Cod sursa(job #245333)

Utilizator marcelcodreaCodrea Marcel marcelcodrea Data 17 ianuarie 2009 19:32:18
Problema Flux maxim de cost minim Scor 10
Compilator cpp Status done
Runda Arhiva educationala Marime 3.77 kb
#include <stdio.h>
#include <assert.h>
#include <vector>

using namespace std;

#define maxn 360
#define inf 2000000000
#define ll long long

int N, M, S, D;
int Drum, L, Sum;
vector <int> A[maxn];
int G[maxn];
int Dist[maxn], From[maxn], Pot[maxn];
int H[maxn], P[maxn];
int C[maxn][maxn], F[maxn][maxn], Cost[maxn][maxn];

void push(int x)
{
    int aux;

    while (x/2>1 && Dist[H[x]]<Dist[H[x/2]])
    {
        aux = H[x], H[x] = H[x/2], H[x/2] = aux;

        P[H[x]] = x;
        P[H[x/2]] = x/2;

        x /= 2;
    }
}

void pop(int x)
{
    int y = 0, aux;

    while (x != y)
    {
        y = x;
        if (y*2<=L && Dist[H[x]]>Dist[H[y*2]]) x = y*2;
        if (y*2+1 <= L && Dist[H[x]]>Dist[H[y*2+1]]) x = y*2+1;

        aux = H[x], H[x] = H[y], H[y] = aux;
        P[H[x]] = x;
        P[H[y]] = y;
    }
}

int BellmanFord()
{
    int i, stop = 0, j, k;

    for (i = 1; i <= N; i++) Dist[i] = inf;
    Dist[S] = 0;

    for (i = 1; i <= N && !stop; i++)
    {
        stop = 1;

        for (j = 1; j <= N; j++)
            for (k = 0; k < G[j]; k++)
                if (C[j][A[j][k]]-F[j][A[j][k]]>0 && Dist[j]+Cost[j][A[j][k]]<Dist[A[j][k]])
                {
                    stop = 0;
                    Dist[A[j][k]] = Dist[j] + Cost[j][A[j][k]];
                }
    }

    Sum = Dist[D];

    return stop;
}

int Dijkstra()
{
    int i, j;

    // Fac transformarea astfel incat sa am doar costuri pozitive pe arcele active (cele cu capacitate > flux)

    for (i = 1; i <= N; i++)
        for (j = 0; j < G[i]; j++)
            if (Dist[i] != inf && Dist[A[i][j]] != inf) Cost[i][A[i][j]] += Dist[i] - Dist[A[i][j]];

    // Initializari

    for (i = 1; i <= N; i++)
    {
        Dist[i] = inf;
        H[i] = i;
        P[i] = i;
        From[i] = -1;
    }

    // Fac Dijkstra

    Dist[S] = 0;
    H[1] = S, H[S] = 1;
    P[1] = S, P[S] = 1;
    L = N;

    while (L>1 && Dist[H[1]] != inf)
    {
        for (i = 0; i < G[H[1]]; i++)
        {
            int v = A[H[1]][i];

            if (C[H[1]][v]-F[H[1]][v]>0) assert(Cost[H[1]][v]>=0); // Verific daca am arce cu cost negativ active

            if (C[H[1]][v]-F[H[1]][v]>0 && Dist[H[1]]+Cost[H[1]][v]<Dist[v])
            {
                Dist[v] = Dist[H[1]] + Cost[H[1]][v];
                From[v] = H[1];
                push(P[v]);
            }
        }

        H[1] = H[L--];
        P[H[1]] = 1;
        if (L > 1) pop(1);
    }

    // Daca am gasit drum, cresc fluxul pe el

    if (Dist[D] != inf)
    {
        int Vmin = inf;
        Drum = 1;

        for (i = D; i != S; i = From[i])
            Vmin = min(Vmin, C[From[i]][i] - F[From[i]][i]);

        for (i = D; i != S; i = From[i])
        {
            F[From[i]][i] += Vmin;
            F[i][From[i]] -= Vmin;
        }

        Sum += Dist[D];
        return Vmin * Sum;
    }

    return 0;
}

ll Flux()
{
    ll Rez = 0;
    Drum = 1;

    // Cat timp mai exista un drum valabil, bag flux

    while (Drum)
    {
        Drum = 0;
        Rez += Dijkstra();
    }

    return Rez;
}

int main()
{
    freopen("fmcm.in", "r", stdin);
    freopen("fmcm.out", "w", stdout);

    int i, x, y, z, cap;

    // Citesc graful

    scanf("%d %d %d %d ", &N, &M, &S, &D);

    for (i = 1; i <= M; i++)
    {
        scanf("%d %d %d %d ", &x, &y, &cap, &z);

        A[x].push_back(y);
        A[y].push_back(x);

        C[x][y] = cap;
        Cost[x][y] = z;
    }

    for (i = 1; i <= N; i++) G[i] = A[i].size();

    // Fac primul Bellman-Ford, cand inca am costuri negative

    assert(BellmanFord());

    // Calculez fluxul maxim de cost minim

    printf("%lld\n", Flux());

    return 0;
}