結果

問題 No.2320 Game World for PvP
コンテスト
ユーザー 🍮かんプリン
提出日時 2023-05-27 00:06:40
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 4 ms / 2,000 ms
コード長 9,144 bytes
コンパイル時間 2,256 ms
コンパイル使用メモリ 144,872 KB
実行使用メモリ 5,248 KB
最終ジャッジ日時 2024-12-25 11:37:28
合計ジャッジ時間 2,966 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge4
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 * 4
other AC * 30
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 # 

#pragma region include
#include <iostream>
#include <iomanip>
#include <stdio.h>
#include <vector>
#include <algorithm>
#include <cmath>
#include <map>
#include <set>
#include <string>
#include <bitset>
#include <complex>
#include <deque>
#include <functional>
#include <limits>
#include <list>
#include <numeric>
#include <queue>
#include <stack>
#include <utility>
#include <array>
#include <random>
#include <tuple>
#include <unordered_map>
#include <unordered_set>
#include <assert.h>
#include <chrono>
#include <cstring>
#include <memory>
#include <unistd.h>
#include <thread>
using namespace std;
typedef long long ll;
#define dump(x) cerr << #x << " = " << (x) << " [" << __LINE__ << ":" << __FUNCTION__ << "] " << endl << flush
// vector???��?��??��?��o???��?��??��?��???��?��??��?��
template < typename T >
ostream& operator<<(ostream& os, vector< T >& v) {
    os << "{";
    for (int i = 0; i < (int)v.size(); i++) {
        os << v[i] << (i < v.size() - 1 ? ", " : "");
    }
    os << "}";
    return os;
}
// pair???��?��??��?��o???��?��??��?��???��?��??��?��
template < typename T, typename U >
ostream& operator<<(ostream& os, const pair< T, U >& p) {
    return os << "(" << p.first << ", " << p.second << ")";
}
// map???��?��??��?��o???��?��??��?��???��?��??��?��
template < typename T, typename U >
ostream& operator<<(ostream& os, const map< T, U >& map_var) {
    os << "{";
    for (auto itr = map_var.begin(); itr != map_var.end(); itr++) {
        os << "(" << itr->first << ", " << itr->second << ")";
        itr++;
        if (itr != map_var.end()) os << ", ";
        itr--;
    }
    os << "}";
    return os;
}
// set ???��?��??��?��o???��?��??��?��???��?��??��?��
template < typename T >
ostream& operator<<(ostream& os, const set< T >& set_var) {
    os << "{";
    for (auto itr = set_var.begin(); itr != set_var.end(); itr++) {
        os << *itr;
        ++itr;
        if (itr != set_var.end()) os << ", ";
        itr--;
    }
    os << "}";
    return os;
}
// multiset ???��?��??��?��o???��?��??��?��???��?��??��?��
template < typename T >
ostream& operator<<(ostream& os, const multiset< T >& set_var) {
    os << "{";
    for (auto itr = set_var.begin(); itr != set_var.end(); itr++) {
        os << *itr;
        ++itr;
        if (itr != set_var.end()) os << ", ";
        itr--;
    }
    os << "}";
    return os;
}
#pragma endregion

/////////////////////////////////////////

// 最大流O(V^2E) 実際もっと早い
// 容量全部同じO(E√E)
struct Dinic {
private:
    struct edge {
        int to;
        ll cap;
        int rev;
        bool isrev;
    };

    vector< vector< edge > > graph;
    vector< int > min_cost, iter;

    bool bfs(int s, int t) {
        min_cost.assign(graph.size(), -1);
        queue< int > que;
        min_cost[s] = 0;
        que.push(s);
        while (!que.empty() && min_cost[t] == -1) {
            int p = que.front();
            que.pop();
            for (auto &e : graph[p]) {
                if (e.cap == 0 || min_cost[e.to] != -1) continue;
                min_cost[e.to] = min_cost[p] + 1;
                que.push(e.to);
            }
        }
        return min_cost[t] != -1;
    }

    ll dfs(const int s, int v, ll flow) {
        if (v == s) return flow;
        ll res = 0;
        int min_cost_v = min_cost[v];
        for (int &i = iter[v]; i < (int)graph[v].size(); i++) {
            edge &e = graph[v][i];
            if (graph[e.to][e.rev].cap == 0 || min_cost_v <= min_cost[e.to]) continue;
            ll d = dfs(s, e.to, min(flow-res, graph[e.to][e.rev].cap));
            if (d <= 0) continue;
            e.cap += d;
            graph[e.to][e.rev].cap -= d;
            res += d;
            if (res == flow) return res;
        }
        min_cost[v] = (int)graph.size();
        return res;
    }
public:

    Dinic() {}
    Dinic(int V) : graph(V) {}

    // from から to への容量capの有向辺
    void add_edge(int from, int to, ll cap) {
        graph[from].push_back({to, cap, (int)graph[to].size(), false});
        graph[to].push_back({from, 0, (int)graph[from].size() - 1, true});
    }

    ll max_flow(int s, int t, ll flow_limit = 1e18 + 6) {
        ll flow = 0;
        while (bfs(s, t)) {
            if (min_cost[t] == -1) break;
            iter.assign(graph.size(), 0);
            ll f = dfs(s, t, flow_limit-flow);
            if (!f) break;
            flow += f;
        }
        return flow;
    }

    // 先にmax_flowが必要
    // s側カットを出力
    vector<int> min_cnt(int s,int t) {
        vector<bool> visited(graph.size());
        vector<int> ret;
        stack<int> sta;
        visited[s] = true;
        sta.push(s); ret.push_back(s);
        while(!sta.empty()) {
            int v = sta.top(); sta.pop();
            for (auto &e : graph[v]) {
                if (visited[e.to] || e.cap == 0) continue;
                visited[e.to] = true;
                sta.push(e.to);
                ret.push_back(e.to);
            }
        }
        return ret;
    }

    void output() {
        for (int i = 0; i < graph.size(); i++) {
            for (auto &e : graph[i]) {
                if (e.isrev) continue;
                auto &rev_e = graph[e.to][e.rev];
                cout << i << "->" << e.to << " (flow: " << rev_e.cap << "/" << e.cap + rev_e.cap << ")" << endl;
            }
        }
    }
};

struct ProjectSelectionProblem {
    const long long INF = 1e18+1; // costには使わない
    int n; // 要素数
    vector<int> k; // 選択肢数
    vector<int> s; // 要素を表す頂点の開始index
    vector<vector<long long>> cost;
    Dinic G;
    long long ans;
    
    // k:各要素の選択肢数
    ProjectSelectionProblem(vector<int> k) : k(k) {
        n = k.size();
        s = vector<int>(n+1);
        s[0] = 0;
        for (int i = 0; i < n; i++) {
            assert(k[i] >= 2);
            s[i+1] = s[i]+k[i]-1;
        }
        cost = vector<vector<long long>>(n);
        for (int i = 0; i < n; i++) cost[i] = vector<long long>(k[i],0);
        G = Dinic(s[n]+2);
        ans = 0;
    }

    // aの選択のコスト
    void add_cost_1(int a,vector<long long> x) {
        assert(0 <= a && a < n);
        assert(k[a] == (int)x.size());
        for (int i = 0; i < k[a]; i++) {
            cost[a][i] += x[i];
        }
    }

    // x:abの選択間のコスト(Monge)
    void add_cost_2(int a,int b,vector<vector<long long>> x) {
        assert(0 <= a && a < n && 0 <= b && b < n);
        assert((int)x.size() == k[a]);
        for (int i = 0; i < k[a]; i++) {
            assert((int)x[i].size() == k[b]);
            cost[a][i] += x[i][0];
            for (int j = k[b]-1; j >= 0; j--) x[i][j] -= x[i][0];
        }
        for (int i = 1; i < k[b]; i++){
            cost[b][i] += x[k[a]-1][i];
            for (int j = 0; j < k[a]; j++) x[j][i] -= x[k[a]-1][i];
        }
        for (int i = 0; i < k[a]-1; i++){
            for (int j = 0; j < k[b]-1; j++){
                long long c = x[i+1][j]+x[i][j+1]-x[i][j]-x[i+1][j+1];
                assert(c >= 0);
                if (c == 0) continue;
                G.add_edge(s[b]+j, s[a]+i, c);
            }
        }
    }

    long long mincost() {
        for (int i = 0; i < n; i++){
            for (int j = 0; j < k[i]-2; j++) G.add_edge(s[i]+j+1, s[i]+j, INF);
            ans += cost[i][k[i]-1];
            for (int j = 0; j < k[i]-1; j++){
                if (cost[i][j] > cost[i][j+1]) {
                    G.add_edge(s[n], s[i]+j, cost[i][j]-cost[i][j+1]);
                }
                else if (cost[i][j] < cost[i][j+1]) {
                    G.add_edge(s[i]+j, s[n]+1, cost[i][j+1]-cost[i][j]);
                    ans -= cost[i][j+1]-cost[i][j];
                }
            }
        }
        return ans+G.max_flow(s[n], s[n]+1);
    }

    // 先にmincostが必要
    // 選択した選択肢
    vector<int> answer() {
        vector<int> ans(n);
        auto v = G.min_cnt(s[n],s[n]+1);
        vector<bool> scut(s[n]+2);
        for (int i = 0; i < v.size(); i++) scut[v[i]] = true;
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < k[i]-1; j++) {
                if (!scut[s[i]+j]) { ans[i] = j; break; }
                else if (j == k[i]-2) { ans[i] = k[i]-1; }
            }
        }
        return ans;
    }
};

int main() {
  int n,s,t;cin >> n >> s >> t;
  ProjectSelectionProblem psp(vector<int>(n,2));
  for (int i = 0; i < s; i++) {
    int e;cin >> e;
    e--;
    psp.add_cost_1(e,{0,(ll)1e18});
  }
  for (int i = 0; i < t; i++) {
    int r;cin >> r;
    r--;
    psp.add_cost_1(r,{(ll)1e18,0});
  }
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) {
      int c;cin >> c;
      if (i >= j) continue;
      psp.add_cost_2(i,j,{{-c,0},{0,-c}});
    }
  }
  cout << -psp.mincost() << endl;
  return 0;
}

/////////////////////////////////////////
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