Cod sursa(job #3361013)

Utilizator Nasa1004Ema Nicole Gheorghe Nasa1004 Data 18 iulie 2026 15:24:06
Problema Flux maxim de cost minim Scor 100
Compilator cpp-64 Status done
Runda Arhiva educationala Marime 3.66 kb
#include <fstream>
#include <vector>
#include <climits>
#include <queue>
#include <algorithm>
#include <bitset>

using namespace std;
const int NMAX = 350;
using ll = long long;
const ll INF = LLONG_MAX;
const int FMAX = 10005;

ifstream cin("fmcm.in");
ofstream cout("fmcm.out");

struct muchie{
    int nod;
    int cost;
    int flux, cap;
    int pereche;
};
vector <vector <muchie>> v;
void addedge(int a, int b, int cap, int cost) {
    v[a].push_back({b, cost, 0, cap, (int)v[b].size()});
    v[b].push_back({a, -cost, 0, 0, (int)(v[a].size() - 1)});
}
int n, sursa, dest;
ll ans = 0;

ll p[NMAX + 2];
bitset <NMAX + 2> incoada;
void bellmanFord() { ///calc potentialele
    for(int i = 1; i <= n; i++)
        p[i] = INF;
    queue <int> q;
    incoada[sursa] = 1;
    p[sursa] = 0;
    q.push(sursa);
    while(!q.empty()) {
        int now = q.front();
        incoada[now] = 0;
        q.pop();
        for(int i = 0; i < v[now].size(); i++) {
            muchie x = v[now][i];
            if(x.flux < x.cap && p[x.nod] > p[now] + x.cost) {
                p[x.nod] = p[now] + x.cost;
                if(!incoada[x.nod]) {
                    incoada[x.nod] = 1;
                    q.push(x.nod);
                }
            }
        }
    }
}

struct noduri{
    ll dist;
    int tata;
    int edge;
}a[NMAX + 2];

struct prio{
    int nod;
    ll dist;
    bool operator <(const prio& rhs) const { ///dist min
        return dist > rhs.dist;
    }
};

bool dijkstra() {
    for(int i = 1; i <= n; i++) {
        a[i].dist = INF;
        a[i].tata = 0;
        a[i].edge = -1;
    }
    a[sursa].dist = 0;
    priority_queue <prio> pq;
    pq.push({sursa, 0});
    while(!pq.empty()) {
        prio now = pq.top();
        pq.pop();
        if(a[now.nod].dist < now.dist) ///deja l-am analizat
            continue;
        // cout << "Suntem la " << now.nod << " " << now.dist << '\n';
        for(int i = 0; i < v[now.nod].size(); i++) {
            muchie x = v[now.nod][i];
            if(x.flux < x.cap && a[x.nod].dist > now.dist + x.cost - p[x.nod] + p[now.nod]) {
                a[x.nod].dist = now.dist + x.cost - p[x.nod] + p[now.nod];
                a[x.nod].tata = now.nod;
                a[x.nod].edge = i;
                pq.push({x.nod, a[x.nod].dist});
            }
        }
    }
    return (a[dest].dist != INF);
}

int recons() {
    int minn = FMAX;
    int nod = dest;
    while(nod != sursa) {
        int urm = a[nod].tata, id = a[nod].edge;
        minn = min(minn, v[urm][id].cap - v[urm][id].flux);
        nod = urm;
    }
    return minn;
}

void change(int a, int id, int cat) {
    v[a][id].flux += cat;
    v[v[a][id].nod][v[a][id].pereche].flux -= cat;
}

void update(int add) {
    int nod = dest;
    while(nod != sursa) {
        int urm = a[nod].tata, id = a[nod].edge;
        change(urm, id, add);
        nod = urm;
    }
}

int main() {
    int m;
    cin >> n >> m >> sursa >> dest;
    v.resize(n + 1);
    for(int i = 1; i <= m; i++) {
        int a, b, cap, cost;
        cin >> a >> b >> cap >> cost;
        addedge(a, b, cap, cost);
    }
    /*for(int i = 1; i <= n; i++) {
        cout << "Nodul " << i << '\n';
        for(auto x : v[i])
            cout << x.nod << " " << x.cost << " " << x.flux << " " << x.cap << " " << x.pereche << '\n';
    }*/
    bellmanFord();
    ///sursa = 1, dest = n
    while(dijkstra()) {
        // cout << "o da\n";
        int add = recons(); ///cat flux
        ans += 1LL * add * (a[dest].dist + p[dest]); /// pt ca se ANULEAZA celelalte potentiale si il pastrezi doar pe ult
        update(add);
        ///Updatezi potentialele
        for(int i = 1; i <= n; i++)
            p[i] += a[i].dist;
    }
    cout << ans;
    return 0;
}