結果

問題 No.1324 Approximate the Matrix
コンテスト
ユーザー carrot46
提出日時 2020-12-23 12:04:47
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 69 ms / 2,000 ms
コード長 4,267 bytes
コンパイル時間 1,988 ms
コンパイル使用メモリ 184,116 KB
実行使用メモリ 6,948 KB
最終ジャッジ日時 2024-09-21 16:21:55
合計ジャッジ時間 4,223 ms
ジャッジサーバーID
（参考情報） 		judge5 / 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 * 3
other AC * 42
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>
//#include <chrono>
#pragma GCC optimize("Ofast")
using namespace std;
#define reps(i,s,n) for(int i = s; i < n; i++)
#define rep(i,n) reps(i,0,n)
#define Rreps(i,n,e) for(int i = n - 1; i >= e; --i)
#define Rrep(i,n) Rreps(i,n,0)
#define ALL(a) a.begin(), a.end()

using ll = long long;
using vec = vector<ll>;
using mat = vector<vec>;

ll N,M,H,W,Q,K,A,B;
string S;
using P = pair<ll, ll>;
const ll INF = (1LL<<60);

template<class T> bool chmin(T &a, const T &b){
    if(a > b) {a = b; return true;}
    else return false;
}
template<class T> bool chmax(T &a, const T &b){
    if(a < b) {a = b; return true;}
    else return false;
}
template<class T> void my_printv(std::vector<T> v,bool endline = true){
    if(!v.empty()){
        for(std::size_t i{}; i<v.size()-1; ++i) std::cout<<v[i]<<" ";
        std::cout<<v.back();
    }
    if(endline) std::cout<<std::endl;
}

struct edge{
    int to, cap, rev;
    ll cost;
    edge(){}
    edge(int a, int b, ll c, int d){
        to = a;
        cap = b;
        cost = c;
        rev = d;
    }
};
using ve = vector<edge>;

void add_edge(int from, int to, int cap, ll cost, vector<ve> &G, bool directed = true){
    rep(_, (directed ? 1 : 2)) {
        G[from].emplace_back(to, cap, cost, (int) G[to].size());
        G[to].emplace_back(from, 0, -cost, (int) G[from].size() - 1);
        swap(to, from);
    }
}

bool bellman_ford_for_flow(int s, vector<ve> &G, vec &dist){
    //O(|V|^2 + |V||E|)
    dist[s] = 0;
    int num(0), sz = G.size();
    while(num++ < sz){
        bool update = false;
        rep(v, sz){
            if(dist[v] != INF) {
                for (edge &e : G[v]) {
                    if (e.cap > 0 && chmin(dist[e.to], dist[v] + e.cost)) update = true;
                }
            }
        }
        if(!update) return true;
    }

    return false; //failed
}

void dijkstra_for_flow(int s, vector<ve> &G, vec &h, vec &dist, vector<int> &prev_v, vector<int> &prev_e){
    typedef struct _comp{
        ll cost;
        int v;
        _comp(){}
        _comp(ll a, int b){
            cost = a;
            v = b;
        }
        bool operator > (const _comp a){
            return cost > a.cost;
        }
    } mp;
    priority_queue<mp, vector<mp>, greater<> > pque;
    dist[s] = 0;
    pque.emplace(0, s);
    while(!pque.empty()){
        mp p = pque.top(); pque.pop();
        if(dist[p.v] < p.cost) continue;
        rep(i, (int)G[p.v].size()){
            edge &e = G[p.v][i];
            if(e.cap > 0 && chmin(dist[e.to], p.cost + e.cost + h[p.v] - h[e.to])){
                prev_v[e.to] = p.v;
                prev_e[e.to] = i;
                pque.emplace(dist[e.to], e.to);
            }
        }
    }
}

//全然Validateできていないので注意
ll min_cost_flow(int s, int t, int f, vector<ve> &G, bool minus_exist = true){
    //minus_exist : if (edge.cost < 0)
    //for graph without negative cycles
    int sz = G.size();
    ll res(0);
    vector<int> prev_v(sz), prev_e(sz);
    vec h(sz, minus_exist ? INF : 0);
    if(minus_exist && (!bellman_ford_for_flow(s, G, h) || h[t] == INF)) return -1;
    while(f > 0){
        vec dist(sz, INF);
        dijkstra_for_flow(s, G, h, dist, prev_v, prev_e);
        if(dist[t] == INF) return -1;
        rep(v, sz) h[v] += dist[v];
        int d = f;
        for(int v = t; v != s; v = prev_v[v]){
            chmin(d, G[prev_v[v]][prev_e[v]].cap);
        }
        f -= d;
        res += h[t] * d;
        for(int v = t; v != s; v = prev_v[v]){
            edge &e = G[prev_v[v]][prev_e[v]];
            e.cap -= d;
            G[v][e.rev].cap += d;
        }
    }
    return res;
}

int main(){
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cin>>N>>K;
    const int st = N * 2, gl = N * 2 + 1;
    vector<ve> G(N * 2 + 2);
    vec a(N), b(N);
    rep(i, N){
        cin>>a[i];
        add_edge(st, i, a[i], 0, G);
    }
    rep(i, N){
        cin>>b[i];
        add_edge(i+N, gl, b[i], 0, G);
    }
    ll sum = 0;
    rep(i, N){
        reps(j, N, N*2){
            cin>>A;
            sum += A * A;
            rep(k, a[i]){
                add_edge(i, j, 1, (k - A) * 2 + 1, G);
            }
        }
    }
    cout<<sum + min_cost_flow(st, gl, K, G, false)<<endl;
}
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