Submission #723825

# Submission time Handle Problem Language Result Execution time Memory
723825 2023-04-14T10:47:36 Z Urvuk3 Split the sequence (APIO14_sequence) C++17
100 / 100
945 ms 86620 KB
#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

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];
      |                         ^
# Verdict Execution time Memory Grader output
1 Correct 1 ms 212 KB contestant found the optimal answer: 108 == 108
2 Correct 1 ms 212 KB contestant found the optimal answer: 999 == 999
3 Correct 0 ms 212 KB contestant found the optimal answer: 0 == 0
4 Correct 0 ms 212 KB contestant found the optimal answer: 1542524 == 1542524
5 Correct 0 ms 212 KB contestant found the optimal answer: 4500000000 == 4500000000
6 Correct 1 ms 212 KB contestant found the optimal answer: 1 == 1
7 Correct 0 ms 212 KB contestant found the optimal answer: 1 == 1
8 Correct 0 ms 212 KB contestant found the optimal answer: 1 == 1
9 Correct 1 ms 212 KB contestant found the optimal answer: 100400096 == 100400096
10 Correct 0 ms 212 KB contestant found the optimal answer: 900320000 == 900320000
11 Correct 0 ms 212 KB contestant found the optimal answer: 3698080248 == 3698080248
12 Correct 1 ms 212 KB contestant found the optimal answer: 3200320000 == 3200320000
13 Correct 1 ms 212 KB contestant found the optimal answer: 140072 == 140072
14 Correct 0 ms 212 KB contestant found the optimal answer: 376041456 == 376041456
15 Correct 1 ms 212 KB contestant found the optimal answer: 805 == 805
16 Correct 1 ms 304 KB contestant found the optimal answer: 900189994 == 900189994
17 Correct 0 ms 212 KB contestant found the optimal answer: 999919994 == 999919994
# Verdict Execution time Memory Grader output
1 Correct 0 ms 212 KB contestant found the optimal answer: 1093956 == 1093956
2 Correct 1 ms 212 KB contestant found the optimal answer: 302460000 == 302460000
3 Correct 1 ms 212 KB contestant found the optimal answer: 122453454361 == 122453454361
4 Correct 1 ms 212 KB contestant found the optimal answer: 93663683509 == 93663683509
5 Correct 1 ms 212 KB contestant found the optimal answer: 1005304678 == 1005304678
6 Correct 0 ms 212 KB contestant found the optimal answer: 933702 == 933702
7 Correct 1 ms 212 KB contestant found the optimal answer: 25082842857 == 25082842857
8 Correct 1 ms 212 KB contestant found the optimal answer: 687136 == 687136
9 Correct 0 ms 212 KB contestant found the optimal answer: 27295930079 == 27295930079
10 Correct 0 ms 212 KB contestant found the optimal answer: 29000419931 == 29000419931
# Verdict Execution time Memory Grader output
1 Correct 1 ms 212 KB contestant found the optimal answer: 610590000 == 610590000
2 Correct 0 ms 212 KB contestant found the optimal answer: 311760000 == 311760000
3 Correct 1 ms 468 KB contestant found the optimal answer: 1989216017013 == 1989216017013
4 Correct 0 ms 340 KB contestant found the optimal answer: 1499437552673 == 1499437552673
5 Correct 1 ms 340 KB contestant found the optimal answer: 1019625819 == 1019625819
6 Correct 1 ms 468 KB contestant found the optimal answer: 107630884 == 107630884
7 Correct 1 ms 468 KB contestant found the optimal answer: 475357671774 == 475357671774
8 Correct 1 ms 340 KB contestant found the optimal answer: 193556962 == 193556962
9 Correct 1 ms 340 KB contestant found the optimal answer: 482389919803 == 482389919803
10 Correct 1 ms 340 KB contestant found the optimal answer: 490686959791 == 490686959791
# Verdict Execution time Memory Grader output
1 Correct 1 ms 340 KB contestant found the optimal answer: 21503404 == 21503404
2 Correct 1 ms 340 KB contestant found the optimal answer: 140412195 == 140412195
3 Correct 9 ms 1108 KB contestant found the optimal answer: 49729674225461 == 49729674225461
4 Correct 1 ms 340 KB contestant found the optimal answer: 37485571387523 == 37485571387523
5 Correct 11 ms 1176 KB contestant found the optimal answer: 679388326 == 679388326
6 Correct 8 ms 980 KB contestant found the optimal answer: 4699030287 == 4699030287
7 Correct 8 ms 1188 KB contestant found the optimal answer: 12418819758185 == 12418819758185
8 Correct 8 ms 1108 KB contestant found the optimal answer: 31093317350 == 31093317350
9 Correct 2 ms 468 KB contestant found the optimal answer: 12194625429236 == 12194625429236
10 Correct 4 ms 596 KB contestant found the optimal answer: 12345131038664 == 12345131038664
# Verdict Execution time Memory Grader output
1 Correct 2 ms 1108 KB contestant found the optimal answer: 1818678304 == 1818678304
2 Correct 2 ms 1108 KB contestant found the optimal answer: 1326260195 == 1326260195
3 Correct 77 ms 8916 KB contestant found the optimal answer: 4973126687469639 == 4973126687469639
4 Correct 3 ms 1108 KB contestant found the optimal answer: 3748491676694116 == 3748491676694116
5 Correct 59 ms 5696 KB contestant found the optimal answer: 1085432199 == 1085432199
6 Correct 60 ms 6484 KB contestant found the optimal answer: 514790755404 == 514790755404
7 Correct 69 ms 6944 KB contestant found the optimal answer: 1256105310476641 == 1256105310476641
8 Correct 56 ms 5852 KB contestant found the optimal answer: 3099592898816 == 3099592898816
9 Correct 58 ms 6484 KB contestant found the optimal answer: 1241131419367412 == 1241131419367412
10 Correct 80 ms 8084 KB contestant found the optimal answer: 1243084101967798 == 1243084101967798
# Verdict Execution time Memory Grader output
1 Correct 20 ms 8340 KB contestant found the optimal answer: 19795776960 == 19795776960
2 Correct 25 ms 8264 KB contestant found the optimal answer: 19874432173 == 19874432173
3 Correct 908 ms 86620 KB contestant found the optimal answer: 497313449256899208 == 497313449256899208
4 Correct 23 ms 9212 KB contestant found the optimal answer: 374850090734572421 == 374850090734572421
5 Correct 945 ms 85704 KB contestant found the optimal answer: 36183271951 == 36183271951
6 Correct 609 ms 62056 KB contestant found the optimal answer: 51629847150471 == 51629847150471
7 Correct 774 ms 66928 KB contestant found the optimal answer: 124074747024496432 == 124074747024496432
8 Correct 550 ms 55924 KB contestant found the optimal answer: 309959349080800 == 309959349080800
9 Correct 720 ms 62604 KB contestant found the optimal answer: 124113525649823701 == 124113525649823701
10 Correct 882 ms 78308 KB contestant found the optimal answer: 124309619349406845 == 124309619349406845