Problem: Examples

Input

4 5 2
0 1 2 1
0 2 1 2
1 2 1 1
1 3 1 3
2 3 2 1


Output

6


Input




Output

Solution (in CPP):

Solution:
#include <iostream>
#include <algorithm>
#include <string>
#include <vector>
#include <cmath>
#include <map>
#include <queue>
#include <iomanip>
#include <set>
#include <tuple>
#define mkp make_pair
#define mkt make_tuple
#define rep(i,n) for(int i = 0; i < (n); ++i)
using namespace std;
typedef long long ll;
const ll MOD=1e9+7;

template< typename flow_t, typename cost_t >
struct MinCostFlow {
  const cost_t INF;

  struct edge {
    int to;
    flow_t cap;
    cost_t cost;
    int rev;
  };
  vector<vector<edge>> graph;
  vector<cost_t> potential,min_cost;
  vector<int> prevv,preve;

  MinCostFlow(int V) : graph(V),INF(numeric_limits< cost_t >::max()) {}

  void add_edge(int from,int to,flow_t cap,cost_t cost){
    graph[from].emplace_back((edge){to,cap,cost,(int)graph[to].size()});
    graph[to].emplace_back((edge){from,0,-cost,(int)graph[from].size()-1});
  }

  cost_t min_cost_flow(int s,int t,flow_t f){
    int V=(int)graph.size();
    cost_t ret=0;
    using Pi = pair<cost_t,int>;
    priority_queue<Pi,vector<Pi>,greater<Pi>> PQ;
    potential.assign(V,0);
    preve.assign(V,-1);
    prevv.assign(V,-1);

    while(f>0){
      min_cost.assign(V,INF);
      PQ.emplace(0,s);
      min_cost[s]=0;
      while(!PQ.empty()){
        cost_t d;
        int now;
        tie(d,now)=PQ.top();
        PQ.pop();
        if(min_cost[now]<d) continue;
        
        for(int i=0;i<graph[now].size();i++){
          edge &e=graph[now][i];
          cost_t nextCost=min_cost[now]+(e.cost+potential[now]-potential[e.to]);
          if(e.cap>0&&min_cost[e.to]>nextCost){
            min_cost[e.to]=nextCost;
            prevv[e.to]=now;
            preve[e.to]=i;
            PQ.emplace(min_cost[e.to],e.to);
          }
        }
      }

      if(min_cost[t]==INF) return -1;

      for(int v=0;v<V;v++) potential[v]+=min_cost[v];
      flow_t addflow=f;
      for(int v=t;v!=s;v=prevv[v]){
        addflow=min(addflow,graph[prevv[v]][preve[v]].cap);
      }
      f-=addflow;
      ret+=addflow*potential[t];
      
      for(int v=t;v!=s;v=prevv[v]){
        edge &e=graph[prevv[v]][preve[v]];
        e.cap-=addflow;
        graph[v][e.rev].cap+=addflow;
      }
    }
    return ret;
  }
};

int N,M,F;
vector<int> A,B,C,D;

int main(){
  cin>>N>>M>>F;
  A.resize(M);
  B.resize(M);
  C.resize(M);
  D.resize(M);
  for(int i=0;i<M;i++) cin>>A[i]>>B[i]>>C[i]>>D[i];

  MinCostFlow<int,int> mcf(N);
  for(int i=0;i<M;i++){
      mcf.add_edge(A[i],B[i],C[i],D[i]);
  }

  cout<<mcf.min_cost_flow(0,N-1,F)<<endl;

  return 0;
}