結果

問題 No.2604 Initial Motion
ユーザー inksamurai
提出日時 2024-01-12 22:16:28
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 189 ms / 3,000 ms
コード長 10,025 bytes
コンパイル時間 2,893 ms
コンパイル使用メモリ 220,004 KB
最終ジャッジ日時 2025-02-18 18:28:49
ジャッジサーバーID
（参考情報） 		judge1 / judge5
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 39
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 #
プレゼンテーションモードにする

#include <bits/stdc++.h>
// cut here
#include <utility>
 
namespace atcoder {
namespace internal {
 
template <class E> struct csr {
    std::vector<int> start;
    std::vector<E> elist;
    explicit csr(int n, const std::vector<std::pair<int, E>>& edges)
        : start(n + 1), elist(edges.size()) {
        for (auto e : edges) {
            start[e.first + 1]++;
        }
        for (int i = 1; i <= n; i++) {
            start[i] += start[i - 1];
        }
        auto counter = start;
        for (auto e : edges) {
            elist[counter[e.first]++] = e.second;
        }
    }
};
 
}  // namespace internal
 
}  // namespace atcoder
 
namespace atcoder {
 
namespace internal {
 
template <class T> struct simple_queue {
    std::vector<T> 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 T& t) { payload.push_back(t); }
    T& front() { return payload[pos]; }
    void clear() {
        payload.clear();
        pos = 0;
    }
    void pop() { pos++; }
};
 
}  // namespace internal
 
}  // namespace atcoder
 
namespace atcoder {
 
template <class Cap, class Cost> struct mcf_graph {
  public:
    mcf_graph() {}
    explicit mcf_graph(int n) : _n(n) {}
 
    int add_edge(int from, int to, Cap cap, Cost cost) {
        int m = int(_edges.size());
        _edges.push_back({from, to, cap, 0, cost});
        return m;
    }
 
    struct edge {
        int from, to;
        Cap cap, flow;
        Cost cost;
    };
 
    edge get_edge(int i) {
        int m = int(_edges.size());
        return _edges[i];
    }
    std::vector<edge> edges() { return _edges; }
 
    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) {
 
        int m = int(_edges.size());
        std::vector<int> edge_idx(m);
 
        auto g = [&]() {
            std::vector<int> degree(_n), redge_idx(m);
            std::vector<std::pair<int, _edge>> elist;
            elist.reserve(2 * m);
            for (int i = 0; i < m; i++) {
                auto e = _edges[i];
                edge_idx[i] = degree[e.from]++;
                redge_idx[i] = degree[e.to]++;
                elist.push_back({e.from, {e.to, -1, e.cap - e.flow, e.cost}});
                elist.push_back({e.to, {e.from, -1, e.flow, -e.cost}});
            }
            auto _g = internal::csr<_edge>(_n, elist);
            for (int i = 0; i < m; i++) {
                auto e = _edges[i];
                edge_idx[i] += _g.start[e.from];
                redge_idx[i] += _g.start[e.to];
                _g.elist[edge_idx[i]].rev = redge_idx[i];
                _g.elist[redge_idx[i]].rev = edge_idx[i];
            }
            return _g;
        }();
 
        auto result = slope(g, s, t, flow_limit);
 
        for (int i = 0; i < m; i++) {
            auto e = g.elist[edge_idx[i]];
            _edges[i].flow = _edges[i].cap - e.cap;
        }
 
        return result;
    }
 
  private:
    int _n;
    std::vector<edge> _edges;
 
    // inside edge
    struct _edge {
        int to, rev;
        Cap cap;
        Cost cost;
    };
 
    std::vector<std::pair<Cap, Cost>> slope(internal::csr<_edge>& g,
                                            int s,
                                            int t,
                                            Cap flow_limit) {
        // 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_dist[i] = (dual[i], dist[i])
        std::vector<std::pair<Cost, Cost>> dual_dist(_n);
        std::vector<int> prev_e(_n);
        std::vector<bool> vis(_n);
        struct Q {
            Cost key;
            int to;
            bool operator<(Q r) const { return key > r.key; }
        };
        std::vector<int> que_min;
        std::vector<Q> que;
        auto dual_ref = [&]() {
            for (int i = 0; i < _n; i++) {
                dual_dist[i].second = std::numeric_limits<Cost>::max();
            }
            std::fill(vis.begin(), vis.end(), false);
            que_min.clear();
            que.clear();
 
            // que[0..heap_r) was heapified
            size_t heap_r = 0;
 
            dual_dist[s].second = 0;
            que_min.push_back(s);
            while (!que_min.empty() || !que.empty()) {
                int v;
                if (!que_min.empty()) {
                    v = que_min.back();
                    que_min.pop_back();
                } else {
                    while (heap_r < que.size()) {
                        heap_r++;
                        std::push_heap(que.begin(), que.begin() + heap_r);
                    }
                    v = que.front().to;
                    std::pop_heap(que.begin(), que.end());
                    que.pop_back();
                    heap_r--;
                }
                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
                Cost dual_v = dual_dist[v].first, dist_v = dual_dist[v].second;
                for (int i = g.start[v]; i < g.start[v + 1]; i++) {
                    auto e = g.elist[i];
                    if (!e.cap) continue;
                    // |-dual[e.to] + dual[v]| <= (n-1)C
                    // cost <= C - -(n-1)C + 0 = nC
                    Cost cost = e.cost - dual_dist[e.to].first + dual_v;
                    if (dual_dist[e.to].second - dist_v > cost) {
                        Cost dist_to = dist_v + cost;
                        dual_dist[e.to].second = dist_to;
                        prev_e[e.to] = e.rev;
                        if (dist_to == dist_v) {
                            que_min.push_back(e.to);
                        } else {
                            que.push_back(Q{dist_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_dist[v].first -= dual_dist[t].second - dual_dist[v].second;
            }
            return true;
        };
        Cap flow = 0;
        Cost cost = 0, prev_cost_per_flow = -1;
        std::vector<std::pair<Cap, Cost>> result = {{Cap(0), Cost(0)}};
        while (flow < flow_limit) {
            if (!dual_ref()) break;
            Cap c = flow_limit - flow;
            for (int v = t; v != s; v = g.elist[prev_e[v]].to) {
                c = std::min(c, g.elist[g.elist[prev_e[v]].rev].cap);
            }
            for (int v = t; v != s; v = g.elist[prev_e[v]].to) {
                auto& e = g.elist[prev_e[v]];
                e.cap += c;
                g.elist[e.rev].cap -= c;
            }
            Cost d = -dual_dist[s].first;
            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;
    }
};
 
}  // namespace atcoder
// cut here
#define int ll
using namespace std;
#define rep(i,n) for(int i=0;i<n;i++)
#define per(i,n) for(int i=n-1;i>=0;i--)
#define rng(i,c,n) for(int i=c;i<n;i++)
#define fi first
#define se second
#define pb push_back
#define sz(a) (int)a.size()
#define vec(...) vector<__VA_ARGS__>
#define _4aNWZeC ios::sync_with_stdio(0),cin.tie(0)
using ll=long long;
using pii=pair<int,int>;
using vi=vector<int>;
void print(){cout<<'\n';}
template<class h,class...t>
void print(const h&v,const t&...u){cout<<v<<' ',print(u...);}
mt19937_64 qrand(chrono::steady_clock::now().time_since_epoch().count());
void slv(){
    int n,k,m;
    cin>>n>>k>>m;
    swap(n,k);
    // k=2000;
    // n=2000;
    // m=2000;
    
    vi cnt_l(n);
    rep(i,k){
        int v;
        // v=qrand()%n;
        cin>>v;
        v-=1;
        cnt_l[v]++;
    }
    
    int s=0;
    vi cnt_r(n);
    rep(i,n){
        int x;
        // x=qrand()%n;
        // s+=x;
        cin>>x;
        cnt_r[i]=x;
    }
    // if(s<k){
    //  cnt_r[0]+=k-s;
    // }
    vec(vec(pii)) adj(n);
    rep(i,m){
        int u,v,w;
        // w=qrand()%(int)(1e12);
        // while(1){
        //  u=qrand()%n;
        //  v=qrand()%n;
        //  if(u!=v) break;
        // }
        cin>>u>>v>>w;
        u-=1,v-=1;
        // print(u,v,w);
        adj[u].pb({w,v}),adj[v].pb({w,u});
    }
    // const int inf=1e18;
    // vec(vi) dist(n,vi(n,inf));
    // rep(s,n){
    //  dist[s][s]=0;
    //  priority_queue<pii,vec(pii),greater<pii>> pq;
    //  pq.push({0,s});
    //  while(sz(pq)){
    //      auto [cosu,v]=pq.top();
    //      pq.pop();
    //      if(cosu!=dist[s][v]) continue;
    //      for(auto [w,u]:adj[v]){
    //          int ncosu=cosu+w;
    //          if(dist[s][u]>ncosu){
    //              dist[s][u]=ncosu;
    //              pq.push({ncosu,u});
    //          }
    //      }
    //  }
    // }
    atcoder::mcf_graph<int,int> g(2*n+2);
    const int src=2*n;
    const int tink=2*n+1;
    rep(v,n){
        g.add_edge(src,v,cnt_l[v],0);
        g.add_edge(v+n,tink,cnt_r[v],0);
    }
    rep(v,n){
        g.add_edge(v,v+n,n,0);
    }
    rep(v,n){
        for(auto [w,u]:adj[v]){
            g.add_edge(v,u,n,w);
        }
    }
    auto res=g.flow(src,tink);
    cout<<res.se<<"\n";
}
signed main(){
_4aNWZeC;
    slv();
}
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