Submission #224769

# Submission time Handle Problem Language Result Execution time Memory
224769 2020-04-18T18:44:07 Z urd05 Split the sequence (APIO14_sequence) C++14
100 / 100
830 ms 5624 KB
#include <bits/stdc++.h>
using namespace std;
 
long long psum[110001];
int n;
 
struct Line {
    long long a,b;
};
 
struct Fraction {
    long long up,down;
};
 
Fraction cross(Line one,Line two) {
    if (one.a<two.a) {
        swap(one,two);
    }
    return {two.b-one.b,one.a-two.a};
}
 
bool cmp(Fraction one,Fraction two) {
    return one.up*two.down<one.down*two.up;
}
 
Line arr[110001];
int sz;
 
void insert(Line l) {
    if (sz>=1&&arr[sz-1].a==l.a) {
        if (l.b>arr[sz-1].b) {
            arr[sz-1]=l;
        }
        return;
    }
    while (sz>1) {
        Fraction before=cross(arr[sz-2],arr[sz-1]);
        Fraction now=cross(arr[sz-1],l);
        if (cmp(before,now)) {
            break;
        }
        sz--;
    }
    arr[sz++]=l;
}

vector<int> ret;
long long before[110005];
long long before2[110005];
long long now[110005];

long long getans(int x1,int y1,int x2,int y2) {
    int ind=0;
    if (y1+1==y2) {
        ret.push_back(x2);
        return 0;
    }
    int mid=(y1+y2)/2;
    for(int i=x1;i<=x2;i++) {
        before[i]=-1e18;
        before2[i]=-1e18;
    }
    before[x1]=0;
    before2[x2]=0;
    for(int i=y1+1;i<=mid;i++) {
        sz=0;
        ind=0;
        for(int j=x1;j<=x2;j++) {
            while (ind+1<sz&&cmp(cross(arr[ind],arr[ind+1]),{psum[j],1})) {
                ind++;
            }
            long long val;
            if (ind>=sz) {
                val=-1e18;
            }
            else {
                val=arr[ind].a*psum[j]+arr[ind].b;
            }
            now[j]=val;
            if (before[j]>=0)
            	insert({psum[j],-psum[j]*psum[j]+before[j]});
        }
        for(int j=x1;j<=x2;j++) {
            before[j]=now[j];
        }
    }
    for(int i=y2-1;i>=mid;i--) {
        sz=0;
        ind=0;
        for(int j=x2;j>=x1;j--) {
            while (ind+1<sz&&cmp(cross(arr[ind],arr[ind+1]),{-psum[j],1})) {
                ind++;
            }
            long long val;
            if (ind>=sz) {
                val=-1e18;
            }
            else {
                val=arr[ind].a*(-psum[j])+arr[ind].b-psum[j]*psum[j];
            }
            now[j]=val;
            if (before2[j]>=0)
            	insert({-psum[j],before2[j]});
        }
        for(int j=x1;j<=x2;j++) {
            before2[j]=now[j];
        }
    }
    int opt=-1;
    long long maxi=-1e18;
    for(int i=x1;i<=x2;i++) {
        if (before[i]+before2[i]>maxi) {
            maxi=before[i]+before2[i];
            opt=i;
        }
    }
    getans(x1,y1,opt,mid);
    getans(opt,mid,x2,y2);
    return maxi;
}
 
int main(void) {
    int k;
    scanf("%d %d\n",&n,&k);
    for(int i=0;i<n;i++) {
        long long x;
        scanf("%lld",&x);
        psum[i+1]=psum[i]+x;
    }
    printf("%lld\n",getans(0,0,n,k+1));
    for(int i=0;i<k;i++) {
        printf("%d ",ret[i]);
    }
    return 0;
}

Compilation message

sequence.cpp: In function 'int main()':
sequence.cpp:124:10: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
     scanf("%d %d\n",&n,&k);
     ~~~~~^~~~~~~~~~~~~~~~~
sequence.cpp:127:14: warning: ignoring return value of 'int scanf(const char*, ...)', declared with attribute warn_unused_result [-Wunused-result]
         scanf("%lld",&x);
         ~~~~~^~~~~~~~~~~
# Verdict Execution time Memory Grader output
1 Correct 4 ms 384 KB contestant found the optimal answer: 108 == 108
2 Correct 4 ms 384 KB contestant found the optimal answer: 999 == 999
3 Correct 4 ms 384 KB contestant found the optimal answer: 0 == 0
4 Correct 4 ms 384 KB contestant found the optimal answer: 1542524 == 1542524
5 Correct 4 ms 384 KB contestant found the optimal answer: 4500000000 == 4500000000
6 Correct 5 ms 384 KB contestant found the optimal answer: 1 == 1
7 Correct 4 ms 384 KB contestant found the optimal answer: 1 == 1
8 Correct 4 ms 384 KB contestant found the optimal answer: 1 == 1
9 Correct 4 ms 384 KB contestant found the optimal answer: 100400096 == 100400096
10 Correct 5 ms 384 KB contestant found the optimal answer: 900320000 == 900320000
11 Correct 4 ms 384 KB contestant found the optimal answer: 3698080248 == 3698080248
12 Correct 4 ms 384 KB contestant found the optimal answer: 3200320000 == 3200320000
13 Correct 4 ms 384 KB contestant found the optimal answer: 140072 == 140072
14 Correct 5 ms 384 KB contestant found the optimal answer: 376041456 == 376041456
15 Correct 5 ms 384 KB contestant found the optimal answer: 805 == 805
16 Correct 4 ms 384 KB contestant found the optimal answer: 900189994 == 900189994
17 Correct 4 ms 384 KB contestant found the optimal answer: 999919994 == 999919994
# Verdict Execution time Memory Grader output
1 Correct 5 ms 384 KB contestant found the optimal answer: 1093956 == 1093956
2 Correct 4 ms 384 KB contestant found the optimal answer: 302460000 == 302460000
3 Correct 4 ms 384 KB contestant found the optimal answer: 122453454361 == 122453454361
4 Correct 4 ms 384 KB contestant found the optimal answer: 93663683509 == 93663683509
5 Correct 4 ms 384 KB contestant found the optimal answer: 1005304678 == 1005304678
6 Correct 4 ms 384 KB contestant found the optimal answer: 933702 == 933702
7 Correct 4 ms 384 KB contestant found the optimal answer: 25082842857 == 25082842857
8 Correct 4 ms 384 KB contestant found the optimal answer: 687136 == 687136
9 Correct 5 ms 384 KB contestant found the optimal answer: 27295930079 == 27295930079
10 Correct 4 ms 384 KB contestant found the optimal answer: 29000419931 == 29000419931
# Verdict Execution time Memory Grader output
1 Correct 5 ms 384 KB contestant found the optimal answer: 610590000 == 610590000
2 Correct 4 ms 384 KB contestant found the optimal answer: 311760000 == 311760000
3 Correct 5 ms 384 KB contestant found the optimal answer: 1989216017013 == 1989216017013
4 Correct 5 ms 384 KB contestant found the optimal answer: 1499437552673 == 1499437552673
5 Correct 5 ms 384 KB contestant found the optimal answer: 1019625819 == 1019625819
6 Correct 6 ms 384 KB contestant found the optimal answer: 107630884 == 107630884
7 Correct 6 ms 384 KB contestant found the optimal answer: 475357671774 == 475357671774
8 Correct 5 ms 384 KB contestant found the optimal answer: 193556962 == 193556962
9 Correct 5 ms 384 KB contestant found the optimal answer: 482389919803 == 482389919803
10 Correct 5 ms 384 KB contestant found the optimal answer: 490686959791 == 490686959791
# Verdict Execution time Memory Grader output
1 Correct 5 ms 384 KB contestant found the optimal answer: 21503404 == 21503404
2 Correct 5 ms 384 KB contestant found the optimal answer: 140412195 == 140412195
3 Correct 10 ms 384 KB contestant found the optimal answer: 49729674225461 == 49729674225461
4 Correct 4 ms 384 KB contestant found the optimal answer: 37485571387523 == 37485571387523
5 Correct 13 ms 384 KB contestant found the optimal answer: 679388326 == 679388326
6 Correct 11 ms 384 KB contestant found the optimal answer: 4699030287 == 4699030287
7 Correct 12 ms 384 KB contestant found the optimal answer: 12418819758185 == 12418819758185
8 Correct 10 ms 384 KB contestant found the optimal answer: 31093317350 == 31093317350
9 Correct 6 ms 384 KB contestant found the optimal answer: 12194625429236 == 12194625429236
10 Correct 8 ms 384 KB contestant found the optimal answer: 12345131038664 == 12345131038664
# Verdict Execution time Memory Grader output
1 Correct 6 ms 768 KB contestant found the optimal answer: 1818678304 == 1818678304
2 Correct 6 ms 768 KB contestant found the optimal answer: 1326260195 == 1326260195
3 Correct 62 ms 768 KB contestant found the optimal answer: 4973126687469639 == 4973126687469639
4 Correct 6 ms 768 KB contestant found the optimal answer: 3748491676694116 == 3748491676694116
5 Correct 60 ms 768 KB contestant found the optimal answer: 1085432199 == 1085432199
6 Correct 57 ms 768 KB contestant found the optimal answer: 514790755404 == 514790755404
7 Correct 62 ms 768 KB contestant found the optimal answer: 1256105310476641 == 1256105310476641
8 Correct 43 ms 768 KB contestant found the optimal answer: 3099592898816 == 3099592898816
9 Correct 53 ms 768 KB contestant found the optimal answer: 1241131419367412 == 1241131419367412
10 Correct 64 ms 768 KB contestant found the optimal answer: 1243084101967798 == 1243084101967798
# Verdict Execution time Memory Grader output
1 Correct 23 ms 4736 KB contestant found the optimal answer: 19795776960 == 19795776960
2 Correct 21 ms 4992 KB contestant found the optimal answer: 19874432173 == 19874432173
3 Correct 540 ms 5624 KB contestant found the optimal answer: 497313449256899208 == 497313449256899208
4 Correct 23 ms 5504 KB contestant found the optimal answer: 374850090734572421 == 374850090734572421
5 Correct 830 ms 5112 KB contestant found the optimal answer: 36183271951 == 36183271951
6 Correct 520 ms 4984 KB contestant found the optimal answer: 51629847150471 == 51629847150471
7 Correct 580 ms 5624 KB contestant found the optimal answer: 124074747024496432 == 124074747024496432
8 Correct 407 ms 5552 KB contestant found the optimal answer: 309959349080800 == 309959349080800
9 Correct 459 ms 5368 KB contestant found the optimal answer: 124113525649823701 == 124113525649823701
10 Correct 598 ms 5368 KB contestant found the optimal answer: 124309619349406845 == 124309619349406845