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Cod sursa(job #933255)
#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;
}