Submission #471884

#	Time	Username	Problem	Language	Result	Execution time	Memory
471884		NicolaAbusaad2014	Split the sequence (APIO14_sequence)	C++14	0 / 100	789 ms	78708 KiB

sequence

/**
 * Prof.Nicola
**/
#include <bits/stdc++.h>

using namespace std;
#define endl "\n"
#define mp make_pair
#define F first
#define S second
#define REP(i,l,r) for(long long i=(l);i<(r);i++)
#define PER(i,l,r) for(long long i=(r)-1;i>=(l);i--)
const long dx[4]={1,0,-1,0},dz[4]={0,1,0,-1};
const long double pi=3.14159265359;
const long long mod=1e9+7;
long long p(long long x){while(x&(x-1)){x=x&(x-1);}return x;}
long long squared(long long x){return (x*x)%mod;}
long long power(long long x,long long p){if(p==0){return 1;}if(p%2==1){return (power(x,p-1)*x)%mod;}return squared(power(x,p/2));}
long long inv(long long x){return power(x,mod-2);}
template<class T>void re(T&x){cin>>x;}
template<class T1,class T2> void re(pair<T1,T2>&x){re(x.first);re(x.second);}
template<class T>void re(vector<T>&x){for(long i=0;i<x.size();i++){re(x[i]);}}
template<class T>void re(deque<T>&x){for(long i=0;i<x.size();i++){re(x[i]);}}
template<class T>void out(T x){cout<<x<<" ";}
template<class T1,class T2>void out(pair<T1,T2>x){out(x.first);out(x.second);cout<<endl;}
template<class T>void out(vector<T>x,long l=0,long r=0){if(!r){r=x.size();}for(long i=l;i<r;i++){out(x[i]);}cout<<endl;}
template<class T>void out(deque<T>x,long l=0,long r=0){if(!r){r=x.size();}for(long i=l;i<r;i++){out(x[i]);}cout<<endl;}
template<class T>void out(set<T>x){while(!x.empty()){out(*x.begin());x.erase(*x.begin());}cout<<endl;}
template<class T1,class T2>void out(map<T1,T2>x){while(!x.empty()){out(*x.begin());x.erase(x.begin()->first);}cout<<endl;}
template<class T>void out(queue<T>x){while(!x.empty()){out(x.front());x.pop();}cout<<endl;}
template<class T>void out(priority_queue<T>x){while(!x.empty()){out(x.top());x.pop();}cout<<endl;}
template<class T>void out(stack<T>x){while(!x.empty()){out(x.top());x.pop();}cout<<endl;}
template<class T>T cross(complex<T>x,complex<T>z){return (conj(x)*z).imag();}
template<class T>T dot(complex<T>x,complex<T>z){return (conj(x)*z).real();}
set<long long>::iterator T;
long long vLE(long long x,vector<long long>&VT,long l=0,long r=-1){if(r==-1){r=VT.size()-1;}if(VT[l]>x){return -1;}long long z=p(r-l);while(z){if(l+z<=r&&VT[l+z]<=x){l+=z;}z/=2;}return l;}
long long vL(long long x,vector<long long>&VT,long l=0,long r=-1){if(r==-1){r=VT.size()-1;}if(VT[l]>=x){return -1;}long long z=p(r-l);while(z){if(l+z<=r&&VT[l+z]<x){l+=z;}z/=2;}return l;}
long long vGE(long long x,vector<long long>&VT,long l=0,long r=-1){if(r==-1){r=VT.size()-1;}if(VT[l]>=x){return l;}l=vL(x,VT,l,r);if(l==r){return -1;}return l+1;}
long long vG(long long x,vector<long long>&VT,long l=0,long r=-1){if(r==-1){r=VT.size()-1;}if(VT[l]>x){return l;}l=vLE(x,VT,l,r);if(l==r){return -1;}return l+1;}
long long sLE(long long x,set<long long>&ST){if(ST.count(x)){return x;}if(*ST.begin()>x){return -1;}ST.insert(x);T=ST.find(x);T--;ST.erase(x);return *T;}
long long sL(long long x,set<long long>&ST){if(*ST.begin()>=x){return -1;}if(ST.count(x)){T=ST.find(x);T--;return *T;}ST.insert(x);T=ST.find(x);T--;ST.erase(x);return *T;}
long long sGE(long long x,set<long long>&ST){if(ST.count(x)){return x;}if(*ST.rbegin()<x){return -1;}ST.insert(x);T=ST.find(x);T++;ST.erase(x);return *T;}
long long sG(long long x,set<long long>&ST){if(*ST.rbegin()<=x){return -1;}if(ST.count(x)){T=ST.find(x);T++;return *T;}ST.insert(x);T=ST.find(x);T++;ST.erase(x);return *T;}
struct line
{
    long long slope,constant,idx;
    void def(long long x,long long z,long i)
    {
        slope=x;
        constant=z;
        idx=i;
    }
    long long sub(long long x)
    {
        return (x*slope)+constant;
    }
    bool operator==(const line&x)const
    {
        if(slope==x.slope&&constant==x.constant){
            return true;
        }
        return false;
    }
    bool operator<(const line&x)const
    {
        if(slope<x.slope){
            return true;
        }
        if(slope==x.slope){
            return (constant<x.constant);
        }
        return false;
    }
    bool operator<=(const line&x)const
    {
        if(slope==x.slope&&constant==x.constant){
            return true;
        }
        if(slope<x.slope){
            return true;
        }
        if(slope==x.slope){
            return (constant<x.constant);
        }
        return false;
    }
    bool operator>(const line&x)const
    {
        if(slope>x.slope){
            return true;
        }
        if(slope==x.slope){
            return (constant>x.constant);
        }
        return false;
    }
    bool operator>=(const line&x)const
    {
        if(slope==x.slope&&constant==x.constant){
            return true;
        }
        if(slope>x.slope){
            return true;
        }
        if(slope==x.slope){
            return (constant>x.constant);
        }
        return false;
    }
};
long long intersection(line x,line z)
{
    return ((x.constant-z.constant)/(z.slope-x.slope));
}
bool parallel(line x,line z)
{
    if(x.slope==z.slope){
        return true;
    }
    return false;
}
struct set_of_lines
{
    set<line>s;
    set<line>::iterator t;
    long long intersect;
    map<line,pair<long long,long long> >range;
    map<long long,line>line_;
    set<long long>intervals;
    pair<long long,long long>p;
    void add(line x)
    {
        if(s.count(x)){
            return;
        }
        range[x]=mp(-1e18,1e18);
        s.insert(x);
        t=s.find(x);
        t--;
        while(!(t==s.end())&&!(x==*t)){
            if(parallel(x,*t)){
                s.erase(x);
                return;
            }
            intersect=intersection(x,*t);
            p=range[*t];
            if(intersect>=p.second){
                intervals.erase(range[*t].first);
                s.erase(*t);
            }
            else if(p.first<=intersect&&intersect<p.second){
                intervals.erase(range[*t].first);
                range[x].second=intersect;
                range[*t].first=intersect+1;
                intervals.insert(range[*t].first);
                line_[range[*t].first]=*t;
                break;
            }
            else{
                range[x].second=p.first-1;
                break;
            }
            t=s.find(x);
            t--;
        }
        t=s.find(x);
        t++;
        while(!(t==s.end())){
            if(parallel(x,*t)){
                intervals.erase(range[*t].first);
                s.erase(*t);
                t=s.find(x);
                t++;
                continue;
            }
            intersect=intersection(x,*t)+1;
            p=range[*t];
            if(intersect<=p.first){
                intervals.erase(range[*t].first);
                s.erase(*t);
            }
            else if(p.first<intersect&&intersect<=p.second){
                intervals.erase(range[*t].first);
                range[x].first=intersect;
                range[*t].second=intersect-1;
                intervals.insert(range[*t].first);
                line_[range[*t].first]=*t;
                break;
            }
            else{
                range[x].first=p.second+1;
                break;
            }
            t=s.find(x);
            t++;
        }
        if(range[x].first>range[x].second){
            s.erase(x);
        }
        else{
            intervals.insert(range[x].first);
            line_[range[x].first]=x;
        }
    }
    pair<long long,long> get(long long x)
    {
        long long z=sLE(x,intervals);
        return mp(line_[z].sub(x),line_[z].idx);
    }
};
vector<long long>pre;
long long f(long l,long r)
{
    if(l==0){
        return pre[r];
    }
    return pre[r]-pre[l-1];
}
int main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    long long n,k;
    cin>>n>>k;
    vector<long long>v(n);
    pre.resize(n);
    re(v);
    pre[0]=v[0];
    REP(i,1,n){
        pre[i]=pre[i-1]+v[i];
    }
    vector<set_of_lines>sol(k+1);
    vector<vector<long long> >dp(n,vector<long long>(k+1));
    vector<vector<long long> >from(n,vector<long long>(k+1));
    REP(i,0,n){
        dp[i][0]=0;
    }
    pair<long long,long>p;
    line l;
    l.def(0,0,0);
    sol[0].add(l);
    REP(i,1,n){
        PER(j,1,k+1){
            if(j>i){
                continue;
            }
            p=sol[j-1].get(f(i,n-1));
            from[i][j]=p.second;
            dp[i][j]=-(p.first-(f(0,i-1)*f(i,n-1)));
            l.def(f(0,i-1),-dp[i][j],i);
            sol[j].add(l);
        }
    }
    long long mx=0,x;
    REP(i,k,n){
        if(dp[i][k]>mx){
            mx=dp[i][k];
            x=i+1;
        }
    }
    cout<<mx<<endl;
    REP(i,0,k){
        cout<<x<<" ";
        x=from[x][k-i];
    }
    return 0;
}

Compilation message (stderr)

sequence.cpp: In instantiation of 'void re(std::vector<_Tp>&) [with T = long long int]':
sequence.cpp:227:9:   required from here
sequence.cpp:22:53: warning: comparison of integer expressions of different signedness: 'long int' and 'std::vector<long long int>::size_type' {aka 'long unsigned int'} [-Wsign-compare]
   22 | template<class T>void re(vector<T>&x){for(long i=0;i<x.size();i++){re(x[i]);}}
      |                                                    ~^~~~~~~~~
sequence.cpp: In function 'int main()':
sequence.cpp:264:17: warning: 'x' may be used uninitialized in this function [-Wmaybe-uninitialized]
  264 |         x=from[x][k-i];
      |                 ^

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