Cod sursa(job #933255)

Utilizator visanrVisan Radu visanr Data 29 martie 2013 19:04:19
Problema Traseu Scor 100
Compilator cpp Status done
Runda Arhiva de probleme Marime 3.77 kb
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <vector>
#include <queue>
#include <algorithm>
using namespace std;

#define Nmax 70
#define Inf 0x3f3f3f3f
#define pb push_back
#define forit(it, v) for(typeof((v).begin()) it = (v).begin(); it != (v).end(); ++ it)

int N, M, Source, Sink, X, Y, C, DegIn[Nmax], DegOut[Nmax], Dist[Nmax];
int Father[Nmax], Cost[Nmax][Nmax], Cap[Nmax][Nmax], Flow[Nmax][Nmax];
bool InQueue[Nmax];
vector<int> G[Nmax];

bool BellmanFord()
{
    for(int i = Source; i <= Sink; ++ i)
    {
        Dist[i] = Inf;
        InQueue[i] = 0;
        Father[i] = 0;
    }
    queue<int> Q;
    Q.push(Source);
    InQueue[Source] = 1;
    Dist[Source] = 0;
    while(!Q.empty())
    {
        int Node = Q.front();
        Q.pop();
        InQueue[Node] = 0;
        forit(it, G[Node])
            if(Cap[Node][*it] > Flow[Node][*it] && Dist[*it] > Dist[Node] + Cost[Node][*it])
            {
                Dist[*it] = Dist[Node] + Cost[Node][*it];
                Father[*it] = Node;
                if(!InQueue[*it])
                {
                    InQueue[*it] = 1;
                    Q.push(*it);
                }
            }
    }
    return (Dist[Sink] != Inf);
}

int MinCostMaxFlow()
{
    int Ans = 0;
    while(BellmanFord())
    {
        int MinFlow = Inf;
        for(int Node = Sink; Node != Source; Node = Father[Node])
            MinFlow = min(MinFlow, Cap[Father[Node]][Node] - Flow[Father[Node]][Node]);
        for(int Node = Sink; Node != Source; Node = Father[Node])
        {
            Flow[Father[Node]][Node] += MinFlow;
            Flow[Node][Father[Node]] -= MinFlow;
        }
        Ans += MinFlow * Dist[Sink];
    }
    return Ans;
}


void RoyFloyd()
{
    for(int k = 1; k <= N; ++ k)
        for(int i = 1; i <= N; ++ i)
            for(int j = 1; j <= N; ++ j)
                if(i != k && j != k && Cost[i][k] + Cost[k][j] < Cost[i][j])
                    Cost[i][j] = Cost[i][k] + Cost[k][j];
}

int main()
{
    //Daca graful este eulerian (in = out pt fiecare nod), costul e suma muchiilor
    //Dar pt ca nu este, incerc practic sa "adaug" niste muchii
    //Imi formez un graf cu 2 multimi, prima multime are nodurile in care intra prea mult
    //In a doua sunt nodurile din care iese prea mult
    //Leg sursa de nodurile in care intra prea mult cu capacitate IN-OUT
    //Leg destinatia de nodurile din care iese prea mult cu capacitate OUT-IN
    //Leg nodurile din cele 2 multimi cu costuri = costul minim in graful initial, calculat cu roy-floyd
    //Rulez algoritmul de flux maxim de cost minim si adun la solutia initiala
    freopen("traseu.in", "r", stdin);
    freopen("traseu.out", "w", stdout);
    int i, j;
    scanf("%i %i", &N, &M);
    for(i = 1; i <= N; ++ i)
        for(j = 1; j <= N; ++ j)
            Cost[i][j] = Inf;
    int Ans = 0;
    for(i = 1; i <= M; ++ i)
    {
        scanf("%i %i %i", &X, &Y, &C);
        Ans += C;
        DegOut[X] ++;
        DegIn[Y] ++;
        Cost[X][Y] = C;
    }
    RoyFloyd();
    Source = 0;
    Sink = N + 1;
    for(i = 1; i <= N; ++ i)
        if(DegOut[i] > DegIn[i])
        {
            G[i].pb(Sink);
            G[Sink].pb(i);
            Cap[i][Sink] = DegOut[i] - DegIn[i];
        }else
        {
            G[i].pb(Source);
            G[Source].pb(i);
            Cap[Source][i] = DegIn[i] - DegOut[i];
        }
    for(i = 1; i <= N; ++ i)
        for(j = 1; j <= N; ++ j)
            if(DegIn[i] > DegOut[i] && DegOut[j] > DegIn[j])
            {
                G[i].pb(j);
                G[j].pb(i);
                Cap[i][j] = Inf;
                Cost[j][i] = -Cost[i][j];
            }
    printf("%i\n", Ans + MinCostMaxFlow());
    return 0;
}