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Submission #45901

# Submission time Handle Problem Language Result Execution time Memory
45901 2018-04-16T11:50:35 Z Extazy Split the sequence (APIO14_sequence) C++17
100 / 100
 1532 ms 95140 KB 
#include <bits/stdc++.h>
#define endl '\n'
 
using namespace std;
 
const int N = 100002;
const int K = 202;
 
struct convex_hull_trick {
    struct line {
        long long a, b;
        int idx;
 
        line(){}
        line(long long x, long long y, int z): a(x), b(y), idx(z) {}
        
        template < class T >
        T eval(T x) {
            return a*x+b;
        }
    };
 
    deque < line > v;

    void clear() {
        v.clear();
    }
 
    double crossx(line l1, line l2) {
        double x=(double)(l2.b-l1.b)/(double)(l1.a-l2.a);
        return x;
    }
 
    double crossy(line l1, line l2) {
        double x=(double)(l2.b-l1.b)/(double)(l1.a-l2.a);
        return l1.eval(x);
    }
 
    void add_line(long long a, long long b, int idx) {
        line l(a,b,idx);
 
        while(v.size()>=2 && crossy(l,v[v.size()-2])>=crossy(v[v.size()-1],v[v.size()-2])) {
            v.pop_back();
        }
 
        v.push_back(l);
    }
 
    long long get(long long x, int &idx) {
        if(v.empty()) return numeric_limits < long long >::min();
 
        long long ans=v[0].eval(x),curr;
        idx=v[0].idx;

        while(v.size()>=2 && (curr=v[1].eval(x))>=ans) {
            v.pop_front();
            ans=curr;
            idx=v[0].idx;
        }

        return ans;
    }
};
 
int n,k,a[N],s[N],all_s;
long long dp[2][K];
int best[N][K];
convex_hull_trick cht[K];
vector < int > path;
 
void restore(int pos, int groups) {
    if(groups==1) return;
    path.push_back(best[pos][groups]-1);
    restore(best[pos][groups],groups-1);
}
 
int main() {
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    int i,j;
 
    scanf("%d %d", &n, &k);
    for(i=1;i<=n;i++) {
        scanf("%d", &a[i]);
        s[i]=a[i]+s[i-1];
    }
 
    all_s=s[n];
 
    for(i=n;i>=1;i--) {
        for(j=min(k+1,n-i+1);j>1;j--) {
            dp[i&1][j]=cht[j-1].get(s[i-1],best[i][j])-s[i-1]*1ll*all_s-s[i-1]*1ll*s[i-1];
            cht[j].add_line(2*s[i-1],s[i-1]*1ll*all_s-s[i-1]*1ll*s[i-1]+dp[i&1][j],i);
        }
 
        dp[i&1][1]=(s[n]-s[i-1])*1ll*(all_s-s[n]+s[i-1]);
        cht[1].add_line(2*s[i-1],s[i-1]*1ll*all_s-s[i-1]*1ll*s[i-1]+dp[i&1][1],i);
    }
 
    printf("%lld\n", dp[1][k+1]/2);
    restore(1,k+1);
    for(i=0;i<(int)(path.size());i++) {
        if(i>0) printf(" ");
        printf("%d", path[i]);
    }
    printf("\n");
 
    return 0;
}

Compilation message

sequence.cpp: In function 'int main()':
sequence.cpp:83:10: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
     scanf("%d %d", &n, &k);
     ~~~~~^~~~~~~~~~~~~~~~~
sequence.cpp:85:14: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
         scanf("%d", &a[i]);
         ~~~~~^~~~~~~~~~~~~

Subtask #1
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 504 KB contestant found the optimal answer: 108 == 108
2 Correct 2 ms 612 KB contestant found the optimal answer: 999 == 999
3 Correct 2 ms 676 KB contestant found the optimal answer: 0 == 0
4 Correct 2 ms 676 KB contestant found the optimal answer: 1542524 == 1542524
5 Correct 2 ms 676 KB contestant found the optimal answer: 4500000000 == 4500000000
6 Correct 2 ms 740 KB contestant found the optimal answer: 1 == 1
7 Correct 2 ms 740 KB contestant found the optimal answer: 1 == 1
8 Correct 2 ms 740 KB contestant found the optimal answer: 1 == 1
9 Correct 2 ms 740 KB contestant found the optimal answer: 100400096 == 100400096
10 Correct 2 ms 740 KB contestant found the optimal answer: 900320000 == 900320000
11 Correct 2 ms 740 KB contestant found the optimal answer: 3698080248 == 3698080248
12 Correct 2 ms 752 KB contestant found the optimal answer: 3200320000 == 3200320000
13 Correct 2 ms 848 KB contestant found the optimal answer: 140072 == 140072
14 Correct 2 ms 848 KB contestant found the optimal answer: 376041456 == 376041456
15 Correct 2 ms 848 KB contestant found the optimal answer: 805 == 805
16 Correct 2 ms 848 KB contestant found the optimal answer: 900189994 == 900189994
17 Correct 2 ms 848 KB contestant found the optimal answer: 999919994 == 999919994

Subtask #2
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 848 KB contestant found the optimal answer: 1093956 == 1093956
2 Correct 2 ms 876 KB contestant found the optimal answer: 302460000 == 302460000
3 Correct 2 ms 876 KB contestant found the optimal answer: 122453454361 == 122453454361
4 Correct 2 ms 876 KB contestant found the optimal answer: 93663683509 == 93663683509
5 Correct 2 ms 876 KB contestant found the optimal answer: 1005304678 == 1005304678
6 Correct 2 ms 876 KB contestant found the optimal answer: 933702 == 933702
7 Correct 2 ms 876 KB contestant found the optimal answer: 25082842857 == 25082842857
8 Correct 2 ms 876 KB contestant found the optimal answer: 687136 == 687136
9 Correct 2 ms 876 KB contestant found the optimal answer: 27295930079 == 27295930079
10 Correct 2 ms 876 KB contestant found the optimal answer: 29000419931 == 29000419931

Subtask #3
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 892 KB contestant found the optimal answer: 610590000 == 610590000
2 Correct 3 ms 892 KB contestant found the optimal answer: 311760000 == 311760000
3 Correct 3 ms 892 KB contestant found the optimal answer: 1989216017013 == 1989216017013
4 Correct 2 ms 892 KB contestant found the optimal answer: 1499437552673 == 1499437552673
5 Correct 3 ms 892 KB contestant found the optimal answer: 1019625819 == 1019625819
6 Correct 3 ms 892 KB contestant found the optimal answer: 107630884 == 107630884
7 Correct 3 ms 892 KB contestant found the optimal answer: 475357671774 == 475357671774
8 Correct 2 ms 892 KB contestant found the optimal answer: 193556962 == 193556962
9 Correct 2 ms 908 KB contestant found the optimal answer: 482389919803 == 482389919803
10 Correct 2 ms 908 KB contestant found the optimal answer: 490686959791 == 490686959791

Subtask #4
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 1532 KB contestant found the optimal answer: 21503404 == 21503404
2 Correct 3 ms 1532 KB contestant found the optimal answer: 140412195 == 140412195
3 Correct 10 ms 1660 KB contestant found the optimal answer: 49729674225461 == 49729674225461
4 Correct 3 ms 1660 KB contestant found the optimal answer: 37485571387523 == 37485571387523
5 Correct 11 ms 1788 KB contestant found the optimal answer: 679388326 == 679388326
6 Correct 10 ms 1788 KB contestant found the optimal answer: 4699030287 == 4699030287
7 Correct 11 ms 1788 KB contestant found the optimal answer: 12418819758185 == 12418819758185
8 Correct 11 ms 1908 KB contestant found the optimal answer: 31093317350 == 31093317350
9 Correct 5 ms 1908 KB contestant found the optimal answer: 12194625429236 == 12194625429236
10 Correct 6 ms 1908 KB contestant found the optimal answer: 12345131038664 == 12345131038664

Subtask #5
21.0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 11 ms 9340 KB contestant found the optimal answer: 1818678304 == 1818678304
2 Correct 10 ms 9340 KB contestant found the optimal answer: 1326260195 == 1326260195
3 Correct 116 ms 10236 KB contestant found the optimal answer: 4973126687469639 == 4973126687469639
4 Correct 10 ms 10236 KB contestant found the optimal answer: 3748491676694116 == 3748491676694116
5 Correct 81 ms 10236 KB contestant found the optimal answer: 1085432199 == 1085432199
6 Correct 88 ms 10236 KB contestant found the optimal answer: 514790755404 == 514790755404
7 Correct 98 ms 10236 KB contestant found the optimal answer: 1256105310476641 == 1256105310476641
8 Correct 79 ms 10364 KB contestant found the optimal answer: 3099592898816 == 3099592898816
9 Correct 89 ms 10364 KB contestant found the optimal answer: 1241131419367412 == 1241131419367412
10 Correct 117 ms 10364 KB contestant found the optimal answer: 1243084101967798 == 1243084101967798

Subtask #6
29.0 / 29.0

# Verdict Execution time Memory Grader output
1 Correct 89 ms 84748 KB contestant found the optimal answer: 19795776960 == 19795776960
2 Correct 87 ms 84748 KB contestant found the optimal answer: 19874432173 == 19874432173
3 Correct 1431 ms 95140 KB contestant found the optimal answer: 497313449256899208 == 497313449256899208
4 Correct 88 ms 95140 KB contestant found the optimal answer: 374850090734572421 == 374850090734572421
5 Correct 1532 ms 95140 KB contestant found the optimal answer: 36183271951 == 36183271951
6 Correct 1065 ms 95140 KB contestant found the optimal answer: 51629847150471 == 51629847150471
7 Correct 1108 ms 95140 KB contestant found the optimal answer: 124074747024496432 == 124074747024496432
8 Correct 949 ms 95140 KB contestant found the optimal answer: 309959349080800 == 309959349080800
9 Correct 993 ms 95140 KB contestant found the optimal answer: 124113525649823701 == 124113525649823701
10 Correct 1345 ms 95140 KB contestant found the optimal answer: 124309619349406845 == 124309619349406845