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// verification-helper: PROBLEM http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=2725 #include <bits/stdc++.h> using namespace std; #define call_from_test #include "../../tools/chminmax.cpp" #include "../../vector/zip.cpp" #include "../../convexhulltrick/linecontainer.cpp" #undef call_from_test signed main(){ cin.tie(0); ios::sync_with_stdio(0); using ll = long long; int n,x; cin>>n>>x; vector<ll> ts(n),ps(n),fs(n); for(int i=0;i<n;i++) cin>>ts[i]>>ps[i]>>fs[i]; auto vt=zip(fs,ps,ts); sort(vt.begin(),vt.end()); for(int i=0;i<n;i++) tie(fs[i],ps[i],ts[i])=vt[i]; vector<MaxLineContainer<ll>> vh(x+1); ll ans=0; for(int i=0;i<n;i++){ for(int j=x;j>ts[i];j--){ if(vh[j-ts[i]].empty()) continue; ll val=vh[j-ts[i]].query(fs[i])+ps[i]-fs[i]*fs[i]; vh[j].add(2*fs[i],val-fs[i]*fs[i]); chmax(ans,val); } vh[ts[i]].add(2*fs[i],ps[i]-fs[i]*fs[i]); chmax(ans,ps[i]); } cout<<ans<<endl; return 0; }
#line 1 "test/aoj/2725.linecontainer.test.cpp" // verification-helper: PROBLEM http://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=2725 #include <bits/stdc++.h> using namespace std; #define call_from_test #line 1 "tools/chminmax.cpp" #line 3 "tools/chminmax.cpp" using namespace std; #endif //BEGIN CUT HERE template<typename T1,typename T2> inline void chmin(T1 &a,T2 b){if(a>b) a=b;} template<typename T1,typename T2> inline void chmax(T1 &a,T2 b){if(a<b) a=b;} //END CUT HERE #ifndef call_from_test signed main(){ return 0; } #endif #line 1 "vector/zip.cpp" #line 3 "vector/zip.cpp" using namespace std; #endif //BEGIN CUT HERE template<typename ...Ts> decltype(auto) zip(vector<Ts>... args){ vector<decltype(make_tuple(args[0]...))> res; int n=min({args.size()...}); res.reserve(n); for(int i=0;i<n;i++) res.emplace_back(args[i]...); return res; } //END CUT HERE #ifndef call_from_test signed main(){ return 0; } #endif #line 1 "convexhulltrick/linecontainer.cpp" #line 3 "convexhulltrick/linecontainer.cpp" using namespace std; #endif //BEGIN CUT HERE enum Objective{ MAXIMIZE = +1, MINIMIZE = -1, }; template<typename T> struct Line { mutable T k,m,p; bool operator<(const Line&o)const{return k<o.k;} bool operator<(T x)const{return p<x;} }; template<typename T> T lc_inf(){return numeric_limits<T>::max();} template<> double lc_inf<double>(){return 1/.0;} template<typename T> T lc_div(T a,T b){return a/b-((a^b)<0 and a%b);} template<> double lc_div(double a,double b){return a/b;}; template<typename T, Objective objective> struct LineContainer : multiset<Line<T>, less<>>{ using super = multiset<Line<T>, less<>>; using super::begin,super::end,super::insert,super::erase; using super::empty,super::lower_bound; const T inf = lc_inf<T>(); bool insect(typename super::iterator x,typename super::iterator y){ if(y==end()) return x->p=inf,false; if(x->k==y->k) x->p=(x->m>y->m?inf:-inf); else x->p=lc_div(y->m-x->m,x->k-y->k); return x->p>=y->p; } void add(T k,T m){ auto z=insert({k*objective,m*objective,0}),y=z++,x=y; while(insect(y,z)) z=erase(z); if(x!=begin() and insect(--x,y)) insect(x,y=erase(y)); while((y=x)!=begin() and (--x)->p>=y->p) insect(x,erase(y)); } T query(T x){ assert(!empty()); auto l=*lower_bound(x); return (l.k*x+l.m)*objective; } }; template<typename T> using MinLineContainer = LineContainer<T, Objective::MINIMIZE>; template<typename T> using MaxLineContainer = LineContainer<T, Objective::MAXIMIZE>; //END CUT HERE #ifndef call_from_test //INSERT ABOVE HERE signed main(){ return 0; } #endif #line 10 "test/aoj/2725.linecontainer.test.cpp" #undef call_from_test signed main(){ cin.tie(0); ios::sync_with_stdio(0); using ll = long long; int n,x; cin>>n>>x; vector<ll> ts(n),ps(n),fs(n); for(int i=0;i<n;i++) cin>>ts[i]>>ps[i]>>fs[i]; auto vt=zip(fs,ps,ts); sort(vt.begin(),vt.end()); for(int i=0;i<n;i++) tie(fs[i],ps[i],ts[i])=vt[i]; vector<MaxLineContainer<ll>> vh(x+1); ll ans=0; for(int i=0;i<n;i++){ for(int j=x;j>ts[i];j--){ if(vh[j-ts[i]].empty()) continue; ll val=vh[j-ts[i]].query(fs[i])+ps[i]-fs[i]*fs[i]; vh[j].add(2*fs[i],val-fs[i]*fs[i]); chmax(ans,val); } vh[ts[i]].add(2*fs[i],ps[i]-fs[i]*fs[i]); chmax(ans,ps[i]); } cout<<ans<<endl; return 0; }