#596144 (C++17) No.1324 Approximate the Matrix

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問題	No.1324 Approximate the Matrix
ユーザー	👑 tute7627
提出日時	2020-12-21 14:50:28
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	TLE
実行時間	-
コード長	6,561 bytes
コンパイル時間	3,296 ms
コンパイル使用メモリ	221,396 KB
実行使用メモリ	22,688 KB
最終ジャッジ日時	2024-09-21 12:58:28
合計ジャッジ時間	7,065 ms
ジャッジサーバーID （参考情報）	judge4 / judge5

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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 13,752 KB
testcase_01	AC	2 ms 6,944 KB
testcase_02	AC	2 ms 6,940 KB
testcase_03	TLE	-
testcase_04	--	-
testcase_05	--	-
testcase_06	--	-
testcase_07	--	-
testcase_08	--	-
testcase_09	--	-
testcase_10	--	-
testcase_11	--	-
testcase_12	--	-
testcase_13	--	-
testcase_14	--	-
testcase_15	--	-
testcase_16	--	-
testcase_17	--	-
testcase_18	--	-
testcase_19	--	-
testcase_20	--	-
testcase_21	--	-
testcase_22	--	-
testcase_23	--	-
testcase_24	--	-
testcase_25	--	-
testcase_26	--	-
testcase_27	--	-
testcase_28	--	-
testcase_29	--	-
testcase_30	--	-
testcase_31	--	-
testcase_32	--	-
testcase_33	--	-
testcase_34	--	-
testcase_35	--	-
testcase_36	--	-
testcase_37	--	-
testcase_38	--	-
testcase_39	--	-
testcase_40	--	-
testcase_41	--	-
testcase_42	--	-
testcase_43	--	-
testcase_44	--	-

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ソースコード

raw source code

//#define _GLIBCXX_DEBUG

#include<bits/stdc++.h>
using namespace std;

#define endl '\n'
#define lfs cout<<fixed<<setprecision(10)
#define ALL(a)  (a).begin(),(a).end()
#define ALLR(a)  (a).rbegin(),(a).rend()
#define spa << " " <<
#define fi first
#define se second
#define MP make_pair
#define MT make_tuple
#define PB push_back
#define EB emplace_back
#define rep(i,n,m) for(ll i = (n); i < (ll)(m); i++)
#define rrep(i,n,m) for(ll i = (ll)(m) - 1; i >= (ll)(n); i--)
using ll = long long;
using ld = long double;
const ll MOD1 = 1e9+7;
const ll MOD9 = 998244353;
const ll INF = 1e18;
using P = pair<ll, ll>;
template<typename T1, typename T2>bool chmin(T1 &a,T2 b){if(a>b){a=b;return true;}else return false;}
template<typename T1, typename T2>bool chmax(T1 &a,T2 b){if(a<b){a=b;return true;}else return false;}
ll median(ll a,ll b, ll c){return a+b+c-max({a,b,c})-min({a,b,c});}
void ans1(bool x){if(x) cout<<"Yes"<<endl;else cout<<"No"<<endl;}
void ans2(bool x){if(x) cout<<"YES"<<endl;else cout<<"NO"<<endl;}
void ans3(bool x){if(x) cout<<"Yay!"<<endl;else cout<<":("<<endl;}
template<typename T1,typename T2>void ans(bool x,T1 y,T2 z){if(x)cout<<y<<endl;else cout<<z<<endl;}  
template<typename T>void debug(vector<vector<T>>&v,ll h,ll w){for(ll i=0;i<h;i++){cout<<v[i][0];for(ll j=1;j<w;j++)cout spa v[i][j];cout<<endl;}};
void debug(vector<string>&v,ll h,ll w){for(ll i=0;i<h;i++){for(ll j=0;j<w;j++)cout<<v[i][j];cout<<endl;}};
template<typename T>void debug(vector<T>&v,ll n){if(n!=0)cout<<v[0];for(ll i=1;i<n;i++)cout spa v[i];cout<<endl;};
template<typename T>vector<vector<T>>vec(ll x, ll y, T w){vector<vector<T>>v(x,vector<T>(y,w));return v;}
ll gcd(ll x,ll y){ll r;while(y!=0&&(r=x%y)!=0){x=y;y=r;}return y==0?x:y;}
vector<ll>dx={1,-1,0,0,1,1,-1,-1};vector<ll>dy={0,0,1,-1,1,-1,1,-1};
template<typename T>vector<T> make_v(size_t a,T b){return vector<T>(a,b);}
template<typename... Ts>auto make_v(size_t a,Ts... ts){return vector<decltype(make_v(ts...))>(a,make_v(ts...));}
template<typename T1, typename T2>ostream &operator<<(ostream &os, const pair<T1, T2>&p){return os << p.first << " " << p.second;}
template<typename T>ostream &operator<<(ostream &os, const vector<T> &v){for(auto &z:v)os << z << " ";cout<<"|"; return os;}
template<typename T>void rearrange(vector<ll>&ord, vector<T>&v){
  auto tmp = v;
  for(int i=0;i<tmp.size();i++)v[i] = tmp[ord[i]];
}
template<typename Head, typename... Tail>void rearrange(vector<ll>&ord,Head&& head, Tail&&... tail){
  rearrange(ord, head);
  rearrange(ord, tail...);
}
//mt19937 mt(chrono::steady_clock::now().time_since_epoch().count());
int popcount(ll x){return __builtin_popcountll(x);};
int poplow(ll x){return __builtin_ctzll(x);};
int pophigh(ll x){return 63 - __builtin_clzll(x);};
template< typename flow_t, typename cost_t >
struct PrimalDual {
  const cost_t INF;

  struct edge {
    ll to;
    flow_t cap;
    cost_t cost;
    ll rev;
    bool isrev;
  };
  vector< vector< edge > > graph;
  vector< cost_t > potential, min_cost;
  vector< ll > prevv, preve;

  PrimalDual(ll V) : graph(V), INF(numeric_limits< cost_t >::max()) {}

  void add_edge(ll from, ll to, flow_t cap, cost_t cost) {
    graph[from].emplace_back((edge) {to, cap, cost, (ll) graph[to].size(), false});
    graph[to].emplace_back((edge) {from, 0, -cost, (ll) graph[from].size() - 1, true});
  }
  void add_edge(ll from, ll to, flow_t cap, cost_t cost,flow_t tmp) {
    graph[from].emplace_back((edge) {to, tmp, cost, (ll) graph[to].size(), false});
    graph[to].emplace_back((edge) {from, cap-tmp, -cost, (ll) graph[from].size() - 1, true});
  }
  cost_t min_cost_flow(ll s, ll t, flow_t f) {
    ll V = (ll) graph.size();
    cost_t ret = 0;
    using Pi = pair< cost_t, ll >;
    priority_queue< Pi, vector< Pi >, greater< Pi > > que;
    potential.assign(V, 0);
    preve.assign(V, -1);
    prevv.assign(V, -1);

    while(f > 0) {
      min_cost.assign(V, INF);
      que.emplace(0, s);
      min_cost[s] = 0;
      while(!que.empty()) {
        Pi p = que.top();
        que.pop();
        if(min_cost[p.second] < p.first) continue;
        for(ll i = 0; i < graph[p.second].size(); i++) {
          edge &e = graph[p.second][i];
          cost_t nextCost = min_cost[p.second] + e.cost + potential[p.second] - potential[e.to];
          if(e.cap > 0 && min_cost[e.to] > nextCost) {
            min_cost[e.to] = nextCost;
            prevv[e.to] = p.second, preve[e.to] = i;
            que.emplace(min_cost[e.to], e.to);
          }
        }
      }
      if(min_cost[t] == INF) return -1;
      for(ll v = 0; v < V; v++) potential[v] += min_cost[v];
      flow_t addflow = f;
      for(ll v = t; v != s; v = prevv[v]) {
        addflow = min(addflow, graph[prevv[v]][preve[v]].cap);
      }
      f -= addflow;
      ret += addflow * potential[t];
      for(ll v = t; v != s; v = prevv[v]) {
        edge &e = graph[prevv[v]][preve[v]];
        e.cap -= addflow;
        graph[v][e.rev].cap += addflow;
      }
    }
    return ret;
  }

  void output() {
    for(ll 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 << "/" << rev_e.cap + e.cap << ")"  spa e.cost<< endl;
      }
    }
  }
  //(from->to,flow,cost)
  using R=vector<pair<pair<ll,ll>,pair<flow_t,cost_t>>>;
  R restore() {
    R ret;
    for(ll i = 0; i < graph.size(); i++) {
      for(auto &e : graph[i]) {
        if(e.isrev) continue;
        auto &rev_e = graph[e.to][e.rev];
        ret.emplace_back(make_pair(i,e.to),make_pair(rev_e.cap,e.cost));
      }
    }
    return ret;
  }
};
int main(){
  cin.tie(nullptr);
  ios_base::sync_with_stdio(false);
  ll res=0,buf=0;
  bool judge = true;
  ll n,k;cin>>n>>k;
  vector<ll>a(n),b(n);
  rep(i,0,n)cin>>a[i];
  rep(i,0,n)cin>>b[i];
  auto p=vec(n,n,0LL);
  rep(i,0,n)rep(j,0,n){
    cin>>p[i][j];
  }
  PrimalDual<ll,ll>flow(2*n+2);
  ll S=2*n,T=2*n+1;
  auto ta=a;
  ll cost=0;
  const ll inf=1e9;
  ll f=0;
  rep(i,0,n){
    rep(j,0,n){
      ll def=min({a[i],p[i][j]});
      flow.add_edge(S,n+j,def,0);
      flow.add_edge(i,T,def,0);
      //flow.add_edge(n+j,i,def,inf);
      f+=def;
      //cost+=-inf*def;
      cost+=(def-p[i][j])*(def-p[i][j]);
      rrep(o,0,def)flow.add_edge(n+j,i,1,2*(p[i][j]-o)-1);
      rep(o,def+1,a[i]+1)flow.add_edge(i,n+j,1,2*(o-p[i][j])-1);
    }
    flow.add_edge(S,i,a[i],0);
    flow.add_edge(n+i,T,b[i],0);
  }
  cout<<cost+flow.min_cost_flow(S,T,k+f)<<endl;
  //flow.output();
  return 0;
}

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