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Submission #112815

# Submission time Handle Problem Language Result Execution time Memory
112815 2019-05-22T05:21:15 Z Kamisama Split the sequence (APIO14_sequence) C++14
71 / 100
 2000 ms 85440 KB 
#include <iostream>
#include <cstdio>
#include <iomanip>
#include <chrono>
//#define Kami
#define taskname "APIO14_sequence"
using namespace std;
const int maxn=1e5+3;
const int maxk=2e2+3;
 
struct TLines{
    long long a, b; int id;
    inline TLines(long long _a=0, long long _b=0, int _id=0){a=_a;b=_b;id=_id;}
    inline long long Value(const long long &x){return a*x+b;}
    friend inline bool isBad(const TLines &d1, const TLines &d2, const TLines &d3){
        return (d2.b-d1.b)*(d1.a-d3.a)>=(d3.b-d1.b)*(d1.a-d2.a);
    }
};
 
int n,k,a[maxn],trace[maxn][maxk];
long long s[maxn],f[maxn],g[maxn];
TLines convex[maxn];
 
inline void Enter(){
    cin>>n>>k;
    for(int i=1;i<=n;i++) cin>>a[i], s[i]=s[i-1]+a[i];
}
 
inline void Solve(){ // f[i] = max{ s[j]*s[i] + f[j] - s[j]^2 }
    for(int t=1;t<=k;t++){
        int best=1;
        int nConvex=0;
        swap(f,g);
        for(int i=1;i<=n;i++){
            long long x=s[i];
            while(best<nConvex && convex[best].Value(x)<=convex[best+1].Value(x)) best++;
            f[i]=convex[best].Value(x);
            trace[i][t]=convex[best].id;
            TLines newline(s[i],g[i]-s[i]*s[i],i);
            while(nConvex>1 && isBad(convex[nConvex-1],convex[nConvex],newline)){
                best-=(best==nConvex);
                nConvex--;
            } convex[++nConvex]=newline;
        }
    }
    cout<<f[n]<<'\n';
    int nG=0;
    for(int x=n,i=k;i>=1;i--) cout<<(x=trace[x][i])<<' ';
}
 
int main(){
    ios_base::sync_with_stdio(false);
    cin.tie(NULL); cout.tie(NULL); if(fopen(taskname".INP","r"))
    freopen(taskname".INP","r",stdin),
    freopen(taskname".OUT","w",stdout);
    #ifdef Kami
    auto start=chrono::steady_clock::now();
    #endif
 
    Enter();
    Solve();
 
    #ifdef Kami
    auto end=chrono::steady_clock::now();
    cerr<<"\nIn milliseconds : "
        <<chrono::duration_cast<chrono::milliseconds>(end-start).count();
    cerr<<'\n'<<"In seconds : "<<fixed<<setprecision(3)
        <<(double)chrono::duration_cast<chrono::milliseconds>(end-start).count()/1000<<'\n';
    #endif
 
    return 0;
}

Compilation message

sequence.cpp: In function 'void Solve()':
sequence.cpp:47:9: warning: unused variable 'nG' [-Wunused-variable]
     int nG=0;
         ^~
sequence.cpp: In function 'int main()':
sequence.cpp:54:38: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)', declared with attribute warn_unused_result [-Wunused-result]
     freopen(taskname".INP","r",stdin),
     ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~^~
     freopen(taskname".OUT","w",stdout);
     ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
sequence.cpp:54:38: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)', declared with attribute warn_unused_result [-Wunused-result]

Subtask #1
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 5 ms 4224 KB contestant found the optimal answer: 108 == 108
2 Correct 5 ms 4224 KB contestant found the optimal answer: 999 == 999
3 Correct 5 ms 4352 KB contestant found the optimal answer: 0 == 0
4 Correct 6 ms 4352 KB contestant found the optimal answer: 1542524 == 1542524
5 Correct 6 ms 4480 KB contestant found the optimal answer: 4500000000 == 4500000000
6 Correct 5 ms 4352 KB contestant found the optimal answer: 1 == 1
7 Correct 5 ms 4224 KB contestant found the optimal answer: 1 == 1
8 Correct 5 ms 4224 KB contestant found the optimal answer: 1 == 1
9 Correct 6 ms 4352 KB contestant found the optimal answer: 100400096 == 100400096
10 Correct 6 ms 4352 KB contestant found the optimal answer: 900320000 == 900320000
11 Correct 5 ms 4224 KB contestant found the optimal answer: 3698080248 == 3698080248
12 Correct 6 ms 4352 KB contestant found the optimal answer: 3200320000 == 3200320000
13 Correct 6 ms 4352 KB contestant found the optimal answer: 140072 == 140072
14 Correct 5 ms 4352 KB contestant found the optimal answer: 376041456 == 376041456
15 Correct 22 ms 4352 KB contestant found the optimal answer: 805 == 805
16 Correct 5 ms 4224 KB contestant found the optimal answer: 900189994 == 900189994
17 Correct 5 ms 4352 KB contestant found the optimal answer: 999919994 == 999919994

Subtask #2
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 5 ms 4352 KB contestant found the optimal answer: 1093956 == 1093956
2 Correct 5 ms 4352 KB contestant found the optimal answer: 302460000 == 302460000
3 Correct 9 ms 4352 KB contestant found the optimal answer: 122453454361 == 122453454361
4 Correct 5 ms 4352 KB contestant found the optimal answer: 93663683509 == 93663683509
5 Correct 6 ms 4352 KB contestant found the optimal answer: 1005304678 == 1005304678
6 Correct 6 ms 4352 KB contestant found the optimal answer: 933702 == 933702
7 Correct 8 ms 4396 KB contestant found the optimal answer: 25082842857 == 25082842857
8 Correct 6 ms 4352 KB contestant found the optimal answer: 687136 == 687136
9 Correct 5 ms 4352 KB contestant found the optimal answer: 27295930079 == 27295930079
10 Correct 6 ms 4352 KB contestant found the optimal answer: 29000419931 == 29000419931

Subtask #3
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 5 ms 4480 KB contestant found the optimal answer: 610590000 == 610590000
2 Correct 5 ms 4480 KB contestant found the optimal answer: 311760000 == 311760000
3 Correct 26 ms 4480 KB contestant found the optimal answer: 1989216017013 == 1989216017013
4 Correct 5 ms 4480 KB contestant found the optimal answer: 1499437552673 == 1499437552673
5 Correct 21 ms 4608 KB contestant found the optimal answer: 1019625819 == 1019625819
6 Correct 25 ms 4480 KB contestant found the optimal answer: 107630884 == 107630884
7 Correct 26 ms 4480 KB contestant found the optimal answer: 475357671774 == 475357671774
8 Correct 9 ms 4480 KB contestant found the optimal answer: 193556962 == 193556962
9 Correct 8 ms 4480 KB contestant found the optimal answer: 482389919803 == 482389919803
10 Correct 11 ms 4480 KB contestant found the optimal answer: 490686959791 == 490686959791

Subtask #4
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 6 ms 5120 KB contestant found the optimal answer: 21503404 == 21503404
2 Correct 6 ms 5120 KB contestant found the optimal answer: 140412195 == 140412195
3 Correct 30 ms 5120 KB contestant found the optimal answer: 49729674225461 == 49729674225461
4 Correct 6 ms 5120 KB contestant found the optimal answer: 37485571387523 == 37485571387523
5 Correct 39 ms 5120 KB contestant found the optimal answer: 679388326 == 679388326
6 Correct 27 ms 5120 KB contestant found the optimal answer: 4699030287 == 4699030287
7 Correct 38 ms 5120 KB contestant found the optimal answer: 12418819758185 == 12418819758185
8 Correct 32 ms 5120 KB contestant found the optimal answer: 31093317350 == 31093317350
9 Correct 10 ms 5120 KB contestant found the optimal answer: 12194625429236 == 12194625429236
10 Correct 16 ms 5120 KB contestant found the optimal answer: 12345131038664 == 12345131038664

Subtask #5
21.0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 12 ms 12416 KB contestant found the optimal answer: 1818678304 == 1818678304
2 Correct 13 ms 12360 KB contestant found the optimal answer: 1326260195 == 1326260195
3 Correct 95 ms 12376 KB contestant found the optimal answer: 4973126687469639 == 4973126687469639
4 Correct 12 ms 12288 KB contestant found the optimal answer: 3748491676694116 == 3748491676694116
5 Correct 61 ms 12416 KB contestant found the optimal answer: 1085432199 == 1085432199
6 Correct 67 ms 12416 KB contestant found the optimal answer: 514790755404 == 514790755404
7 Correct 71 ms 12288 KB contestant found the optimal answer: 1256105310476641 == 1256105310476641
8 Correct 59 ms 12416 KB contestant found the optimal answer: 3099592898816 == 3099592898816
9 Correct 68 ms 12416 KB contestant found the optimal answer: 1241131419367412 == 1241131419367412
10 Correct 83 ms 12416 KB contestant found the optimal answer: 1243084101967798 == 1243084101967798

Subtask #6
0 / 29.0

# Verdict Execution time Memory Grader output
1 Correct 93 ms 84956 KB contestant found the optimal answer: 19795776960 == 19795776960
2 Correct 93 ms 84984 KB contestant found the optimal answer: 19874432173 == 19874432173
3 Execution timed out 2062 ms 85440 KB Time limit exceeded
4 Halted 0 ms 0 KB -