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Cod sursa(job #932379)
//La fiecare moment de timp adaugam cate un set de N noduri
//Daca suntem la momentul de timp T, ducem muchiile din input
//Un capat e in multimea de la momentul T - 1, celalalt in multimea de la momentul T
//Facem flux pana cand ii ducem pe toti
//O unitate de flux inseamna calatoria unuia dintre membrii
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <queue>
#include <vector>
#include <algorithm>
using namespace std;
#define Nmax 5010
#define forit(it, v) for(typeof((v).begin()) it = (v).begin(); it != (v).end(); it++)
#define mp make_pair
#define pb push_back
#define f first
#define s second
int N, M, X, Y, C, Source, Sink, T, TotalFlow, A[Nmax];
int Cap[Nmax][Nmax], Flow[Nmax][Nmax], Father[Nmax];
bool Used[Nmax];
vector<pair<int, int> > G[Nmax];
vector<int> FlowG[Nmax];
void AddNodes(int Time)
{
int i, j;
for(i = 1; i <= N; ++ i)
{
int X = (Time - 1) * N + i;
FlowG[X].pb(X + N);
FlowG[X + N].pb(X);
Cap[X][X + N] = 1000;
forit(it, G[i])
{
int Y = Time * N + it -> f;
FlowG[X].pb(Y);
FlowG[Y].pb(X);
Cap[X][Y] = it -> s;
}
}
}
bool BFS()
{
memset(Used, 0, sizeof(Used));
memset(Father, 0, sizeof(Father));
queue<int> Q;
Used[Source] = 1;
Q.push(Source);
while(!Q.empty())
{
int Node = Q.front();
Q.pop();
if(Node == Sink) continue;
forit(it, FlowG[Node])
if(!Used[*it] && Cap[Node][*it] > Flow[Node][*it])
{
Used[*it] = 1;
Father[*it] = Node;
Q.push(*it);
}
}
return Used[Sink];
}
void MaxFlow()
{
while(BFS())
{
int MinFlow = 10000;
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;
}
TotalFlow -= MinFlow;
}
}
int main()
{
freopen("algola.in", "r", stdin);
freopen("algola.out", "w", stdout);
int i, j;
scanf("%i %i", &N, &M);
for(i = 1; i <= N; ++ i)
{
scanf("%i", &A[i]);
TotalFlow += A[i];
FlowG[Source].pb(i);
FlowG[i].pb(Source);
Cap[Source][i] = A[i];
}
for(i = 1; i <= M; ++ i)
{
scanf("%i %i %i", &X, &Y, &C);
G[X].pb(mp(Y, C));
G[Y].pb(mp(X, C));
}
T = 1;
while(TotalFlow)
{
AddNodes(T);
Sink = T * N + 1;
MaxFlow();
T ++;
}
printf("%i\n", T - 1);
return 0;
}