Cod sursa(job #2961517)

Utilizator Senth30Denis-Florin Cringanu Senth30 Data 6 ianuarie 2023 16:50:44
Problema Cuplaj maxim in graf bipartit Scor 90
Compilator cpp-64 Status done
Runda Arhiva educationala Marime 3.7 kb
#include <bits/stdc++.h>
#define MAX 131072

using namespace std;
const short NMAX = 20300;

struct obj {
    short first, second;
};

int N1, N2, M, S, D, ansFlow;

bool wasSeen[NMAX];
short dad[NMAX];

map <short, obj> flow[NMAX];
vector <short> edges[NMAX], directedEdges[NMAX];

// flow.first = capacity
// flow.second = flow

void read(){
    scanf("%d%d%d", &N1, &N2, &M);
    int x, y;
    S = 0;
    D = N1 + N2 + 1;
    for(int i = 1; i <= M; i++){
        scanf("%d%d", &x, &y);
        directedEdges[x].push_back(N1 + y);
        edges[x].push_back(N1 + y);
        edges[N1 + y].push_back(x);
        flow[x][N1 + y] = {1, 0};
    }
    for(short node = 1; node <= N1; node++){
        directedEdges[S].push_back(node);
        edges[S].push_back(node);
        edges[node].push_back(S);
        flow[S][node] = {1, 0};
    }
    for(short node = N1 + 1; node <= N1 + N2; node++){
        directedEdges[node].push_back(D);
        edges[D].push_back(node);
        edges[node].push_back(D);
        flow[node][D] = {1, 0};
    }
}

// rezolvare cerinta a
// aplic algoritmul de flux, pornesc un BFS din nodul 1 si incerc sa ajung in nodul N pe muchiile care inca nu
// si-au atins capacitatea maxima, iar pentru fiecare nod retin nodul de unde am venit
// pentru toti vecinii lui N, calculez fluxul cu care pot sa ajung intr-un vecin de a lui, uitandu-ma la tatii acestuia
// insumez toate fluxurile gasite si obtin rezultatul

void printMinimumCut(short node){
    for(short i = 0; i <= D; i++)
        wasSeen[i] = false;
    vector <pair <short, short> > cutEdges;
    queue <short> Q;
    Q.push(node);
    wasSeen[node] = true;
    while(!Q.empty()){
        node = Q.front();
        Q.pop();
        for(auto it : directedEdges[node]){
            if(node != S && it != D && flow[node][it].first - flow[node][it].second == 0){
                cutEdges.push_back(make_pair(node, it - N1));
                continue;
            }
            if(!wasSeen[it]) {
                wasSeen[it] = true;
                Q.push(it);
            }
        }
    }
    for(auto it : cutEdges)
        printf("%d %d\n", it.first, it.second);
}

bool generateFlow(short node){
    for(short i = 0; i <= D; i++){
        wasSeen[i] = false;
        dad[i] = 0;
    }
    queue <short> Q;
    Q.push(node);
    wasSeen[node] = true;
    while(!Q.empty()){
        node = Q.front();
        Q.pop();
        for(auto it : edges[node]){
            if(!wasSeen[it] && flow[node][it].first - flow[node][it].second > 0){
                wasSeen[it] = true;
                dad[it] = node;
                Q.push(it);
            }
        }
    }

    if(!dad[D])
        return false;

    node = D;
    for(auto it : edges[node]){
        short MinFlow = flow[it][node].first - flow[it][node].second;
        short PosFlow = 0;
        if(MinFlow > 0){
            for(short j = it; j != 0; j = dad[j]){
                PosFlow = flow[dad[j]][j].first - flow[dad[j]][j].second;
                if(PosFlow < MinFlow)
                    MinFlow = PosFlow;
            }
            flow[it][node].second += MinFlow;
            flow[node][it].second -= MinFlow;
            for(short j = it; j != 0; j = dad[j]){
                flow[dad[j]][j].second += MinFlow;
                flow[j][dad[j]].second -= MinFlow;
            }
            ansFlow += MinFlow;
        }
    }

    return true;
}

int main() {

    freopen("cuplaj.in", "r", stdin);
    freopen("cuplaj.out", "w", stdout);

    read();

    bool repeat = true;
    while(repeat)
        repeat = generateFlow(0);
    printf("%d\n", ansFlow);
    printMinimumCut(0);

    return 0;
}