Submission #723825

#	Time	Username	Problem	Language	Result	Execution time	Memory
723825		Urvuk3	Split the sequence (APIO14_sequence)	C++17	100 / 100	945 ms	86620 KiB

sequence

#include <bits/stdc++.h>
 
using namespace std;
 
#define ll long long
const int INF=1e9,MOD=1e9+7;
const ll LINF=1e18;
#define fi first
#define se second
#define pii pair<int,int>
#define pll pair<ll,ll>
#define mid ((l+r)/2)
#define sz(a) (int((a).size()))
#define all(a) a.begin(),a.end()
#define endl "\n"
#define pb push_back
 
struct Line{
    ll k,m,l,r,id;
    ll operator ()(ll x){
        return k*x+m;
    }
};
 
void PRINT(int x) {cerr << x;}
void PRINT(ll x) {cerr << x;}
void PRINT(double x) {cerr << x;}
void PRINT(char x) {cerr << '\'' << x << '\'';}
void PRINT(string x) {cerr << '\"' << x << '\"';}
void PRINT(bool x) {cerr << (x ? "true" : "false");}
void PRINT(Line f){
    cerr<<f.k<<"x+"<<f.m<<" ["<<f.l<<","<<f.r<<"]";
}
 
template<typename T,typename V>
void PRINT(pair<T,V>& x){
    cerr<<"{";
    PRINT(x.fi);
    cerr<<",";
    PRINT(x.se);
    cerr<<"}";
}
template<typename T>
void PRINT(T &x){
    int id=0;
    cerr<<"{";
    for(auto _i:x){
        cerr<<(id++ ? "," : "");
        PRINT(_i);
    }
    cerr<<"}";
}
void _PRINT(){
    cerr<<"]\n";
}
template<typename Head,typename... Tail>
void _PRINT(Head h,Tail... t){
    PRINT(h);
    if(sizeof...(t)) cerr<<", ";
    _PRINT(t...);
}
 
#define Debug(x...) cerr<<"["<<#x<<"]=["; _PRINT(x)
 
ll Intersect(Line l1,Line l2){
    ll ret=(l2.m-l1.m)/(l1.k-l2.k);
    return ret;
}
 
deque<Line> Hull;
 
int it;
 
void AddLine(Line f){
    if(!Hull.empty() && Hull[0].k==f.k){
        if(Hull[0].m<f.k){
            Hull.pop_front();
            Hull[0].l=-LINF;
            if(it) it--;
        }
        else return;
    }
    if(sz(Hull)==0){
        f.l=-LINF,f.r=LINF;
        Hull.push_front(f);
        it++;
    }
    else if(sz(Hull)==1){
        ll sec=Intersect(f,Hull[0]);
        f.l=-LINF,f.r=sec;
        Hull[0].l=sec+1;
        Hull.push_front(f);
        it++;
    }
    else{
        while(Hull[0].r<=Intersect(f,Hull[0])){
            Hull.pop_front();
            Hull[0].l=-LINF;
            if(it) it--;
        }
        ll sec=Intersect(f,Hull[0]);
        f.l=-LINF,f.r=sec;
        Hull[0].l=sec+1;
        Hull.push_front(f);
        it++;
    }
}
 
void Solve(){
    int N,K; cin>>N>>K;
    vector<ll> a(N+1);
    for(int i=1;i<=N;i++) cin>>a[i];
    vector<ll> p(N+1,0);
    for(int i=1;i<=N;i++) p[i]=p[i-1]+a[i];
    vector<vector<int>> where(K+1,vector<int>(N+1,0));
    //vector<vector<pll>> dp(K+1,vector<pll>(N+1,{0,0}));
    vector<vector<ll>> dp(2,vector<ll>(N+1,0));
    for(int j=1;j<=K;j++){
        it=sz(Hull)-1;
        for(int i=j;i<=N-1;i++){
            ll x=p[N]-p[i];
            Line f={-p[i-1],dp[0][i-1],0,0,i-1};
            AddLine(f);
            while(!(Hull[it].l<=x && x<=Hull[it].r)){
                it--;
            }
            ll dp_new=Hull[it](p[N]-p[i])+p[i]*(p[N]-p[i]);
            if(dp[1][i]<dp_new){
                dp[1][i]=dp_new;
                where[j][i]=Hull[it].id;
            }
        }
        dp[0]=dp[1];
        fill(all(dp[1]),0);
        Hull.clear();
    }
    ll res=0;
    int idx;
    int c=K;
    for(int i=1;i<=N-1;i++){
        if(res<=dp[0][i]){
            idx=i;
            res=dp[0][i];
        }
    }
    cout<<res<<endl;
    while(c!=0){
        cout<<idx<<" ";
        idx=where[c][idx];
        c--;
    }
}
 
int main(){
    ios::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);
    int t; t=1;
    //cin>>t;
    while(t--){
        Solve();
    }
    return 0;
}
 
/*
7 3
4 1 3 4 0 2 3
*/

Compilation message (stderr)

sequence.cpp: In function 'void Solve()':
sequence.cpp:149:25: warning: 'idx' may be used uninitialized in this function [-Wmaybe-uninitialized]
  149 |         idx=where[c][idx];
      |                         ^

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