#include <iostream>
#include <sstream>
#include <iomanip>
#include <vector>
#include <string>
#include <map>
#include <set>
#include <algorithm>
#include <numeric>
#include <iterator>
#include <functional>
#include <complex>
#include <queue>
#include <stack>
#include <cmath>
#include <cassert>
using namespace std;
typedef long long LL;
typedef long double LD;
typedef complex<double> CMP;
int bitcnt(int x)
{
int c = 0;
for(; x; x>>=1)
c += x&1;
return c;
}
class TravellingPurchasingMan { public:
static const int INF = 0x3fffffff;
struct Store {
int open;
int close;
int shopping;
};
int maxStores(int N, vector <string> interestingStores, vector <string> roads)
{
vector< vector<int> > d(N, vector<int>(N, INF));
for(int i=0; i<N; ++i)
d[i][i] = 0;
for(int i=0; i<roads.size(); ++i)
{
stringstream sin(roads[i]);
int a, b, len;
sin >> a >> b >> len;
d[a][b] = d[b][a] = len;
}
for(int k=0; k<N; ++k)
for(int i=0; i<N; ++i)
for(int j=0; j<N; ++j)
d[i][j] = min(d[i][j], d[i][k]+d[k][j]);
const int M = interestingStores.size();
vector<Store> s;
for(int i=0; i<interestingStores.size(); ++i)
{
stringstream sin(interestingStores[i]);
int op,cl,du;
sin >> op >> cl >> du;
Store st = {op,cl+1,du}; // [,)
s.push_back(st);
}
vector< pair<int,int> > pop_mask;
for(int mask=0; mask<(1<<M); ++mask)
pop_mask.push_back(make_pair(bitcnt(mask), mask));
sort(pop_mask.begin(), pop_mask.end());
vector< vector<int> > tbl(M, vector<int>(1<<M, INF));
for(int u=0; u<M; ++u) {
int t=0, v=N-1, mask=0;
int ta = t + d[v][u];
int to = max(ta, s[u].open);
if(to < s[u].close) {
int td = to + s[u].shopping;
tbl[u][mask|(1<<u)] = min(tbl[u][mask|(1<<u)], td);
}
}
int best = 0;
for(int i=0; i<pop_mask.size(); ++i) {
int mask = pop_mask[i].second;
for(int v=0; v<M; ++v) if((mask&(1<<v)) && tbl[v][mask]!=INF)
{
best = pop_mask[i].first;
int t = tbl[v][mask];
for(int u=0; u<M; ++u) if(!(mask&(1<<u))) {
int ta = t + d[v][u];
int to = max(ta, s[u].open);
if(to < s[u].close) {
int td = to + s[u].shopping;
tbl[u][mask|(1<<u)] = min(tbl[u][mask|(1<<u)], td);
}
}
}
}
return best;
}
};
// BEGIN CUT HERE
#include <ctime>
double start_time; string timer()
{ ostringstream os; os << " (" << int((clock()-start_time)/CLOCKS_PER_SEC*1000) << " msec)"; return os.str(); }
template<typename T> ostream& operator<<(ostream& os, const vector<T>& v)
{ os << "{ ";
for(typename vector<T>::const_iterator it=v.begin(); it!=v.end(); ++it)
os << '\"' << *it << '\"' << (it+1==v.end() ? "" : ", "); os << " }"; return os; }
void verify_case(const int& Expected, const int& Received) {
bool ok = (Expected == Received);
if(ok) cerr << "PASSED" << timer() << endl; else { cerr << "FAILED" << timer() << endl;
cerr << "\to: \"" << Expected << '\"' << endl << "\tx: \"" << Received << '\"' << endl; } }
#define CASE(N) {cerr << "Test Case #" << N << "..." << flush; start_time=clock();
#define END verify_case(_, TravellingPurchasingMan().maxStores(N, interestingStores, roads));}
int main(){
CASE(0)
int N = 3;
string interestingStores_[] = {"1 10 10" , "1 55 31", "10 50 100" };
vector <string> interestingStores(interestingStores_, interestingStores_+sizeof(interestingStores_)/sizeof(*interestingStores_));
string roads_[] = {"1 2 10"};
vector <string> roads(roads_, roads_+sizeof(roads_)/sizeof(*roads_));
int _ = 1;
END
CASE(1)
int N = 3;
string interestingStores_[] = {"1 10 10" , "1 55 30", "10 50 100" };
vector <string> interestingStores(interestingStores_, interestingStores_+sizeof(interestingStores_)/sizeof(*interestingStores_));
string roads_[] = {"1 2 10"};
vector <string> roads(roads_, roads_+sizeof(roads_)/sizeof(*roads_));
int _ = 2;
END
CASE(2)
int N = 5;
string interestingStores_[] = {"0 1000 17"};
vector <string> interestingStores(interestingStores_, interestingStores_+sizeof(interestingStores_)/sizeof(*interestingStores_));
string roads_[] = {"2 3 400", "4 1 500", "4 3 300", "1 0 700", "0 2 400"};
vector <string> roads(roads_, roads_+sizeof(roads_)/sizeof(*roads_));
int _ = 0;
END
CASE(3)
// if no wf is done.
int N = 3;
string interestingStores_[] = {"0 100 1"};
vector <string> interestingStores(interestingStores_, interestingStores_+sizeof(interestingStores_)/sizeof(*interestingStores_));
string roads_[] = {"0 1 10", "1 2 10"};
vector <string> roads(roads_, roads_+sizeof(roads_)/sizeof(*roads_));
int _ = 1;
END
/*
CASE(4)
int N = ;
string interestingStores_[] = ;
vector <string> interestingStores(interestingStores_, interestingStores_+sizeof(interestingStores_)/sizeof(*interestingStores_));
string roads_[] = ;
vector <string> roads(roads_, roads_+sizeof(roads_)/sizeof(*roads_));
int _ = ;
END
*/
}
// END CUT HERE