india.cpp

#include <iostream>
#include <vector>
#include <algorithm>

// BGL includes
#include <boost/graph/adjacency_list.hpp>
#include <boost/graph/cycle_canceling.hpp>
#include <boost/graph/push_relabel_max_flow.hpp>
#include <boost/graph/successive_shortest_path_nonnegative_weights.hpp>
#include <boost/graph/find_flow_cost.hpp>

// Graph Type with nested interior edge properties for Cost Flow Algorithms
typedef boost::adjacency_list_traits<boost::vecS, boost::vecS, boost::directedS> traits;
typedef boost::adjacency_list<boost::vecS, boost::vecS, boost::directedS, boost::no_property,
    boost::property<boost::edge_capacity_t, long,
        boost::property<boost::edge_residual_capacity_t, long,
            boost::property<boost::edge_reverse_t, traits::edge_descriptor,
                boost::property <boost::edge_weight_t, long> > > > > graph; // new! weightmap corresponds to costs

typedef boost::graph_traits<graph>::edge_descriptor             edge_desc;
typedef boost::graph_traits<graph>::out_edge_iterator           out_edge_it; // Iterator
typedef traits::vertex_descriptor vertex_desc;

// Custom edge adder class
class edge_adder {
 graph &G;

 public:
  explicit edge_adder(graph &G) : G(G) {}
  void add_edge(int from, int to, long capacity, long cost) {
    auto c_map = boost::get(boost::edge_capacity, G);
    auto r_map = boost::get(boost::edge_reverse, G);
    auto w_map = boost::get(boost::edge_weight, G); // new!
    const edge_desc e = boost::add_edge(from, to, G).first;
    const edge_desc rev_e = boost::add_edge(to, from, G).first;
    c_map[e] = capacity;
    c_map[rev_e] = 0; // reverse edge has no capacity!
    r_map[e] = rev_e;
    r_map[rev_e] = e;
    w_map[e] = cost;   // new assign cost
    w_map[rev_e] = -cost;   // new negative cost
  }
};

using namespace std;

int t, c, g, b, k, a;

bool feasible(graph& G, const vertex_desc& v_src, const vertex_desc& v_tar, int luggage_num){
    boost::successive_shortest_path_nonnegative_weights(G, v_src, v_tar);
    int cost = boost::find_flow_cost(G);
    auto c_map = boost::get(boost::edge_capacity, G);
    auto rc_map = boost::get(boost::edge_residual_capacity, G);
    int s_flow = 0;
    out_edge_it e, eend;
    for(boost::tie(e, eend) = boost::out_edges(boost::vertex(v_src,G), G); e != eend; ++e) {
        s_flow += c_map[*e] - rc_map[*e];     
    }
    return s_flow == luggage_num && cost <= b;
}


void solve(){
    cin >> c >> g >> b >> k >> a;
    graph G(c);
    const vertex_desc v_src = boost::add_vertex(G);
    const vertex_desc v_tar = boost::add_vertex(G);
    edge_adder adder(G);
    int max_amount = 0;
    for(int i = 0; i < g; i++){
        int x, y, d, e; cin >> x >> y >> d >> e;
        adder.add_edge(x, y, e, d);
        max_amount += e;
    }
    adder.add_edge(v_src, k, max_amount, 0);
    adder.add_edge(a, v_tar, max_amount, 0);
    const auto c_map = boost::get(boost::edge_capacity, G);
    int l = 0, r = max_amount;
    while(l < r){
        int mid = (l + r + 1)/2;
        c_map[boost::edge(v_src, k, G).first] = mid;
        if(feasible(G, v_src, v_tar, mid)){
            l = mid;
        } else {
            r = mid - 1;
        }
    }
    cout << l << endl;
}

int main(){
    ios_base::sync_with_stdio(false);
    cin.tie(0);
    cin >> t;
    while(t--){
        solve();
    }
    return 0;
}