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Submission #81554

# Submission time Handle Problem Language Result Execution time Memory
81554 2018-10-25T09:51:33 Z kimjg1119 Split the sequence (APIO14_sequence) C++17
100 / 100
 490 ms 85544 KB 
#include <bits/stdc++.h>
#define MAXN 100005
using namespace std;
typedef long long ll;
typedef pair<ll,int> pli;
typedef vector<int> vi;

typedef struct CHT{
    ll la[MAXN], lb[MAXN]; int lz[MAXN];
    int stkn=0,pt=1;
    void insert(ll a, ll b, int z){
        while(stkn>pt){
            if(a==la[stkn] && b>=lb[stkn]) stkn--;
            else if((lb[stkn]-b)*(la[stkn]-la[stkn-1])<(a-la[stkn])*(lb[stkn-1]-lb[stkn])) stkn--;
            else break;
        }
        // (lb[stkn]-b)/(a-la[stkn]) <(lb[stkn-1]-lb[stkn])/(la[stkn]-la[stkn-1]) 일 때 stkn--; 인데
        // 기울기가 일정하게 되면 a-la[stkn] 또는 la[stkn]-la[stkn-1]이 0이 될 수 있음.
        // la[stkn]==la[stkn-1] 이거나 a==la[stkn]인 상황이 오면 교점이 존재하지 않음.
        // la[stkn]==la[stkn-1] 인 상황이 없다고 가정하자. 그러면 a==la[stkn]인 상황만 처리해주면 됨.
        // 두 직선의 기울기가 같으면 y절편이 큰 직선을 남기는 게 이득이라는 것이 자명함.
        if(a==la[stkn] && b>=lb[stkn] && z!=0){
            //lz[stkn]=z;
            return;
        }
        la[++stkn]=a;
        lb[stkn]=b;
        lz[stkn]=z;
    }
    pli query(ll x){
        while(pt<stkn && (lb[pt]-lb[pt+1])<(la[pt+1]-la[pt])*x) pt++;
        return make_pair(la[pt]*x+lb[pt],lz[pt]);
    }
}CHT;

ll a[MAXN],D[2][MAXN],S[MAXN];
int pre[205][MAXN];

int main(){
    int n,k;
    scanf("%d %d",&n,&k);
    for(int i=1;i<=n;i++) scanf("%lld",&a[i]), S[i]=S[i-1]+a[i];
    for(int i=1;i<=k;i++){
        CHT c; c.insert(0,0,0);
        for(int j=1;j<=n;j++){
            pli temp=c.query(S[j]);
            D[i%2][j]=temp.first;
            pre[i][j]=temp.second;
            c.insert(S[j],D[(i-1)%2][j]-S[j]*S[j],j);
        }
    }
    printf("%lld\n",D[k%2][n]);
    int here=n;
    vi ans;
    ans.push_back(-1);
    for(int i=1;i<=k;i++){
        ans.push_back(pre[k-i+1][here]);
        here=pre[k-i+1][here];
    }
    sort(ans.begin(),ans.end());
    for(int i=1;i<=k;i++){
        if(ans[i]==0) ans[i]=1;
        if(ans[i]<=ans[i-1]) ans[i]=ans[i-1]+1;
        printf("%d ",ans[i]);
    }
    /*printf("\n");
    for(int i=1;i<=k;i++)
        for(int j=1;j<=n;j++)
            printf("%d%c",pre[i][j]," \n"[j==n]);*/
    return 0;
}

Compilation message

sequence.cpp: In function 'int main()':
sequence.cpp:41:10: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
     scanf("%d %d",&n,&k);
     ~~~~~^~~~~~~~~~~~~~~
sequence.cpp:42:46: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
     for(int i=1;i<=n;i++) scanf("%lld",&a[i]), S[i]=S[i-1]+a[i];
                           ~~~~~~~~~~~~~~~~~~~^~~~~~~~~~~~~~~~~~

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 508 KB contestant found the optimal answer: 999 == 999
3 Correct 2 ms 508 KB contestant found the optimal answer: 0 == 0
4 Correct 2 ms 540 KB contestant found the optimal answer: 1542524 == 1542524
5 Correct 2 ms 648 KB contestant found the optimal answer: 4500000000 == 4500000000
6 Correct 2 ms 648 KB contestant found the optimal answer: 1 == 1
7 Correct 2 ms 648 KB contestant found the optimal answer: 1 == 1
8 Correct 2 ms 664 KB contestant found the optimal answer: 1 == 1
9 Correct 2 ms 664 KB contestant found the optimal answer: 100400096 == 100400096
10 Correct 2 ms 664 KB contestant found the optimal answer: 900320000 == 900320000
11 Correct 2 ms 664 KB contestant found the optimal answer: 3698080248 == 3698080248
12 Correct 2 ms 664 KB contestant found the optimal answer: 3200320000 == 3200320000
13 Correct 2 ms 664 KB contestant found the optimal answer: 140072 == 140072
14 Correct 2 ms 664 KB contestant found the optimal answer: 376041456 == 376041456
15 Correct 2 ms 664 KB contestant found the optimal answer: 805 == 805
16 Correct 2 ms 664 KB contestant found the optimal answer: 900189994 == 900189994
17 Correct 2 ms 664 KB contestant found the optimal answer: 999919994 == 999919994

Subtask #2
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 664 KB contestant found the optimal answer: 1093956 == 1093956
2 Correct 2 ms 664 KB contestant found the optimal answer: 302460000 == 302460000
3 Correct 2 ms 852 KB contestant found the optimal answer: 122453454361 == 122453454361
4 Correct 2 ms 852 KB contestant found the optimal answer: 93663683509 == 93663683509
5 Correct 2 ms 852 KB contestant found the optimal answer: 1005304678 == 1005304678
6 Correct 2 ms 852 KB contestant found the optimal answer: 933702 == 933702
7 Correct 2 ms 852 KB contestant found the optimal answer: 25082842857 == 25082842857
8 Correct 2 ms 852 KB contestant found the optimal answer: 687136 == 687136
9 Correct 2 ms 852 KB contestant found the optimal answer: 27295930079 == 27295930079
10 Correct 2 ms 852 KB contestant found the optimal answer: 29000419931 == 29000419931

Subtask #3
11.0 / 11.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 852 KB contestant found the optimal answer: 610590000 == 610590000
2 Correct 2 ms 852 KB contestant found the optimal answer: 311760000 == 311760000
3 Correct 3 ms 1700 KB contestant found the optimal answer: 1989216017013 == 1989216017013
4 Correct 3 ms 1700 KB contestant found the optimal answer: 1499437552673 == 1499437552673
5 Correct 3 ms 1700 KB contestant found the optimal answer: 1019625819 == 1019625819
6 Correct 4 ms 1700 KB contestant found the optimal answer: 107630884 == 107630884
7 Correct 3 ms 1704 KB contestant found the optimal answer: 475357671774 == 475357671774
8 Correct 2 ms 1704 KB contestant found the optimal answer: 193556962 == 193556962
9 Correct 3 ms 1704 KB contestant found the optimal answer: 482389919803 == 482389919803
10 Correct 2 ms 1704 KB contestant found the optimal answer: 490686959791 == 490686959791

Subtask #4
17.0 / 17.0

# Verdict Execution time Memory Grader output
1 Correct 2 ms 1704 KB contestant found the optimal answer: 21503404 == 21503404
2 Correct 3 ms 1704 KB contestant found the optimal answer: 140412195 == 140412195
3 Correct 6 ms 2492 KB contestant found the optimal answer: 49729674225461 == 49729674225461
4 Correct 2 ms 2492 KB contestant found the optimal answer: 37485571387523 == 37485571387523
5 Correct 6 ms 2520 KB contestant found the optimal answer: 679388326 == 679388326
6 Correct 6 ms 2520 KB contestant found the optimal answer: 4699030287 == 4699030287
7 Correct 6 ms 2520 KB contestant found the optimal answer: 12418819758185 == 12418819758185
8 Correct 6 ms 2524 KB contestant found the optimal answer: 31093317350 == 31093317350
9 Correct 3 ms 2524 KB contestant found the optimal answer: 12194625429236 == 12194625429236
10 Correct 4 ms 2524 KB contestant found the optimal answer: 12345131038664 == 12345131038664

Subtask #5
21.0 / 21.0

# Verdict Execution time Memory Grader output
1 Correct 4 ms 2524 KB contestant found the optimal answer: 1818678304 == 1818678304
2 Correct 4 ms 2524 KB contestant found the optimal answer: 1326260195 == 1326260195
3 Correct 37 ms 10108 KB contestant found the optimal answer: 4973126687469639 == 4973126687469639
4 Correct 4 ms 10108 KB contestant found the optimal answer: 3748491676694116 == 3748491676694116
5 Correct 31 ms 10108 KB contestant found the optimal answer: 1085432199 == 1085432199
6 Correct 32 ms 10108 KB contestant found the optimal answer: 514790755404 == 514790755404
7 Correct 38 ms 10108 KB contestant found the optimal answer: 1256105310476641 == 1256105310476641
8 Correct 26 ms 10108 KB contestant found the optimal answer: 3099592898816 == 3099592898816
9 Correct 33 ms 10108 KB contestant found the optimal answer: 1241131419367412 == 1241131419367412
10 Correct 35 ms 10108 KB contestant found the optimal answer: 1243084101967798 == 1243084101967798

Subtask #6
29.0 / 29.0

# Verdict Execution time Memory Grader output
1 Correct 20 ms 10108 KB contestant found the optimal answer: 19795776960 == 19795776960
2 Correct 21 ms 10108 KB contestant found the optimal answer: 19874432173 == 19874432173
3 Correct 306 ms 85268 KB contestant found the optimal answer: 497313449256899208 == 497313449256899208
4 Correct 21 ms 85268 KB contestant found the optimal answer: 374850090734572421 == 374850090734572421
5 Correct 490 ms 85544 KB contestant found the optimal answer: 36183271951 == 36183271951
6 Correct 310 ms 85544 KB contestant found the optimal answer: 51629847150471 == 51629847150471
7 Correct 345 ms 85544 KB contestant found the optimal answer: 124074747024496432 == 124074747024496432
8 Correct 242 ms 85544 KB contestant found the optimal answer: 309959349080800 == 309959349080800
9 Correct 249 ms 85544 KB contestant found the optimal answer: 124113525649823701 == 124113525649823701
10 Correct 333 ms 85544 KB contestant found the optimal answer: 124309619349406845 == 124309619349406845