Submission #285284

#	Time	Username	Problem	Language	Result	Execution time	Memory
285284		user202729	Aliens (IOI16_aliens)	C++17	100 / 100	859 ms	11108 KiB

aliens

// moreflags=grader.cpp
// it's too late.
//
// ...

#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{int u; double t; int numPhoto;};
		std::vector<Item> hull;

		auto const add=[&](int pos)->void{
			Item const cur{points[pos].first, t(pos), value[pos].second};
			if(hull.empty()){hull.push_back(cur); return;}

			assert(cur.u>hull.back().u);

			auto const bad=[&]{
				auto [u1, t1, n1]=hull.end()[-2];
				auto [u2, t2, n2]=hull.end()[-1];
				auto [u3, t3, n3]=cur;
				assert(u1<u2); assert(u2<u3);

				u1-=u2; t1-=t2;
				u3-=u2; t3-=t2;

				return u3*t1-u1*t3<=0;
			};
			while(hull.size()>=2 and bad()) hull.pop_back();
			hull.push_back(cur);
		};

		auto const query=[&](double slope){
			int result=0;
			auto const value=[&](int pos){
				auto [u, t, numPhoto]=hull[pos];
				return t+u*slope;
			};
			auto curValue=value(result);

			for(int step=1<<(31^__builtin_clz((int)hull.size())); step; step>>=1){
				if(result+step<(int)hull.size() and value(result+step)<curValue){
					curValue=value(result+=step);
				}
				if(result-step>=0 and value(result-step)<curValue){
					curValue=value(result-=step);
				}
			}
			return std::make_pair(curValue, hull[result].numPhoto+1);
		};

		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: 19 / 19
• Subtask 6: 40 / 40