제출 #285270

#	제출 시각	아이디	문제	언어	결과	실행 시간	메모리
285270		user202729	Aliens (IOI16_aliens)	C++17	41 / 100	2052 ms	4056 KiB

aliens

// moreflags=grader.cpp
// {}

#include "aliens.h"
// 15
#include<algorithm>
#include<map>
#include<cmath>
#include<cstdint>
#include<climits>
#include<cfloat>
#if not LOCAL
#define NDEBUG
#endif
#include<cassert>

long long take_photos(int n, int m, int numPhoto, std::vector<int> r, std::vector<int> c) {
	std::vector<std::pair<int, int>> points(r.size());
	for(int index=0; index<(int)r.size(); ++index)
		points[index]=std::minmax({r[index], c[index]});
	std::sort(begin(points), end(points),
			[&](auto first, auto sec){return first.first!=sec.first ? first.first<sec.first: first.second>sec.second;
			});
	{ // keep only extreme points
		auto out=points.begin()+1;
		std::for_each(out, points.end(),[&](auto it){
			assert(it.first>=out[-1].first);
			if(it.second>out[-1].second){
				assert(it.first>out[-1].first);
				*out++=it;
			}
		});
		points.erase(out, points.end());
	}
	r.clear(); c.clear(); n=-1;

	auto const square=[&](int it)->int64_t{return (int64_t)it*it;};

	auto const check=[&](double slope)->std::pair<int64_t, int>{
		std::vector<std::pair<double, int>> value(points.size()+1);
		value[0]={0, 0};

		auto const t=[&](int last)->double{
			return value[last].first
				-(double)square(last==0 ? 0: std::max(0, points[last-1].second-points[last].first+1))
				+(double)square(points[last].first);
		};

		struct Item{double t; int numPhoto;};
		std::map<int, Item> hull;
		auto const add=[&](int pos)->void{
			int const u=points[pos].first; double const t_=t(pos);
			auto const [iterator, inserted]=hull.insert({u, {t_, value[pos].second}});
			if(not inserted){
				if(t_>=iterator->second.t) return;
				iterator->second.t=t_;
			}
			assert(iterator->second.t==t_);

			auto const bad=[&](auto iterator){
				auto [u1_, i1]=*std::prev(iterator);
				auto [u2_, i2]=*iterator;
				auto [u3_, i3]=*std::next(iterator);
				assert(u1_<u2_); assert(u2_<u3_);

				auto const u1=u1_-u2_, u3=u3_-u2_;
				double const t1=i1.t-i2.t;
				double const t3=i3.t-i2.t;

				return u3*t1-u1*t3<=0;
			};

			if(iterator!=hull.begin() and std::next(iterator)!=hull.end() and bad(iterator)){
				hull.erase(iterator);
				return;
			}

			while(std::next(iterator)!=hull.end() and
					std::next(std::next(iterator))!=hull.end() and
					bad(std::next(iterator)))
				hull.erase(std::next(iterator));

			while(iterator!=hull.begin() and std::prev(iterator)!=hull.begin() and
					bad(std::prev(iterator)))
				hull.erase(std::prev(iterator));
		};

		auto const query=[&](double slope){
			std::pair<double, int> cur{DBL_MAX, 0};
			for(auto [u, item]: hull){
				cur=std::min(cur, std::make_pair(
							item.t + u* slope
							, item.numPhoto +1));
			}
			return cur;
		};

		add(0);
		for(int pos=1; ; ++pos){
			auto& cur=value[pos];
			cur={DBL_MAX, 0};
			double const tmp2=-double(points[pos-1].second+1)*2;
			/*
			for(int last=0; last<pos; ++last){
				cur=std::min(cur, std::make_pair(
							(double)t(last) + points[last].first * tmp2
							, value[last].second+1));
			}
			*/

			cur=query(tmp2);

			cur.first+=tmp2*tmp2/4+slope;
			if(pos==(int)points.size()) break;
			add(pos);
		}
		auto const [result, resultf]=value[points.size()];
		return {(int64_t)std::round(result-resultf*slope), resultf};
	};

	// the numPhoto>=(int)points.size() case can be special-handled
	double slope1=0;
	auto [v1, nf1]=check(slope1);
	if(numPhoto>=nf1) return v1;
	assert(nf1>=(int)points.size());

	double slope2; int64_t v2; int nf2;
	for(slope2=1;; slope2*=2){
		std::tie(v2, nf2)=check(slope2);
		if(nf2<=numPhoto) break;
	}

	while(true){
		assert(nf2<=numPhoto); assert(numPhoto<=nf1);
		if(nf1==numPhoto and nf2==numPhoto){
			assert(v1==v2);
			return v1;
		}

		int64_t const lower=(int64_t)std::ceil(
				std::max(
					(double)v1+slope1*(nf1-numPhoto),
					(double)v2+slope2*(nf2-numPhoto)
					)-1e-12);
		assert(nf1>nf2);
		int64_t const upper=(v1*(numPhoto-nf2)+v2*(nf1-numPhoto))/(nf1-nf2);
		assert(upper>=0);
		assert(lower<=upper);

		if(lower==upper) return lower;

		assert(nf2<numPhoto); assert(numPhoto<nf1);
		auto const slope3=(slope1+slope2)/2;
		auto const [v3, nf3]=check(slope3);
		(nf3<=numPhoto ? std::tie(v2, nf2, slope2): std::tie(v1, nf1, slope1))=std::tuple(v3, nf3, slope3);
	}
}

• Subtask 1: 4 / 4
• Subtask 2: 12 / 12
• Subtask 3: 9 / 9
• Subtask 4: 16 / 16
• Subtask 5: 0 / 19
• Subtask 6: 0 / 40