結果

問題 No.1678 Coin Trade (Multiple)
ユーザー fumofumofunifumofumofuni
提出日時 2021-09-11 01:18:37
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 454 ms / 5,000 ms
コード長 6,787 bytes
コンパイル時間 2,313 ms
コンパイル使用メモリ 223,696 KB
実行使用メモリ 16,316 KB
最終ジャッジ日時 2023-09-03 16:41:51
合計ジャッジ時間 11,783 ms
ジャッジサーバーID
（参考情報） 		judge14 / judge13
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 1 ms
4,376 KB
testcase_01 AC 1 ms
4,380 KB
testcase_02 AC 1 ms
4,380 KB
testcase_03 AC 50 ms
9,228 KB
testcase_04 AC 221 ms
13,140 KB
testcase_05 AC 121 ms
15,604 KB
testcase_06 AC 98 ms
14,492 KB
testcase_07 AC 183 ms
10,188 KB
testcase_08 AC 132 ms
11,016 KB
testcase_09 AC 132 ms
15,520 KB
testcase_10 AC 39 ms
6,028 KB
testcase_11 AC 165 ms
12,576 KB
testcase_12 AC 32 ms
6,256 KB
testcase_13 AC 341 ms
14,960 KB
testcase_14 AC 98 ms
8,896 KB
testcase_15 AC 130 ms
12,380 KB
testcase_16 AC 56 ms
12,236 KB
testcase_17 AC 132 ms
15,840 KB
testcase_18 AC 2 ms
4,376 KB
testcase_19 AC 1 ms
4,380 KB
testcase_20 AC 2 ms
4,380 KB
testcase_21 AC 1 ms
4,376 KB
testcase_22 AC 2 ms
4,380 KB
testcase_23 AC 1 ms
4,380 KB
testcase_24 AC 2 ms
4,376 KB
testcase_25 AC 2 ms
4,384 KB
testcase_26 AC 2 ms
4,376 KB
testcase_27 AC 1 ms
4,376 KB
testcase_28 AC 1 ms
4,376 KB
testcase_29 AC 1 ms
4,376 KB
testcase_30 AC 1 ms
4,384 KB
testcase_31 AC 1 ms
4,376 KB
testcase_32 AC 1 ms
4,380 KB
testcase_33 AC 2 ms
4,376 KB
testcase_34 AC 1 ms
4,376 KB
testcase_35 AC 1 ms
4,380 KB
testcase_36 AC 2 ms
4,376 KB
testcase_37 AC 1 ms
4,380 KB
testcase_38 AC 1 ms
4,376 KB
testcase_39 AC 1 ms
4,380 KB
testcase_40 AC 2 ms
4,376 KB
testcase_41 AC 1 ms
4,380 KB
testcase_42 AC 1 ms
4,380 KB
testcase_43 AC 1 ms
4,376 KB
testcase_44 AC 2 ms
4,380 KB
testcase_45 AC 2 ms
4,376 KB
testcase_46 AC 2 ms
4,380 KB
testcase_47 AC 2 ms
4,376 KB
testcase_48 AC 435 ms
16,072 KB
testcase_49 AC 424 ms
15,944 KB
testcase_50 AC 439 ms
15,956 KB
testcase_51 AC 451 ms
16,316 KB
testcase_52 AC 454 ms
15,948 KB
testcase_53 AC 443 ms
16,032 KB
testcase_54 AC 432 ms
15,976 KB
testcase_55 AC 436 ms
16,152 KB
testcase_56 AC 432 ms
16,136 KB
testcase_57 AC 438 ms
16,132 KB
testcase_58 AC 281 ms
15,612 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) for(ll i=0;i<n;i++)
#define repl(i,l,r) for(ll i=(l);i<(r);i++)
#define per(i,n) for(ll i=(n)-1;i>=0;i--)
#define perl(i,r,l) for(ll i=r-1;i>=l;i--)
#define fi first
#define se second
#define pb push_back
#define ins insert
#define pqueue(x) priority_queue<x,vector<x>,greater<x>>
#define all(x) (x).begin(),(x).end()
#define CST(x) cout<<fixed<<setprecision(x)
#define rev(x) reverse(x);
using ll=long long;
using vl=vector<ll>;
using vvl=vector<vector<ll>>;
using pl=pair<ll,ll>;
using vpl=vector<pl>;
using vvpl=vector<vpl>;
const ll MOD=1000000007;
const ll MOD9=998244353;
const int inf=2e9+1;
const ll INF=4e18;
const ll dy[8]={-1,0,1,0,1,1,-1,-1};
const ll dx[8]={0,-1,0,1,1,-1,1,-1};
template <typename T> inline bool chmax(T &a, T b) {
  return ((a < b) ? (a = b, true) : (false));
}
template <typename T> inline bool chmin(T &a, T b) {
  return ((a > b) ? (a = b, true) : (false));
}


template <class Cap, class Cost> struct MinCostFlow {
  public:
    MinCostFlow() {}
    MinCostFlow(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);
        int m = int(pos.size());
        pos.push_back({from, int(g[from].size())});
        g[from].push_back(_edge{to, int(g[to].size()), cap, cost});
        g[to].push_back(_edge{from, int(g[from].size()) - 1, 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<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
        std::vector<Cost> dual(_n, 0), dist(_n);
        std::vector<int> pv(_n), pe(_n);
        std::vector<bool> vis(_n);
        auto dual_ref = [&]() {
            std::fill(dist.begin(), dist.end(),
                      std::numeric_limits<Cost>::max());
            std::fill(pv.begin(), pv.end(), -1);
            std::fill(pe.begin(), pe.end(), -1);
            std::fill(vis.begin(), vis.end(), false);
            struct Q {
                Cost key;
                int to;
                bool operator<(Q r) const { return key > r.key; }
            };
            std::priority_queue<Q> que;
            dist[s] = 0;
            que.push(Q{0, s});
            while (!que.empty()) {
                int v = que.top().to;
                que.pop();
                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(Q{dist[e.to], e.to});
                    }
                }
            }
            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;
        };
        Cap flow = 0;
        Cost cost = 0, prev_cost = -1;
        std::vector<std::pair<Cap, Cost>> result;
        result.push_back({flow, cost});
        while (flow < flow_limit) {
            if (!dual_ref()) 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 == d) {
                result.pop_back();
            }
            result.push_back({flow, cost});
            prev_cost = cost;
        }
        return result;
    }

  private:
    int _n;

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

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


int main(){
  ll n,k;cin >> n >> k;
  vl a(n);
  vvpl g(n);
  rep(i,n-1)g[i].push_back({i+1,0});
  rep(i,n){
    cin >> a[i];
    ll m;cin >> m;
    rep(j,m){
      ll from;cin >> from;from--;
      ll w=a[i]-a[from];
      if(w<=0)continue;
      g[from].push_back({i,-w});
    }
  }
  vl dp(n,INF);//ポテンシャル
  dp[0]=0;
  rep(i,n){
    for(auto [to,weight]:g[i]){
      chmin(dp[to],dp[i]+weight);
    }
  }
  MinCostFlow<ll,ll> mcf(n);
  rep(i,n){
    for(auto [to,weight]:g[i]){
      if(weight==0)mcf.add_edge(i,to,INF,weight+dp[i]-dp[to]);
      else mcf.add_edge(i,to,1,weight+dp[i]-dp[to]);
    }
  }
  /*for(auto p:mcf.edges()){
    cout << p.from <<" " << p.to <<" " << p.cap << " " << p.cost << endl;
  }*/
  cout << -(dp[n-1]*k+mcf.flow(0,n-1,k).second) << endl;
}
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