
        auto _re = g[_e.to][_e.rev];
        return edge{
            pos[i].first, _e.to, _e.cap + _re.cap, _re.cap, _e.cost,
        };
    }
    std::vector<edge> edges() {
        int m = int(pos.size());
        std::vector<edge> result(m);
        for (int i = 0; i < m; i++) { result[i] = get_edge(i); }
        return result;
    }

    std::pair<Cap, Cost> flow(int s, int t) { return flow(s, t, std::numeric_limits<Cap>::max()); }
    std::pair<Cap, Cost> flow(int s, int t, Cap flow_limit) { return slope(s, t, flow_limit).back(); }
    std::vector<std::pair<Cap, Cost>> slope(int s, int t) { return slope(s, t, std::numeric_limits<Cap>::max()); }

    std::vector<Cost> dual, dist;
    std::vector<int> pv, pe;
    std::vector<bool> vis;
    struct Q {
        Cost key;
        int to;
        bool operator<(Q r) const { return key > r.key; }
    };
    std::vector<Q> que;
    bool _dual_ref(int s, int t) {
        std::fill(dist.begin(), dist.end(), std::numeric_limits<Cost>::max());
        std::fill(vis.begin(), vis.end(), false);
        que.clear();

        dist[s] = 0;
        que.push_back(Q{0, s});
        std::push_heap(que.begin(), que.end());
        while (!que.empty()) {
            int v = que.front().to;
            std::pop_heap(que.begin(), que.end());
            que.pop_back();
            if (vis[v]) continue;
            vis[v] = true;
            if (v == t) break;
            // dist[v] = shortest(s, v) + dual[s] - dual[v]
            // dist[v] >= 0 (all reduced cost are positive)
            // dist[v] <= (n-1)C
            for (int i = 0; i < int(g[v].size()); i++) {
                auto e = g[v][i];
                if (vis[e.to] || !e.cap) continue;
                // |-dual[e.to] + dual[v]| <= (n-1)C
                // cost <= C - -(n-1)C + 0 = nC
                Cost cost = e.cost - dual[e.to] + dual[v];
                if (dist[e.to] - dist[v] > cost) {
                    dist[e.to] = dist[v] + cost;
                    pv[e.to] = v;
                    pe[e.to] = i;
                    que.push_back(Q{dist[e.to], e.to});
                    std::push_heap(que.begin(), que.end());
                }
            }
        }
        if (!vis[t]) { return false; }

        for (int v = 0; v < _n; v++) {
            if (!vis[v]) continue;
            // dual[v] = dual[v] - dist[t] + dist[v]
            //         = dual[v] - (shortest(s, t) + dual[s] - dual[t]) + (shortest(s, v) + dual[s] - dual[v])
            //         = - shortest(s, t) + dual[t] + shortest(s, v)
            //         = shortest(s, v) - shortest(s, t) >= 0 - (n-1)C
            dual[v] -= dist[t] - dist[v];
        }
        return true;
    }

    std::vector<std::pair<Cap, Cost>> slope(int s, int t, Cap flow_limit) {
        assert(0 <= s && s < _n);
        assert(0 <= t && t < _n);
        assert(s != t);
        // variants (C = maxcost):
        // -(n-1)C <= dual[s] <= dual[i] <= dual[t] = 0
        // reduced cost (= e.cost + dual[e.from] - dual[e.to]) >= 0 for all edge
        dual.assign(_n, 0), dist.assign(_n, 0);
        pv.assign(_n, 0), pe.assign(_n, 0);
        vis.assign(_n, false);
        Cap flow = 0;
        Cost cost = 0, prev_cost_per_flow = -1;
        std::vector<std::pair<Cap, Cost>> result;
        result.push_back({flow, cost});
        while (flow < flow_limit) {
            if (!_dual_ref(s, t)) break;
            Cap c = flow_limit - flow;
            for (int v = t; v != s; v = pv[v]) { c = std::min(c, g[pv[v]][pe[v]].cap); }
            for (int v = t; v != s; v = pv[v]) {
                auto &e = g[pv[v]][pe[v]];
                e.cap -= c;
                g[v][e.rev].cap += c;
            }
            Cost d = -dual[s];
            flow += c;
            cost += c * d;
            if (prev_cost_per_flow == d) { result.pop_back(); }
            result.push_back({flow, cost});
            prev_cost_per_flow = d;
        }
        return result;
    }

    struct _edge {
        int to, rev;
        Cap cap;
        Cost cost;
    };

    int _n;
    std::vector<std::pair<int, int>> pos;
    std::vector<std::vector<_edge>> g;
};

// https://github.com/beet-aizu/library/blob/master/bflow/capacityscaling.cpp
// O(m^2 \log m \log U)
// U: maximum capacity
enum Objective{
  MINIMIZE = +1,
  MAXIMIZE = -1,
};
template<typename Flow, typename Cost,
         Objective objective = Objective::MINIMIZE>
struct MinCostFlow{
  template<typename T> inline void chmin(T &x,T y){x=min(x,y);}

  struct Edge{
    int src,dst;
    Flow flow,cap;
    Cost cost;
    int rev;
    Edge(int src,int dst,Flow cap,Cost cost,int rev):
      src(src),dst(dst),flow(0),cap(cap),cost(cost),rev(rev){}
    Flow residual_cap()const{return cap-flow;}
  };

  struct EdgePtr{
    int v,e;
    EdgePtr(int v,int e):v(v),e(e){}
  };

  int n;
  vector<vector<Edge>> G;
  vector<Flow> b;
  vector<Cost> p;

  MinCostFlow(int n):n(n),G(n),b(n,0){}

  EdgePtr add_edge(int src,int dst,Flow lower,Flow upper,Cost cost){
    int e=G[src].size();
    int r=(src==dst?e+1:G[dst].size());
    assert(lower<=upper);
    G[src].emplace_back(src,dst,+upper,+cost*objective,r);
    G[dst].emplace_back(dst,src,-lower,-cost*objective,e);
    return EdgePtr(src,e);
  }

  const Edge &get_edge(EdgePtr ep)const{return G[ep.v][ep.e];}

  void push(Edge &e,Flow amount){
    e.flow+=amount;
    G[e.dst][e.rev].flow-=amount;
  }

  void add_supply(int v,Flow amount){b[v]+=amount;}
  void add_demand(int v,Flow amount){b[v]-=amount;}

  Cost residual_cost(const Edge &e){
    return e.cost+p[e.src]-p[e.dst];
  }

  vector<int> excess_vs,deficit_vs;
  void saturate_negative(const Flow delta){
    for(auto &es:G){
      for(auto &e:es){
        Flow cap=e.residual_cap();
        cap-=cap%delta;
        if(cap<0 or residual_cost(e)<0){
          push(e,cap);
          b[e.src]-=cap;
          b[e.dst]+=cap;
        }
      }
    }

    excess_vs.clear();
    deficit_vs.clear();
    for(int v=0;v<n;v++){
      if(b[v]>0) excess_vs.emplace_back(v);
      if(b[v]<0) deficit_vs.emplace_back(v);
    }
  }

  const Cost unreachable = std::numeric_limits<Cost>::max();
  Cost farthest;
  vector<Cost> dist;
  vector<Edge*> parent;

  struct P{
    Cost first;
    int second;
    P(Cost first,int second):first(first),second(second){}
    bool operator<(const P o)const{return first>o.first;}
  };

  priority_queue<P> pq;

  template<typename Predicate>
  void eliminate(vector<int> &vs,Predicate predicate){
    vs.erase(remove_if(begin(vs),end(vs),predicate),end(vs));
  }

  bool dual(const Flow delta){
    eliminate(excess_vs, [&](int v){return b[v]<+delta;});
    eliminate(deficit_vs,[&](int v){return b[v]>-delta;});

    dist.assign(n,unreachable);
    for(int v:excess_vs) pq.emplace(dist[v]=0,v);

    parent.assign(n,nullptr);
    auto emplace=[&](Edge& e){
      if(e.residual_cap()<delta) return;
      Cost nxt=dist[e.src]+residual_cost(e);
      if(nxt>=dist[e.dst]) return;
      pq.emplace(dist[e.dst]=nxt,e.dst);
      parent[e.dst]=&e;
    };

    farthest=0;
    int deficit_count=0;
    while(!pq.empty()){
      Cost d=pq.top().first;
      int v=pq.top().second;
      pq.pop();
      if(dist[v]<d) continue;
      farthest=d;

      if(b[v]<=-delta) deficit_count++;
      if(deficit_count>=(int)deficit_vs.size()) break;

      for(auto &e:G[v]) emplace(e);
    }
    pq=decltype(pq)();

    for(int v=0;v<n;v++)
      p[v]+=min(dist[v],farthest);

    return deficit_count>0;
  }

  void primal(const Flow delta){
    for(int t:deficit_vs){
      if(dist[t]>farthest) continue;
      Flow f=-b[t];
      int v;
      for(v=t;parent[v];v=parent[v]->src)
        chmin(f,parent[v]->residual_cap());
      chmin(f,b[v]);

      f-=f%delta;
      if(f<=0) continue;

      for(v=t;parent[v];){
        auto &e=*parent[v];
        push(e,f);
        int u=parent[v]->src;
        if(e.residual_cap()<=0) parent[v]=nullptr;
        v=u;
      }
      b[t]+=f;
      b[v]-=f;
    }
  }

  template<Flow SCALING_FACTOR=2>
  bool build(){
    p.resize(n);
    Flow max_flow=1;
    for(auto t:b) max_flow=max({max_flow,t,-t});
    for(auto &es:G)
      for(auto &e:es)
        max_flow=max({max_flow,e.residual_cap(),-e.residual_cap()});

    Flow delta=1;
    while(delta<max_flow) delta*=SCALING_FACTOR;
    for(;delta;delta/=SCALING_FACTOR){
      saturate_negative(delta);
      while(dual(delta)) primal(delta);
    }

    return excess_vs.empty() and deficit_vs.empty();
  }

  template<typename T=Cost>
  T get_cost(){
    T res=0;
    for(auto &es:G)
      for(auto &e:es)
        res+=T(e.flow)*T(e.cost)/T(objective);
    return res/T(2);
  }
  template<typename T=Cost> T get_gain(){return get_cost();}

  vector<Cost> get_potential(){
    fill(p.begin(),p.end(),0);
    for(int i=0;i<n;i++)
      for(auto &es:G)
        for(auto &e:es)
          if(e.residual_cap()>0)
            chmin(p[e.dst],p[e.src]+e.cost);
    return p;
  }
};


void bad()
{
    puts("NO");
    exit(0);
}

int main() {
    int N;
    lint M;
    cin >> N >> M;
    vector<lint> A(N), B(N), C(N);
    REP(i, N) {
        cin >> A[i] >> B[i] >> C[i];
        if (A[i] == C[i]) bad();
        if (A[i] > C[i]) swap(A[i], C[i]);
    }


    vector<pint> asort(N), csort(N);
    REP(i, N) asort[i] = make_pair(A[i], i);
    REP(i, N) csort[i] = make_pair(C[i], i);
    sort(ALL(asort));
    sort(ALL(csort));

    const int gs = N * 4, gt = gs + 1;
    const lint UP = 0;


    MinCostFlow<int, lint> g2(gt + 1);

    REP(i, N) g2.add_edge(gs, i, 0, 1, 0);

    REP(i, N) g2.add_edge(i + N, i + 3 * N, 0, 1, -C[i]);
    REP(i, N) g2.add_edge(i + 2 * N, i + 3 * N, 0, 1, UP);

    REP(i, N - 1) {
        int j = asort[i].second, k = asort[i + 1].second;
        g2.add_edge(N + j, N + k, 0, N - 1, 0);
    }

    REP(i, N - 1) {
        int j = csort[i].second, k = csort[i + 1].second;
        g2.add_edge(N * 2 + k, N * 2 + j, 0, N - 1, 0);
    }

    REP(i, N) g2.add_edge(i + 3 * N, gt, 0, 1, 0);

    REP(i, N) {
        int j = lower_bound(ALL(asort), pint(B[i] + 1, 0)) - asort.begin();
        if (j < N) {
            int to = asort[j].second;
            g2.add_edge(i, to + N, 0, 1, UP);
        }
        j = lower_bound(ALL(csort), pint(B[i], 0)) - csort.begin() - 1;
        if (j >= 0) {
            int to = csort[j].second;
            g2.add_edge(i, to + N * 2, 0, 1, UP - B[i]);
        }
    }
    g2.add_supply(gs, N);
    g2.add_demand(gt, N);
    if (!g2.build()) bad();
    else puts("YES");

    // auto f2 = g2.(gs, gt, N);
    lint k = N * UP * 2 - g2.get_cost();
    // if (f2.first < N) bad();
    if (k < M) bad();
    puts("KADOMATSU!");
}
yukicoder

結果

テストケース

ソースコード
