Submission #264727

#	Time	Username	Problem	Language	Result	Execution time	Memory
264727		kaage	Split the sequence (APIO14_sequence)	C++17	50 / 100	2084 ms	21228 KiB

sequence

#line 2 "/Users/kaage/Desktop/ProgrammingWorkspace/library/other/template.hpp"
#define _CRT_SECURE_NO_WARNINGS
#pragma target("avx2")
#pragma optimize("O3")
#pragma optimize("unroll-loops")
#include <algorithm>
#include <bitset>
#include <cassert>
#include <cfloat>
#include <climits>
#include <cmath>
#include <complex>
#include <ctime>
#include <deque>
#include <fstream>
#include <functional>
#include <iomanip>
#include <iostream>
#include <iterator>
#include <list>
#include <map>
#include <memory>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <string.h>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
#define rep(i,n) for(int i=0;i<(n);i++)
#define REP(i,n) for(int i=1;i<=(n);i++)
#define all(V) V.begin(),V.end()
typedef long long lint;
typedef unsigned long long ulint;
typedef std::pair<int, int> P;
typedef std::pair<lint, lint> LP;
constexpr int INF = INT_MAX/2;
constexpr lint LINF = LLONG_MAX/2;
constexpr double eps = DBL_EPSILON;
constexpr double PI=3.141592653589793238462643383279;
template<class T>
class prique :public std::priority_queue<T, std::vector<T>, std::greater<T>> {};
template <class T, class U>
inline bool chmax(T& lhs, const U& rhs) {
	if (lhs < rhs) {
		lhs = rhs;
		return 1;
	}
	return 0;
}
template <class T, class U>
inline bool chmin(T& lhs, const U& rhs) {
	if (lhs > rhs) {
		lhs = rhs;
		return 1;
	}
	return 0;
}
inline lint gcd(lint a, lint b) {
	while (b) {
		lint c = a;
		a = b; b = c % b;
	}
	return a;
}
inline lint lcm(lint a, lint b) {
	return a / gcd(a, b) * b;
}
bool isprime(lint n) {
	if (n == 1)return false;
	for (int i = 2; i * i <= n; i++) {
		if (n % i == 0)return false;
	}
	return true;
}
template<typename T>
T mypow(T a, lint b) {
	T res(1);
	while(b){
		if(b&1)res*=a;
		a*=a;
		b>>=1;
	}
	return res;
}
lint modpow(lint a, lint b, lint m) {
	lint res(1);
	while(b){
		if(b&1){
			res*=a;res%=m;
		}
		a*=a;a%=m;
		b>>=1;
	}
	return res;
}
template<typename T>
void printArray(std::vector<T>& vec) {
	rep(i, vec.size()){
		std::cout << vec[i];
		std::cout<<(i==(int)vec.size()-1?"\n":" ");
	}
}
template<typename T>
void printArray(T l, T r) {
	T rprev = std::prev(r);
	for (T i = l; i != rprev; i++) {
		std::cout << *i << " ";
	}
	std::cout << *rprev << std::endl;
}
LP extGcd(lint a,lint b) {
	if(b==0)return {1,0};
	LP s=extGcd(b,a%b);
	std::swap(s.first,s.second);
	s.second-=a/b*s.first;
	return s;
}
LP ChineseRem(const lint& b1,const lint& m1,const lint& b2,const lint& m2) {
	lint p=extGcd(m1,m2).first;
	lint tmp=(b2-b1)*p%m2;
	lint r=(b1+m1*tmp+m1*m2)%(m1*m2);
	return std::make_pair(r,m1*m2);
}
/*template<typename F>
inline constexpr decltype(auto) lambda_fix(F&& f){
	return [f=std::forward<F>(f)](auto&&... args){
		return f(f,std::forward<decltype(args)>(args)...);
	};
}*/
#line 2 "/Users/kaage/Desktop/ProgrammingWorkspace/library/data-structure/ConvexHullTrick.hpp"
template<bool isMin>
class ConvexHullTrick{
	static constexpr double INF=DBL_MAX;
	class Line{
	public:
		double m,b,val,x;
		int id;
		bool isQuery;
		inline Line(int id=-1,double m=0,double b=0):id(id),m(m),b(b),isQuery(false){}
		double eval(double x)const{return m*x+b;}
		bool parallel(const Line& l)const{return m==l.m;}
		double intersect(const Line& l)const{
			return parallel(l)?INF:(l.b-b)/(m-l.m);
		}
		inline bool operator<(const Line &l)const{
			if(l.isQuery)return x<l.val;
			return m<l.m;
		}
	};
	int index=1;
	std::set<Line> st;
	using iter=typename std::set<Line>::iterator;
	inline bool cPrev(iter it)const{return it!=st.begin();}
	inline bool cNext(iter it)const{return it!=st.end()&&std::next(it)!=st.end();}
	bool bad(const Line& l1,const Line& l2,const Line& l3)const{
		return l1.intersect(l3)<=l1.intersect(l2);
	}
	bool bad(iter it)const{
		return cPrev(it)&&cNext(it)&&bad(*std::prev(it),*it,*std::next(it));
	}
	iter update(iter it){
		if(!cPrev(it))return it;
		double x=it->intersect(*std::prev(it));
		Line tmp(*it);
		tmp.x=x;
		it=st.erase(it);
		return st.insert(it,tmp);
	}
public:
	void addLine(double m,double b){
		if(isMin)m=-m,b=-b;
		Line l(index,m,b);
		if(st.empty())l.x=-INF;
		iter it=st.lower_bound(l);
		if(it!=st.end()&&l.parallel(*it)){
			if(it->b<b)it=st.erase(it);
			else{
				index++;
				return;
			}
		}
		it=st.insert(it,l);
		if(bad(it)){
			st.erase(it);
			index++;
			return;
		}
		while(cPrev(it)&&bad(std::prev(it)))st.erase(std::prev(it));
		while(cNext(it)&&bad(std::next(it)))st.erase(std::next(it));
		it=update(it);
		if(cPrev(it))update(std::prev(it));
		if(cNext(it))update(std::next(it));
		index++;
	}
	std::pair<double,int> query(double x){
		Line q;
		q.val=x;q.isQuery=true;
		iter it=--st.lower_bound(q);
		if(isMin)return {-it->eval(x),it->id};
		return {it->eval(x),it->id};
	}
	void clear(){
		st.clear();index=0;
	}
};
#line 3 "main.cpp"
int n,k,a[100010];
lint b[100010],dp[2][100010];
int from[210][100010];
int main(){
	scanf("%d%d",&n,&k);
	rep(i,n){
		scanf("%d",a+i);
		b[i]=a[i];
		if(i)b[i]+=b[i-1];
	}
	ConvexHullTrick<false> cht;
	rep(i,k){
		cht.clear();
		for(int j=i+1;j<n;j++){
			cht.addLine(b[j-1],dp[0][j-1]-b[j-1]*b[j-1]);
			auto p=cht.query(b[j]);
			from[i][j]=p.second+i;
			dp[1][j]=p.first;
		}
		std::move(dp[1],dp[1]+n,dp[0]);
		std::fill(dp[1],dp[1]+n,0);
	}
	std::vector<int> vec;
	int now=n-1;
	for(int i=k-1;i>=0;i--){
		now=from[i][now];
		vec.push_back(now+1);
	}
	std::reverse(all(vec));
	printf("%lld\n",dp[0][n-1]);
	printArray(vec);
}

Compilation message (stderr)

/Users/kaage/Desktop/ProgrammingWorkspace/library/other/template.hpp:3: warning: ignoring #pragma target  [-Wunknown-pragmas]
/Users/kaage/Desktop/ProgrammingWorkspace/library/other/template.hpp:4: warning: ignoring #pragma optimize  [-Wunknown-pragmas]
/Users/kaage/Desktop/ProgrammingWorkspace/library/other/template.hpp:5: warning: ignoring #pragma optimize  [-Wunknown-pragmas]
/Users/kaage/Desktop/ProgrammingWorkspace/library/other/template.hpp: In instantiation of 'void printArray(std::vector<_Tp>&) [with T = int]':
main.cpp:33:16:   required from here
/Users/kaage/Desktop/ProgrammingWorkspace/library/other/template.hpp:33:31: warning: comparison of integer expressions of different signedness: 'int' and 'std::vector<int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
/Users/kaage/Desktop/ProgrammingWorkspace/library/other/template.hpp:102:2: note: in expansion of macro 'rep'
/Users/kaage/Desktop/ProgrammingWorkspace/library/data-structure/ConvexHullTrick.hpp: In instantiation of 'ConvexHullTrick<isMin>::Line::Line(int, double, double) [with bool isMin = false]':
/Users/kaage/Desktop/ProgrammingWorkspace/library/data-structure/ConvexHullTrick.hpp:43:8:   required from 'void ConvexHullTrick<isMin>::addLine(double, double) [with bool isMin = false]'
main.cpp:17:47:   required from here
/Users/kaage/Desktop/ProgrammingWorkspace/library/data-structure/ConvexHullTrick.hpp:8:7: warning: 'ConvexHullTrick<false>::Line::id' will be initialized after [-Wreorder]
/Users/kaage/Desktop/ProgrammingWorkspace/library/data-structure/ConvexHullTrick.hpp:7:10: warning:   'double ConvexHullTrick<false>::Line::m' [-Wreorder]
/Users/kaage/Desktop/ProgrammingWorkspace/library/data-structure/ConvexHullTrick.hpp:10:10: warning:   when initialized here [-Wreorder]
main.cpp: In function 'int main()':
main.cpp:7:7: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
main.cpp:9:8: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]

• Subtask 1: 11 / 11
• Subtask 2: 11 / 11
• Subtask 3: 11 / 11
• Subtask 4: 17 / 17
• Subtask 5: 0 / 21
• Subtask 6: 0 / 29