Cod sursa(job #2960862)

Utilizator Petrica81Simion Petrica Petrica81 Data 5 ianuarie 2023 01:46:26
Problema Cuplaj maxim in graf bipartit Scor 50
Compilator cpp-64 Status done
Runda Arhiva educationala Marime 3.09 kb
#include <iostream>
#include <fstream>
#include <vector>
#include <queue>

using namespace std;

ifstream fin ("cuplaj.in");
ofstream fout ("cuplaj.out");

//Complexitatea algotirmului este O(N^2 * M)
int n,m;
bool BFS(vector<vector<int>>& graf, vector<vector<int>>& capacitati, vector<int>& nivel){
    for(int i = 1; i <= n+m+1; i++)
        nivel[i] = -1;
    nivel[0] = 0;

    queue<int> q;
    q.push(0);

    while(!q.empty()){
        int nod = q.front();
        q.pop();
        for(int i = 0; i < graf[nod].size(); i++){
            int nod_aux = graf[nod][i];
            if (capacitati[nod][nod_aux] > 0 && nivel[nod_aux] < 0){
                nivel[nod_aux] = nivel[nod] + 1;
                q.push(nod_aux);
            }
        }
    }
    //daca nu ajung la destinatie returnez false
    if(nivel[n+m+1] < 0) return false;
    else return true;
};

int trimite_flux(vector<vector<int>>& graf, vector<vector<int>>& capacitati, vector<int>& nivel, vector<int>& count, int nod , int flow){
    if(nod == n+m+1)
        return flow;
    if(count[nod] == graf[nod].size())
        return 0;

    for(auto nod2 : graf[nod]){
        if(capacitati[nod][nod2] > 0){
            count[nod]++;
            if(nivel[nod2] == nivel[nod]+1){
                int flow_aux = min(flow,capacitati[nod][nod2]);

                int capac_minima = trimite_flux(graf,capacitati,nivel,count,nod2,flow_aux);
                if(capac_minima > 0){
                    if(capacitati[nod2][nod] == 0)
                        graf[nod2].push_back(nod);
                    capacitati[nod][nod2] -= capac_minima;
                    capacitati[nod2][nod] += capac_minima;

                    return capac_minima;
                }
            }
        }
    }


    return 0;
}

int main() {
    int e;
    fin>>n>>m>>e;
    vector<vector<int>> graf, capacitati; //lista de adiacenta, respectiv matrice cu capacitati

    graf.resize(n+m+2);
    capacitati.resize(n+m+2, vector<int> (n+m+2, 0));

    for(int i = 1; i <= n; i++) {
        capacitati[0][i] = 1;
        graf[0].push_back(i);
    }
    for(int i = n+1; i <= n+m; i++) {
        capacitati[i][n + m + 1] = 1;
        graf[i].push_back(n+m+1);
    }

    //citesc datele
    for(int i = 0; i < e; i++){
        int sursa,destinatie;
        fin>>sursa>>destinatie;
        capacitati[sursa][n+destinatie] = 1;
        graf[sursa].push_back(n+destinatie);
    }
    //rezolvare (folosesc algoritmul Edmonds–Karp)
    int flow_max = 0;
    vector<int> nivel(n+m+2,-1);
    while(BFS(graf, capacitati, nivel)){
        vector<int> count(n+m+2, 0);
        int aux = trimite_flux(graf,capacitati,nivel,count,0,10000);
        while(aux){
            flow_max += aux;
            aux = trimite_flux(graf,capacitati,nivel,count,0,10000);
        }
    }
    fout<<flow_max<<'\n';

    for(int i = 1; i <= n; i++){
        int j;
        for( j = 0; j < graf[i].size(); j++){
            if(capacitati[i][graf[i][j]] == 0 && graf[i][j] > n) {
                fout << i << " " << graf[i][j] - n;
                break;
            }
        }
        cout<<j<<" ";
        if(j != graf[i].size()) fout<<'\n';
    }
}