oj.uz

Submission #147150

# Submission time Handle Problem Language Result Execution time Memory
147150 2019-08-28T06:03:14 Z jh05013 Split the sequence (APIO14_sequence) C++17
100 / 100
 1574 ms 87096 KB 
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define entire(X) X.begin(),X.end()
#define dbgv(V) for(auto x:V)cout<<x<<' ';cout<<endl;
void OJize(){cin.tie(NULL); ios_base::sync_with_stdio(false);}

template <typename T>
struct CHT{
    vector<tuple<T,T,int>> hull; int p=0;
    long double cr(int x){
        auto [ax,bx,_] = hull[x]; auto [ay,by,__] = hull[x+1];
        return (long double)(by-bx) / (ax-ay);
    }

    void insert(T a, T b, int i){
        if(!hull.empty()){
            auto [aa,bb,_] = hull.back();
            if(aa == a && bb <= b) return;
            if(aa == a) hull.pop_back();
        }
        hull.push_back({a,b,i});
        while(hull.size() > 2 && cr(hull.size()-3) >
            cr(hull.size()-2)) hull.erase(hull.end()-2);
    }

    pair<T,int> get(T x){
        while(p+1 < hull.size() && cr(p) <= x) p++;
        auto [a,b,i] = hull[p];
        return {a*x + b, i};
    }
};

ll DP[2][100005], S[100005];
int prv[202][100005];
int main(){OJize();
    int n, k; cin>>n>>k; k++;
    for(int i=0; i<n; i++){
        ll x; cin>>x;
        S[i+1] = S[i] + x;
    }

    for(int j=2; j<=k; j++){
        CHT<ll> cht;
        cht.insert(-S[j-1], S[j-1]*S[j-1]-DP[1-j%2][j-1], j-1);
        for(int i=j; i<=n; i++){
            auto [val,idx] = cht.get(S[i]);
            DP[j%2][i] = -val, prv[j][i] = idx;
            cht.insert(-S[i], S[i]*S[i]-DP[1-j%2][i], i);
        }
    }
    
    cout << DP[k%2][n] << '\n';
    vector<int> trace;
    int last = n;
    while(k >= 2){
        last = prv[k--][last];
        trace.push_back(last);
    }
    reverse(entire(trace));
    dbgv(trace);
}

Compilation message

sequence.cpp: In instantiation of 'void CHT<T>::insert(T, T, int) [with T = long long int]':
sequence.cpp:45:62:   required from here
sequence.cpp:18:26: warning: unused variable '_' [-Wunused-variable]
             auto [aa,bb,_] = hull.back();
                          ^
sequence.cpp: In instantiation of 'std::pair<_BiIter, int> CHT<T>::get(T) [with T = long long int]':
sequence.cpp:47:42:   required from here
sequence.cpp:28:19: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
         while(p+1 < hull.size() && cr(p) <= x) p++;
sequence.cpp: In instantiation of 'long double CHT<T>::cr(int) [with T = long long int]':
sequence.cpp:23:36:   required from 'void CHT<T>::insert(T, T, int) [with T = long long int]'
sequence.cpp:45:62:   required from here
sequence.cpp:12:22: warning: unused variable '_' [-Wunused-variable]
         auto [ax,bx,_] = hull[x]; auto [ay,by,__] = hull[x+1];
                      ^
sequence.cpp:12:49: warning: unused variable '__' [-Wunused-variable]
         auto [ax,bx,_] = hull[x]; auto [ay,by,__] = hull[x+1];
                                                 ^

Subtask #1
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 376 KB contestant found the optimal answer: 108 == 108
2 Correct 2 ms 376 KB contestant found the optimal answer: 999 == 999
3 Correct 2 ms 376 KB contestant found the optimal answer: 0 == 0
4 Correct 2 ms 376 KB contestant found the optimal answer: 1542524 == 1542524
5 Correct 2 ms 376 KB contestant found the optimal answer: 4500000000 == 4500000000
6 Correct 2 ms 376 KB contestant found the optimal answer: 1 == 1
7 Correct 2 ms 376 KB contestant found the optimal answer: 1 == 1
8 Correct 2 ms 376 KB contestant found the optimal answer: 1 == 1
9 Correct 2 ms 376 KB contestant found the optimal answer: 100400096 == 100400096
10 Correct 2 ms 376 KB contestant found the optimal answer: 900320000 == 900320000
11 Correct 2 ms 376 KB contestant found the optimal answer: 3698080248 == 3698080248
12 Correct 2 ms 376 KB contestant found the optimal answer: 3200320000 == 3200320000
13 Correct 2 ms 376 KB contestant found the optimal answer: 140072 == 140072
14 Correct 2 ms 376 KB contestant found the optimal answer: 376041456 == 376041456
15 Correct 2 ms 376 KB contestant found the optimal answer: 805 == 805
16 Correct 2 ms 376 KB contestant found the optimal answer: 900189994 == 900189994
17 Correct 2 ms 376 KB contestant found the optimal answer: 999919994 == 999919994

Subtask #2
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 376 KB contestant found the optimal answer: 1093956 == 1093956
2 Correct 2 ms 376 KB contestant found the optimal answer: 302460000 == 302460000
3 Correct 2 ms 632 KB contestant found the optimal answer: 122453454361 == 122453454361
4 Correct 2 ms 376 KB contestant found the optimal answer: 93663683509 == 93663683509
5 Correct 2 ms 376 KB contestant found the optimal answer: 1005304678 == 1005304678
6 Correct 2 ms 380 KB contestant found the optimal answer: 933702 == 933702
7 Correct 2 ms 504 KB contestant found the optimal answer: 25082842857 == 25082842857
8 Correct 2 ms 376 KB contestant found the optimal answer: 687136 == 687136
9 Correct 2 ms 376 KB contestant found the optimal answer: 27295930079 == 27295930079
10 Correct 2 ms 504 KB contestant found the optimal answer: 29000419931 == 29000419931

Subtask #3
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 376 KB contestant found the optimal answer: 610590000 == 610590000
2 Correct 2 ms 376 KB contestant found the optimal answer: 311760000 == 311760000
3 Correct 4 ms 1328 KB contestant found the optimal answer: 1989216017013 == 1989216017013
4 Correct 2 ms 376 KB contestant found the optimal answer: 1499437552673 == 1499437552673
5 Correct 3 ms 1144 KB contestant found the optimal answer: 1019625819 == 1019625819
6 Correct 4 ms 1272 KB contestant found the optimal answer: 107630884 == 107630884
7 Correct 4 ms 1404 KB contestant found the optimal answer: 475357671774 == 475357671774
8 Correct 3 ms 632 KB contestant found the optimal answer: 193556962 == 193556962
9 Correct 2 ms 504 KB contestant found the optimal answer: 482389919803 == 482389919803
10 Correct 3 ms 632 KB contestant found the optimal answer: 490686959791 == 490686959791

Subtask #4
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 504 KB contestant found the optimal answer: 21503404 == 21503404
2 Correct 2 ms 504 KB contestant found the optimal answer: 140412195 == 140412195
3 Correct 11 ms 2040 KB contestant found the optimal answer: 49729674225461 == 49729674225461
4 Correct 3 ms 504 KB contestant found the optimal answer: 37485571387523 == 37485571387523
5 Correct 11 ms 2168 KB contestant found the optimal answer: 679388326 == 679388326
6 Correct 10 ms 1912 KB contestant found the optimal answer: 4699030287 == 4699030287
7 Correct 12 ms 2168 KB contestant found the optimal answer: 12418819758185 == 12418819758185
8 Correct 9 ms 2168 KB contestant found the optimal answer: 31093317350 == 31093317350
9 Correct 4 ms 760 KB contestant found the optimal answer: 12194625429236 == 12194625429236
10 Correct 6 ms 1144 KB contestant found the optimal answer: 12345131038664 == 12345131038664

Subtask #5
21.0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 5 ms 1140 KB contestant found the optimal answer: 1818678304 == 1818678304
2 Correct 5 ms 1024 KB contestant found the optimal answer: 1326260195 == 1326260195
3 Correct 131 ms 9912 KB contestant found the optimal answer: 4973126687469639 == 4973126687469639
4 Correct 6 ms 1384 KB contestant found the optimal answer: 3748491676694116 == 3748491676694116
5 Correct 75 ms 6248 KB contestant found the optimal answer: 1085432199 == 1085432199
6 Correct 78 ms 6956 KB contestant found the optimal answer: 514790755404 == 514790755404
7 Correct 119 ms 7792 KB contestant found the optimal answer: 1256105310476641 == 1256105310476641
8 Correct 87 ms 6556 KB contestant found the optimal answer: 3099592898816 == 3099592898816
9 Correct 96 ms 7244 KB contestant found the optimal answer: 1241131419367412 == 1241131419367412
10 Correct 123 ms 9036 KB contestant found the optimal answer: 1243084101967798 == 1243084101967798

Subtask #6
29.0 / 29.0

# Verdict Execution time Memory Grader output
1 Correct 34 ms 9004 KB contestant found the optimal answer: 19795776960 == 19795776960
2 Correct 33 ms 8924 KB contestant found the optimal answer: 19874432173 == 19874432173
3 Correct 1408 ms 87096 KB contestant found the optimal answer: 497313449256899208 == 497313449256899208
4 Correct 35 ms 9840 KB contestant found the optimal answer: 374850090734572421 == 374850090734572421
5 Correct 1574 ms 86412 KB contestant found the optimal answer: 36183271951 == 36183271951
6 Correct 608 ms 60896 KB contestant found the optimal answer: 51629847150471 == 51629847150471
7 Correct 1365 ms 67244 KB contestant found the optimal answer: 124074747024496432 == 124074747024496432
8 Correct 967 ms 56084 KB contestant found the optimal answer: 309959349080800 == 309959349080800
9 Correct 999 ms 63300 KB contestant found the optimal answer: 124113525649823701 == 124113525649823701
10 Correct 1282 ms 78812 KB contestant found the optimal answer: 124309619349406845 == 124309619349406845