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Submission #158360

# Submission time Handle Problem Language Result Execution time Memory
158360 2019-10-16T16:54:32 Z arnold518 Split the sequence (APIO14_sequence) C++14
100 / 100
 1753 ms 87544 KB 
#include <bits/stdc++.h>
using namespace std;

typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;

const int MAXN = 1e5;
const int MAXK = 200;

int N, K;
ll A[MAXN+10], dp[MAXN+10], dp2[MAXN+10];
int memo[MAXN+10][MAXK+10];

struct CHT
{
    void init()
    {
        S.clear();
        pos=0;
    }

    struct Line { ll a, b, c; };
    double cross(const Line &p, const Line &q) { return (double)(q.b-p.b)/(p.a-q.a); }
    vector<Line> S;

    void update(Line p)
    {
        if(!S.empty() && S[S.size()-1].a==p.a)
        {
            if(S[S.size()-1].b>=p.b) return;
            else S.pop_back();
        }
        while(S.size()>1 && (S[S.size()-1].a!=p.a && cross(S[S.size()-1], p)<=cross(S[S.size()-2], S[S.size()-1]))) S.pop_back();
        S.push_back(p);
    }

    int pos=0;
    pll query(ll x)
    {
        if(S.size()<=pos) pos=S.size()-1;
        else while(pos+1<S.size() && cross(S[pos], S[pos+1])<=x) pos++;
        return {S[pos].a*x+S[pos].b, S[pos].c};
    }
};
CHT cht;

int main()
{
    int i, j;

    scanf("%d%d", &N, &K);
    for(i=1; i<=N; i++) scanf("%lld", &A[i]), A[i]+=A[i-1];

    for(j=1; j<=K; j++)
    {
        cht.init();
        cht.update({A[j], dp2[j]-A[j]*A[j], j});
        for(i=j+1; i<=N; i++)
        {
            pll t=cht.query(A[i]);
            dp[i]=t.first;
            memo[i][j]=t.second;
            cht.update({A[i], dp2[i]-A[i]*A[i], i});
        }
        for(i=j+1; i<=N; i++) dp2[i]=dp[i];
        //for(i=1; i<=N; i++) printf("%lld ", dp[i]); printf("\n");
    }
    printf("%lld\n", dp[N]);
    int now=N;
    for(i=K; i>=1; i--)
    {
        now=memo[now][i];
        printf("%d ", now);
    }
}

Compilation message

sequence.cpp: In member function 'pll CHT::query(ll)':
sequence.cpp:41:20: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
         if(S.size()<=pos) pos=S.size()-1;
            ~~~~~~~~^~~~~
sequence.cpp:42:25: warning: comparison between signed and unsigned integer expressions [-Wsign-compare]
         else while(pos+1<S.size() && cross(S[pos], S[pos+1])<=x) pos++;
                    ~~~~~^~~~~~~~~
sequence.cpp: In function 'int main()':
sequence.cpp:52:10: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
     scanf("%d%d", &N, &K);
     ~~~~~^~~~~~~~~~~~~~~~
sequence.cpp:53:45: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
     for(i=1; i<=N; i++) scanf("%lld", &A[i]), A[i]+=A[i-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 3 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 380 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 376 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 376 KB contestant found the optimal answer: 933702 == 933702
7 Correct 2 ms 376 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 376 KB contestant found the optimal answer: 29000419931 == 29000419931

Subtask #3
11.0 / 11.0

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

Subtask #4
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 3 ms 1144 KB contestant found the optimal answer: 21503404 == 21503404
2 Correct 3 ms 1272 KB contestant found the optimal answer: 140412195 == 140412195
3 Correct 8 ms 1272 KB contestant found the optimal answer: 49729674225461 == 49729674225461
4 Correct 3 ms 1272 KB contestant found the optimal answer: 37485571387523 == 37485571387523
5 Correct 9 ms 1272 KB contestant found the optimal answer: 679388326 == 679388326
6 Correct 7 ms 1272 KB contestant found the optimal answer: 4699030287 == 4699030287
7 Correct 8 ms 1272 KB contestant found the optimal answer: 12418819758185 == 12418819758185
8 Correct 8 ms 1272 KB contestant found the optimal answer: 31093317350 == 31093317350
9 Correct 4 ms 1192 KB contestant found the optimal answer: 12194625429236 == 12194625429236
10 Correct 5 ms 1272 KB contestant found the optimal answer: 12345131038664 == 12345131038664

Subtask #5
21.0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 10 ms 9144 KB contestant found the optimal answer: 1818678304 == 1818678304
2 Correct 13 ms 9144 KB contestant found the optimal answer: 1326260195 == 1326260195
3 Correct 108 ms 9176 KB contestant found the optimal answer: 4973126687469639 == 4973126687469639
4 Correct 11 ms 9204 KB contestant found the optimal answer: 3748491676694116 == 3748491676694116
5 Correct 70 ms 9144 KB contestant found the optimal answer: 1085432199 == 1085432199
6 Correct 70 ms 9144 KB contestant found the optimal answer: 514790755404 == 514790755404
7 Correct 83 ms 9204 KB contestant found the optimal answer: 1256105310476641 == 1256105310476641
8 Correct 70 ms 9076 KB contestant found the optimal answer: 3099592898816 == 3099592898816
9 Correct 79 ms 9200 KB contestant found the optimal answer: 1241131419367412 == 1241131419367412
10 Correct 102 ms 9076 KB contestant found the optimal answer: 1243084101967798 == 1243084101967798

Subtask #6
29.0 / 29.0

# Verdict Execution time Memory Grader output
1 Correct 122 ms 86924 KB contestant found the optimal answer: 19795776960 == 19795776960
2 Correct 107 ms 87112 KB contestant found the optimal answer: 19874432173 == 19874432173
3 Correct 1565 ms 87268 KB contestant found the optimal answer: 497313449256899208 == 497313449256899208
4 Correct 102 ms 87392 KB contestant found the optimal answer: 374850090734572421 == 374850090734572421
5 Correct 1753 ms 86940 KB contestant found the optimal answer: 36183271951 == 36183271951
6 Correct 903 ms 86880 KB contestant found the optimal answer: 51629847150471 == 51629847150471
7 Correct 955 ms 87400 KB contestant found the optimal answer: 124074747024496432 == 124074747024496432
8 Correct 865 ms 87396 KB contestant found the optimal answer: 309959349080800 == 309959349080800
9 Correct 1192 ms 87124 KB contestant found the optimal answer: 124113525649823701 == 124113525649823701
10 Correct 1234 ms 87544 KB contestant found the optimal answer: 124309619349406845 == 124309619349406845